Tag: Philosophy

Mathematics of Atalanta

May 27th, 2023
Paradoxes are an excellent way of introducing someone to philosophy if that someone shows at least some interest in questioning their most closely held assumptions. The first and most famous of these come from Zeno of Elea (not to be confused with the other Zeno, the founder of Stoic philosophy). Continuing and probably modifying the central points made by Parmenides, Zeno is said to have written a book of paradoxes to defend Eleatic philosophy (Huggett, 2019). This book has not survived, but we know some of these through second-hand sources like Aristotle. Believe it or not, some 2500-year-old arguments that purport to show how motion is impossible continue to influence our understanding of space, time, change, motion, and infinity. With that said, I’d like to invite you to consider one of these arguments in more detail.

Here I’m concerned with the relationship between Zeno’s first paradox of motion (“the dichotomy”), Aristotle’s response to it, modern mathematics, infinity machines, and supertasks. I will attempt to show, as clearly as I can, how advances made in 19th-century mathematics by Augustin-Louis Cauchy can supplement Aristotle’s response to the paradox and thereby take us a step further toward resolving it. I will also show how it is possible to complete an infinite number of tasks in a finite amount of time. I say “take us a step further” because a “complete” resolution that would satisfy even the Eleatics themselves seems near-impossible. As Wesley C. Salmon wrote:

It would, of course, be rash to conclude that we had actually arrived at a complete resolution of all problems that come out of Zeno’s paradoxes. Each age, from Aristotle on down, seems to find in the paradoxes difficulties that are roughly commensurate with the mathematical, logical, and philosophical resources then available. When more powerful tools emerge, philosophers seem willing to acknowledge deeper difficulties that would have proved insurmountable for more primitive methods. We may have resolutions which are appropriate to our present level of understanding, but they may appear quite inadequate when we have advanced further. (Salmon, 1970/2001, pp. 43-44)
The Dichotomy

I won’t attempt to extend the discussion to other paradoxes of motion or plurality, even if the paradox of Achilles and the tortoise expresses the same idea as the dichotomy. I chose the latter because it is simpler.

Here’s the dichotomy paradox, as conveyed by Aristotle:

The first is the one which declares movement to be impossible because, however near the mobile is to any given point, it will always have to cover the half, and then the half of that, and so on without limit before it gets there. (Aristotle, Physics, 239b)

In other words, Atalanta (a heroine in Greek mythology known for her swiftness) has to run a 100-meter track. Before she gets to the finish line, she must get 1/2 of the way there. Before she can get halfway there, she must get 1/4 of the way there. Before that, she must get 1/8 of the way there, and so on, ad infinitum. So Atalanta seems to be facing an impossible “supertask”: she must complete an infinite series of smaller and smaller runs. Is completing this task possible? Zeno seems to have taken it as self-evident that the answer is “no.”

The obvious response to this is that of Diogenes of Sinope. According to one story, he stood up and walked out after hearing Zeno’s argument (Huggett, 2019). But to dismiss the argument in such a way is to miss out on its value. Sure, you won’t start believing that motion is impossible because you can’t resolve Zeno’s paradoxes, but they force us to rethink our assumptions about space, time, change, motion, and infinity.

Aristotle’s Response

Aristotle, unlike Diogenes, tried to combat the Eleatics on their own terms. So here is Aristotle’s response: suppose that with constant speed, we believe that Atalanta would need 10 seconds to complete the run. If this is so, the time needed to complete the infinite series of tasks can be divided just the same way as the distance. So, Atalanta would need 5 seconds to cover the first half of the whole distance, 2.5 seconds to complete another 1/4th of the distance, and so on.

Some think that this is enough to resolve the paradox (For example). But even by Aristotle’s own admition (Physics, 263a), this isn’t enough: what is needed is an account of how a sum of an infinite number of finite things can be equal to anything other than infinity, and this is exactly what 19th-century advances in mathematics can provide.

Aristotle extended the paradox in a way that lets the Parmenidean claim that there can be no finite time. He even conceded that if an infinite amount of intervals existed in actuality (instead of existing merely in potentiality), then the sum would indeed equal infinity.

This answer is, of course, unsatisfactory: a 100-meter track isn’t only ‘potentially’ made up of smaller intervals. Yet there is an argument to be made about whether physical space is a continuum:

The track on which he runs has a finite number of pebbles, grains of earth, and blades of grass!’ each of which in turn has a finite, though enormous number of atoms. For all of these are things that have a beginning and end in space or time. But if anybody says we must imagine that the atoms themselves occupy space and so are divisible “in thought,” he is no longer talking about spatia-temporal things. To divide a thing “in thought” is merely to halve the numerical interval which we have assigned to it. Or else it is to suppose what is in fact physically impossible beyond a certain point, the actual separation of the physical thing into discrete parts. We can of course choose to say that we shall represent a distance by a numerical interval, and that every part of that numerical interval shall also count as representing a distance; then it will be true a priori that there are infinitely many “distances.” But the class of what will then be called “distances” will be a series of pairs of numbers, not an infinite series of spatia-temporal things. The infinity of this series is then a feature of one way in which we find it useful to describe the physical reality. (Black, 1950, p. 80)

On this interpretation, Zeno’s paradoxes arise from our failure to separate how we conceive of space, time, and motion in mathematics from how space, time, and motion operate in physical reality. Considering that nothing guarantees, a priori, that space is a continuum, this resolution seems plausible:

… the premiss really is “Achilles’ physical distance is 1+1/2+1/4+etc.” It is this that is self-contradictory. In other words “Achilles’ distance is 1+1/2+1/4+etc.” and “Achilles’ distance is physical” are contradictory. (Wisdom, 1951, p. 86)

For some, including A. N. Whitehead, Zeno’s arguments don’t prove that motion isn’t real, but they do show that changes occur discretely rather than continuously. But we don’t necessarily have to buy into the idea that space is not a continuum. Even if we agree with Zeno and other Eleatics that there is an infinity of smaller and smaller intervals, we can, with Cauchy’s help, still show that the sum is finite.

Convergence and Divergence

Before we prove that a sum of an infinite number of finite things can be equal to a finite number, we must understand that even simple addition doesn’t work conventionally when we’re working with infinite sums. Consider Nick Huggett’s (2010, p. 20) example: x=1-1+1-1+1-1+… What is the value of x? Suppose that we rewrite it in the following way: x=(1-1)+(1-1)+(1-1)+… Then, x=0+0+0+…=0. Now suppose that we rewrite the original equation in the following way: x=1-(1-1+1-1+…) but 1-1+1-1+…=0 so x=1-0=1. Now we have a contradiction whereby x=0 and x=1 are both true (some even think, mistakenly, that 1-1+1-1+…=1/2). So our assumption that we can apply the same reasoning to infinite and finite sums is somehow false.

How so? Modern mathematics can resolve this by dividing infinite sums into two different categories: convergent and divergent sums. If an infinite sum approaches something (such as infinity, minus infinity, or some finite number), then the sum is convergent. If not, then it is divergent or undefined. For example, the sum 1+1+1+… is convergent and approaches infinity, but our example above (1-1+1-1+…) does not approach anything, so it is divergent or undefined.

So is the geometric sequence in Zeno’s dichotomy paradox (1/2+1/4+1/8+…) divergent or convergent? There are many ways to prove that the sequence is convergent and approaches 1. First, we know that the series will never exceed 1 because of Zeno’s own reasoning (the series has no last member or last half-run). Second, we know that an infinite geometric series is convergent if the absolute value of the common ratio is less than 1:
- S=a/(1-r) (where S is the sum, a is the first term of the series, and r is the common ratio);
- In our case, S=(1/2)/(1-(1/2))=(1/2)/(1/2)=1.
Alternatively:

${\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+\cdots =\sum _{n=1}^{\infty }\left({\frac {1}{2}}\right)^{n}=1.$

We can also prove this by using partial sums:
- x=1/2+1/4+1/8+…
- 2x=2(1/2+1/4+1/8+…)=1+1/2+1/4+1/8+…
- 2x=1+x
- x=1
Notice that we needed a new rule of addition for distinguishing different infinite sums: the rules of finite addition gave us 1=0 when we used them for infinite sums, so we had to introduce the concepts of convergence and divergence. With this, we have shown that mathematics can explain how an infinite sum of a finite number of things can be equal to something other than infinity.

Infinity Machines

Is the paradox completely resolved? Of course not, because one could still question whether these definitions of infinity correspond to physical reality. We still haven’t proved if Cauchy’s definitions can be correctly applied to physical actions (like Atalanta’s half-runs). This involves a premise about the applicability of mathematical language to physical phenomena in general. For example, simple laws of arithmetic break down if we mix an x amount of water and a y amount of alcohol, because the volume of the mixture won’t be x+y. So how do we know that infinite sequences of physical actions are, in all relevant respects, analogous to Cauchy sums? The points about the supposed infinite divisibility of physical space raised by Max Black and J. O. Wisdom (as quoted above) are still relevant. Furthermore, the relevance of infinity machines becomes apparent.

Max Black, James Thomson, and their followers attempted to show that Zeno’s paradoxes of motion (the dichotomy and Achilles and the tortoise in particular) are based on contradictory premises. Thomson brings out this self-contradictory nature of “supertasks” by use of thought experiments that involve infinity machines, the most famous of which is the lamp:

There are certain reading lamps that have a button in the base. If the lamp is off and you press the button the lamp goes on, and if the lamp is on and you press the button the lamp goes off. So if the lamp was originally off, and you pressed the button an odd number of times, the lamp is on, and if you pressed the button an even number of times the lamp is off. Suppose now that the lamp is off, and I succeed in pressing the button an infinite number of times, perhaps making one jab in one minute, another jab in the next half minute, and so on (…) After I have completed the whole infinite sequence of jabs, i.e. at the end of the two minutes, is the lamp on or off? It seems impossible to answer this question. It cannot be on, because I did not ever turn it on without at once turning it off. It cannot be off, because I did in the first place turn it on, and thereafter I never turned it off without at once turning it on. But the lamp must be either on or off. This is a contradiction. (Thomson, 1954, pp. 94-95)

But this apparent contradiction can be resolved if we realize that Thomson’s description of how the infinity machine operates applies only to any point in time before the two minutes are up (Benacerraf, 1962). It tells us nothing about the lamp after the two minutes have passed. Thomson’s infinite series has no last element. In mathematical terms, Thomson describes a set exhibiting order type ω, which means that:
- The set has a first element;
- Each element except the first has a unique immediate predecessor;
- Every element has a unique immediate successor.
Because of the last characteristic, the set has no last element. Atalanta’s run in Zeno’s paradox has the same character: there is no last half of the remaining track, yet she completes the course. In essence, Thomson’s argument gives information about the state of an object at any point in time (t), where t₀≤t<t₁, and asks us to deduce from this the state of the object at t₁. The reason it “seems impossible to answer this question” is that we are given absolutely no information about the state of the lamp at t₁.

There are, of course, other infinity machines, but I won’t discuss each. What I want to end this essay with is a demonstration of how Atalanta could complete her run even if we conceive of it as an infinite series of runs that are separated with periods of rest.

Atalanta’s Supertask

So we know that ‘infinity machines’ might not show an inherent contradiction in the idea of a supertask, but can we show how Atalanta can complete her supertask? Adolf Grünbaum (1970) offered an interesting proof of this which has been updated by Huggett (2010). Here’s the solution: imagine that Atalanta has to run a 100 meter course in 10 seconds. Instead of a continuous run, she will have to complete ℵ₀ runs that are separated by ℵ₀ periods of rest (ℵ₀ being the cardinal number of the set of natural numbers). The purpose of separating each run with a period of rest is to show that an infinite number of runs can be completed in a finite amount of time even if space and time are infinitely divisible.

Each run involves covering 3/4 of the remaining distance at 1/2 the speed of the previous run and then resting for the same amount of time as she ran. For example, imagine that the initial speed is 30m/s. She would need 2.5 s to cover 75 m; she would then rest for 2.5 s; then run the next 18.75 m at 15 m/s; rest for 1.25 s; and so on (Huggett, 2010, p.21).

Notice that each distance is 1/4 times as long as the previous one. The total distance is, therefore, 75 m ×(1+1/4+[1/4×1/4]+[1/4×1/4×1/4]+…). And 1+1/4+[1/4×1/4]+[1/4×1/4×1/4]+… is convergent, so we can calculate the sum:
- x=1+1/4+[1/4×1/4]+[1/4×1/4×1/4]+…
- 4x=4+1+1/4+[1/4×1/4]+[1/4×1/4×1/4]+…
- 4x=4+x
- 3x=4
- x=4/3
Therefore, 75×(1+1/4+[1/4×1/4]+[1/4×1/4×1/4]+…)=100, which means that the infinite sequence of runs does cover the whole distance. Now we need to check whether she can do this in a finite amount of time.

Each distance is 1/4 as large as the previous, the speed is 1/2 of the previous, and the time required to complete the run must be doubled because of the rest time. Taking all of this into account, we see that each consecutive run takes 1/2 as long as the previous one. If she needed 2.5 seconds to cover the first run and 2.5 more for rest, the whole run would take 2×2.5×(1+1/2+1/4+1/8+…) seconds. Since we already established that 1/2+1/4+1/8+…=1, we can calculate the time needed:
- 2×2.5×(1+1/2+1/4+1/8+…)=2×2.5×(1+1)
- 2×2.5×(1+1)=10
Therefore, Atalanta will have traveled 100 m in exactly 10 s. In other words, she will have completed an infinite number of discrete tasks in a finite amount of time. All this shows that there can be a supertask-like conception of Atalanta’s run that doesn’t involve any logical contradictions.

Conclusion

So where does all this leave us? We saw that Aristotle’s response wasn’t sufficient. We also saw that Cauchy’s contributions could supplement Aristotle’s response. We also saw that even if we think that a run is infinitely divisible, Thomson’s arguments about the contradictory nature of supertasks don’t necessarily hold up. So we know that there is no reason to think that it is impossible to perform an infinite series of tasks in a finite amount of time. We even saw a proof of how Atalanta could complete her run even if it involved ℵ₀ rest periods.

What we haven’t done is give a conclusive answer to whether using mathematical language to describe physical phenomena is appropriate in this case. Whatever theory one subscribes to or finds useful, the preceding discussion clearly shows that for any theory of space, time, motion, change, or infinity, Zeno’s paradoxes can be a sharpening stone.

References

Aristotle. (1934). Physics (P. H. Wicksteed & F. M. Cornford, Trans.). Harvard University Press. https://doi.org/10.4159/DLCL.aristotle-physics.1957

Benacerraf, P. (1962). Tasks, Super-Tasks, and the Modern Eleatics. In W. C. Salmon (Ed.), Zeno’s Paradoxes (pp. 103-129). Bobbs-Merrill.

Black, M. (1950). Achilles and the Tortoise. In W. C. Salmon (Ed.), Zeno’s Paradoxes (pp. 67–81). Bobbs-Merrill.

Grünbaum, A. (1970). Modern Science and Zeno’s Paradoxes of Motion. In W. C. Salmon (Ed.), Zeno’s Paradoxes (pp. 200–250). Bobbs-Merrill.

Huggett, N. (2019). Zeno’s Paradoxes. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2019). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/win2019/entries/paradox-zeno/

Huggett, N. (2010). Everywhere and Everywhen: Adventures in Physics and Philosophy. Oxford University Press.

Salmon, W. C. (2001). Zeno’s Paradoxes. Bobbs-Merrill. (Original work published 1970)

Thomson, J. (1954). Tasks and Supertasks. In W. C. Salmon (Ed.), Zeno’s Paradoxes (pp. 89-102). Bobbs-Merrill.

Wisdom, J. O. (1951). Achilles on a Physical Racecourse. In W. C. Salmon (Ed.), Zeno’s Paradoxes (pp. 82-88). Bobbs-Merrill.
The Author and the Vase

May 22nd, 2023
1.

At an inn in Kyoto, Noriko and her father, Shukichi, are lying down on separate futons and conversing before moving on with their new lives. Noriko is getting married reluctantly, and Shukichi is getting married for a second time. After Noriko tells her father that she found the idea of his remarriage distasteful, she looks over and sees that Shukichi is already asleep. She looks up at the ceiling and appears to be smiling when the film cuts to the shot above.

The shot lasts for six seconds, after which we see Noriko again, but her smile has turned into a frown. Then we get a ten-second shot of the same vase. Without any further explanation or direct follow-up, it is no surprise that this shot from Yasujirō Ozu’s Late Spring[1] has generated a myriad of interpretations. As Abé Mark Nornes wrote: “Nothing in all of Ozu’s films has sparked such conflicting explanations; everyone seems compelled to weigh in on this scene, invoking it as a key example in their arguments.”[2]

The shot is significant, as made apparent by its unusual placement, length, and repetition. The fact that a change (in Noriko’s expression) occurs in the background when all we see is this shot is also a reason to pay close attention. It’s an unnatural choice. What we would expect is for the shot to stay on Noriko’s face as joy morphs into sadness, but that transition is overridden by one of Ozu’s signature pillow shots.[3]

So what is the “real” meaning behind this shot? Is it a “container for our emotions”?[4] An expression of something “unified, permanent, transcendent”?[5] Is it “a non-narrative element wedged into the action”?[6] Is it a shot of an urn rather than a vase, thereby representing Noriko’s dead mother? Is it a deliberate use of a false point of view, since the shot is clearly not from Noriko’s perspective?[7] Or is it, as Gilles Deleuze thought, an example of a time-image: “The vase in Late Spring is interposed between the daughter’s half smile and the beginning of her tears. There is becoming, change, passage. But the form of what changes does not itself change, does not pass on. This is time, time itself, ‘a little time in its pure state’: a direct time-image, which gives what changes the unchanging form in which the change is produced. […] Ozu’s still lifes endure, have a duration, over ten seconds of the vase: this duration of the vase is precisely the representation of that which endures, through the succession of changing states.”[8]

To pose the question in the way presented above, as if the task of the viewer is to decipher the “correct” interpretation is to miss the mark.[9] Ask yourself this: for the readings above, “What difference does it make who is speaking?”[10] In other words, does the author’s—Yasujirō Ozu’s—original intention for the vase shot have any bearing on the value of the interpretations above? If, hypothetically, Ozu claimed that all he wanted to do with the shot was to confuse the interpreters, would this make, say, Deleuze’s reading “wrong”?

My intention with this essay is related to a certain anxiety. An anxiety that plagues me once I set out to close-read anything. Instead of defining what I mean directly, a concrete example will suffice: In Poems, Poets, Poetry, Helen Vendler argues that poets don’t approach the task of writing analytically, that is, they don’t begin with a conscious plan of what they want to convey and how they will do so: “A composer does not say, “I think this is the point for a diminished seventh,” or “Perhaps it would be effective to follow eighth-note triplets with a dotted quarter note.” No, the composer “hears the music” and writes it down; it is only later that analysts demonstrate the patterns that make the music seem intended, not chaotic. A poet, too, “hears the poem,’’ writes it down, and then further refines its visible patterns. Naturally, when a given pattern precedes the composition of the poem (“I want to write a sonnet”), much will be dictated by the preexistent formal requirements; but even then, the swift internal processes of composition organize the temporal, spatial, grammatical, and syntactic shapes of the poem more by instinct than by conscious plan. One could say that artists are people who think naturally in highly patterned ways.”[11]

If this were true—I thought—wouldn’t any in-depth analysis of a few lines of poetry be bound to go beyond the author’s intentions and thereby be “false”? I thought that what keeps one’s interpretations from becoming akin to those of Charles Kinbote/Vseslav Botkin from Pale Fire[12] is grounding them in the author’s original intentions. I no longer believe this, and there will be no good reason for you to ground your interpretation of this essay in my original intention for writing it.

I will argue, contrary to the habit of privileging the author’s original intent, that the value of an interpretation does not necessarily stand or fall with its proximity to it. My main point is that while considerations of original intentions may often be useful, our analyses and interpretations should not be bound by these: as Georges Canguilhem noted, philosophy is a type of reflection for which all matters, all topics are worthy of consideration.[13] Consequently, there are no necessary conditions (e.g., the existence of an author) that must be satisfied by a text, film, painting, etc. before it can become an object of interpretation.

2.

“The explanation of a work is always sought in the man or woman who produced it, as if it were always in the end, through the more or less transparent allegory of the fiction, the voice of a single person, the author ‘confiding’ in us.”[14] People generally think of a text as a less-than-perfect lens under which we may grasp what the author “really” intended to convey.

It is possible to go beyond this approach. Barthes cites Stéphane Mallarmé as the original critic of this approach, who claimed that language itself speaks, not the author. This echoes in contemporary poets like Charles Simic, who writes that no one “wills” metaphors and poems into existence:

We may start believing that we are recreating an experience, that we are making an attempt at mimesis, but then the language takes over. Suddenly the words have a mind of their own.

It’s like saying, “I wanted to go to church but the poem took me to the dog races.”

When it first happened I was horrified. It took me years to admit that the poem is
smarter than I am. Now I go where it wants to go.[15]

Even without touching the question of determinism and free will, it is clear that we can analyze language without reference to who wrote it. The notion of the ‘subject’ is enough: “language knows a ‘subject’, not a ‘person’, and this subject, empty outside of the very enunciation which defines it, suffices to make language ‘hold together’, suffices, that is to say, to exhaust it.”[16]

Consider the following example: In the woods, the wind arranges fallen leaves in such a way as to resemble a readable poem in a language familiar to you. Unless you believe in divine intervention, you’ll think that this is just an unlikely chance occurrence without a conscious author. The wind did not intend to convey any specific meaning to you, yet nothing stops you from interpreting the poem of leaves. The only thing that’s different is that it would be wise to leave out any considerations of original intentions.

Let’s now say that you bring this poem to the attention of literary critics, who then come up with differing and sometimes contradictory interpretations. In such a scenario, the differing interpretations will necessarily be evaluated based on the text itself since, even if one believes that the poem was the work of a divine being, one knows absolutely nothing about its intentions.

The interpretation of one’s dreams functions similarly: There is no need for you or your psychotherapist to believe that your unconscious has the capacity for intentionality to interpret your dreams and get some practical value out of doing so.

3.

Tied to this devaluation of intent is the question of originality. The author does not have the final word on the meaning of a text because the author did not create it ex nihilo: “a text is not a line of words releasing a single ‘theological’ meaning (the ‘message’ of the Author-God) but a multi-dimensional space in which a variety of writings, none of them original, blend and clash.” The author’s “only power is to mix writings, to counter the ones with the others, in such a way as never to rest on any one of them. Did he wish to express himself, he ought at least to know that the inner ‘thing’ he thinks to ‘translate’ is itself only a ready-formed dictionary, its words only explainable through other words, and so on indefinitely.”[17] Cormac McCarthy made a similar point about literature when he said in an interview that “books are made out of books. The novel depends for its life on the novels that have been written.”[18]

In other words, Hume’s Copy Principle[19] and his idea that the “creative power of the mind amounts to no more than the faculty of compounding transposing, augmenting, or diminishing the materials afforded us by the senses and experience”[20], may be extended to any endeavor, whereby no work of art is created without being preceded and influenced by a plethora of corresponding impressions.

4.

You may have already noticed that these arguments have an ethical dimension. In a sense, they liberate the text from its owner and challenge perceived authority. If you remove the author from the text, there is nothing to “decipher.” Viewing a text in relation to its author gives it an ultimate meaning and makes the reader’s work more akin to problem-solving than interpretation.

In the multiplicity of writing, everything is to be disentangled, nothing deciphered; the structure can be followed, ‘run’ (like the thread of a stocking) at every point and at every level, but there is nothing beneath: the space of writing is to be ranged over, not pierced; writing ceaselessly posits meaning ceaselessly to evaporate it, carrying out a systematic exemption of meaning. In precisely this way literature (it would be better from now on to say writing), by refusing to assign a ‘secret’, an ultimate meaning, to the text (and to the world as text), liberates what may be called an anti-theological activity, an activity that is truly revolutionary since to refuse to fix meaning is, in the end, to refuse God and his hypostases – reason, science, law.[21]

What this reevaluation of the author’s significance for a work of art calls for is not the effacement of the figure. It asks new questions along with the old ones. Instead of viewing the text as a tainted lens through which the critic/reader/viewer/interpreter must try to decipher the “real” meaning of the work and check their results, like a natural scientist, against the “objective” criterion in the form of the author’s original intentions, we may analyze the work on its own and use it as the ultimate criterion. If one’s interpretation conflicts with the author’s original intentions, the conclusion isn’t that the interpretation is “false.” What may falsify one’s interpretation isn’t the author’s intention but the work of art itself.

Consider again our initial example of the vase shot and its various interpretations. None of these would be invalidated if Ozu’s intentions were entirely different. Instead of trying to answer questions like: “Who really spoke? Is it really he and not someone else? With what authenticity or originality? And what part of his deepest self did he express in his discourse?”, we may consider conflicting interpretations alongside the question: “What difference does it make who is speaking?”[22]

Notes
1. Ozu, Y. (Director). (1972, July 21). Banshun (Late Spring). Shochiku.
2. Nornes, A. M. (2007). The Riddle of the Vase: Ozu Yasujirō’s Late Spring (1949). In Phillips, A., & Stringer, J. (2007). Japanese Cinema: Texts and Contexts. Routledge.
3. Richie, D. (1974). Ozu: His Life and Films. University of California Press.
4. Ibid., p. 174.
5. Schrader, P. (1988). Transcendental style in film: Ozu, Bresson, Dreyer. Da Capo Press. pp. 49-51.
6. Thompson, K. (1988). Breaking the Glass Armor: Neoformalist Film Analysis. Princeton University Press. pp. 339-340.
7. Bordwell, D. (1988). Ozu and the Poetics of Cinema. BFI Pub. p. 117.
8. Deleuze, G. (1989). Cinema 2: The time-image. Athlone. p. 17.
9. Clearly, a film is not a product of a single author: one look at the credit sequence of a film is sufficient evidence for this. For a more in-depth discussion of the issues of authorship in cinema, see Wartenberg, T. (2015). Philosophy of Film. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2015). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/win2015/entries/film/
10. Foucault, M. (1998). Aesthetics, Method, and Epistemology. The New Press. p. 222.
11. Vendler, H. (2009). Poems, Poets, Poetry: An Introduction and Anthology. Bedford/St. Martin’s. p. 29.
12. Nabokov, V. V. (1962). Pale Fire. Putnam.
13. Bonicco-Donato, Céline (2016), «Ville (GP)», dans Maxime Kristanek (dir.), l’Encyclopédie philosophique, consulté le …, https://encyclo-philo.fr/villes-gp
14. Barthes, R. (1977). Image, Music, Text. Fontana. p. 143.
15. Simic, C. (2015). Notes on Poetry and Philosophy. In The Life of Images: Selected Prose. HarperCollins.
16. Barthes, R. (1977). Image, Music, Text. Fontana. p. 145.
17. Ibid., p. 146.
18. Cormac McCarthy in an interview for the New York Times (1992).
19. David Hume’s Copy Principle refers to his claim that all our ideas are copies of our impressions: “all our ideas or more feeble perceptions are copies of pure impressions or more lively ones.” Hume, D. (1907). An enquiry concerning human understanding; and Selections from a treatise of human nature. La Salle, Ill. Open Court Pub. Co. http://archive.org/details/enquiryconcernin00humeuoft (Original work published 1748)
20. Ibid., p. 16.
21. Barthes, R. (1977). Image, Music, Text. Fontana. p. 147.
22. Foucault, M. (1998). Aesthetics, Method, and Epistemology. The New Press. p. 222.
The Three Paths of Night

April 8th, 2023

The metaphysical poem of the Eleatic philosopher Parmenides begins with a description of a journey to “where the gate of the paths of Night and Day is” (Parmenides, 2016, p. 35). There he meets the goddess, supposedly Night herself (Burkert, 1969), who informs him of the ways of inquiry that lead to wavering and unwavering understanding.

The traditional understanding of the revelation given to Parmenides by Night is that she outlines two paths, one of which is true and another false. If we follow this reading of the poem, Parmenides seems to be advocating a strict form of monism that denies all plurality and change. However, due to several considerations that will become clear as we go along, there is reason to think that the goddess is making a different argument.

In Parmenides’ poem, the goddess is not distinguishing the only way of being from non-being but rather distinguishing three different modes of being: (1) necessary being; (2) necessary non-being; and (3) contingent being. According to her, two paths of investigation lead to understanding instead of wandering:

The one, that “is,” and that it is not possible that “is not,” Is the path of conviction (peithô), for it accompanies truth; the other, that “is not,” and that it is necessary that “is not” (Parmenides, 2016, p. 39)

These are the paths of necessary being and necessary non-being, respectively. The understanding gained through either is not subject to change. The goddess then warns Parmenides of the second path:

I show you that it is a path that cannot be inquired into at all. For you could not know that which is not (for this is impracticable) Nor could you show it. (Parmenides, 2016, p. 39)

That which cannot be cannot be thought or shown. For example, imagine a square circle or show me a married bachelor.

The third path is that of mortals, of those who suppose that ““this is and is not” is the same and not the same, and that of all things the path is backward-turning” (Parmenides, 2016, p. 41). The goddess seems to be saying that mortals mistakenly think that objects of genuine understanding (i.e., objects that must exist and objects that must not exist) can be subject to change. Nevertheless, wandering or wavering understanding is still understanding (Palmer, 2020).

Two-path interpretations of the poem tend to equate the path of the mortals with the path “that “is not,” and that it is necessary that “is not””” (Parmenides, 2016, p. 39). These interpretations, however, ignore that the first two paths lead to unwavering understanding (eisi noêsai) while the third leads to wandering understanding (plagkton nöon).

Furthermore, why does Parmenides bother to present a fundamentally flawed cosmology—the path of the mortals—if his reasoning shows that such things cannot possibly exist? If we recognize three paths instead of two, we solve this apparent mystery. So the goddess is not suggesting, as many interpreters think, that nothing exists in the way mortals believe, but that things that exist only contingently cannot lead to certain understanding.

Parmenides is not denying the existence of change. He is merely distinguishing that which necessarily is from that which is but may not be. He denies change only for the objects of unwavering understanding. Parmenides’ deductions about the nature of What Is (to eon) in later fragments make perfect sense on this interpretation: What must be cannot have an origin or end, nor can it change in any way, for change would require that it be in some way different from what it necessarily is.

References

Burkert, W. (1969). Das Proömium des Parmenides und die “Katabasis” des Pythagoras. Phronesis, 14(1), 1–30.

Palmer, J. (2020). Parmenides. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2020). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/win2020/entries/parmenides/

Parmenides. (2016). Testimonia, Part 2: Doctrine (D) (A. Laks & G. W. Most, Trans.). Harvard University Press. https://doi.org/10.4159/DLCL.parmenides-doctrine.2016
On the Existence of Things

March 28th, 2023

Through exploring the distinction between what we ordinarily think of as an experience and what Nishida Kitarō, the founder of the Kyoto School of philosophy, calls “pure” or “direct” experience, I will claim that things don’t exist as those things. My claim is that the existence of natural kinds conflicts with pure experience.

What I mean by experience is all that exists for you here and now. I mean experience as we use it in sentences such as: “I’m experiencing X.” Experience, therefore, includes arising feelings, thoughts, sounds, sights, etc. It includes everything that is perceived. So, I don’t mean the word experience as we use it in sentences such as: “I have a lot of experience in X.” Pure experience is a specific kind of experience in the former sense.

Pure experience is experience prior to conceptualization (Nishida, 1992). It is unitary. It has no distinctions of self/other, subject/object, sound/sight, etc. All of these come after we apply our concepts to the experience we have here and now. What we usually call experience is already clothed in concepts and corroded with words.

Colour’s five hues from th’ eyes their sight will take;
Music’s five notes the ears as deaf can make;
The flavours five deprive the mouth of taste;
The chariot course, and the wild hunting waste
Make mad the mind; and objects rare and strange,
Sought for, men’s conduct will to evil change.
Laozi, Tao Te Ching, 12

Our habit of categorizing colors, sounds, and so on impairs our ability to perceive their uniqueness. Our habit of categorizing experiences impairs our ability to experience directly and without artificial divisions. Convention decides which signifiers correspond to which signifieds and sets the boundaries of those signifieds (Saussure, 1916/1959). One learns early on how “culture has tacitly agreed to divide things from each other, to mark out the boundaries within our daily experience” (Watts, 1999, pp. 20-21).

The moment of seeing a color or hearing a sound, for example, is prior not only to the thought that the color or sound is the activity of an external object or that one is sensing it, but also to the judgment of what the color or sound might be. (Nishida, 1992, p. 3)

If we recognize the distinction between ordinary and pure experience, we see that things don’t exist as we usually think. They exist in our experience only arbitrarily: they are distinct from everything else because of the concepts we apply to understand them. It is possible to drop conceptualization even for a brief moment, and that’s what often happens during meditation sessions. The belief in grammar and our thinking habits affect one’s metaphysical beliefs (Nietzsche, 2003, p. 21).

Consider the question of the existence of an ocean wave or a constellation of stars. Both of these are perceived as distinct objects only because we choose to. There are no “natural” boundaries between signifieds and no “natural” definitions for them. Things don’t exist as those things: we label them because of the instrumental value of doing so and without implying any metaphysical truth.

References

Laozi. (1970). Tao Te Ching. Penguin Books.

Nietzsche, F. (2003). Nietzsche: Writings from the Late Notebooks. Cambridge University Press.

Nishida, K. (1992). An Inquiry into the Good. Yale University Press.

Saussure, F. de, (1959). Course in General Linguistics. Philosophical Library. (Original work published 1916)

Watts, A. (1999). The Way of Zen. Knopf Doubleday Publishing Group.
For Whom?

January 14th, 2023

While reading secondary texts about Sophocles’ Theban Plays, I found an interesting note about lines 1153-4 of Oedipus Rex. The note is relevant not just for analyzing the play itself but also for contemporary political discussions.

Oedipus is trying to uncover the truth about his identity and his past. At this stage of the play, Oedipus suspects that his identity connects with King Laius. As part of his investigation, Oedipus sends for a herdsman known to have been in Laius’ service. When the herdsman arrives, Oedipus starts questioning him about a child given to him by Laius to abandon in the mountains. The herdsman initially refuses to speak, but Oedipus threatens him with pain:

If you’ll not talk to gratify me, you will talk with pain to urge you. (Oedipus Rex, line 1153)

The herdsman is not a slave, but the use of pain to get the truth was a familiar practice to Athenians. Athenian law not only permitted the use of torture, but required it for slaves giving evidence in court (Sophocles & Segal, 1994, p. 195). The Romans had a similar idea. In Greek and Roman political thought, it was often thought that slaves are truthful if and only if they are subjected to torture.

What reason lies underneath this belief? Slaves had drastically different incentive structures because of their material conditions. Slaves, it was thought, would only testify to those things they believed would please their master. Slaves, being subject to punishment, had the incentive to lie, and the Greeks and Romans used torture to overcome this incentive. While their solution is detestable, the Greeks and Romans highlighted a vital problem: material conditions influence an individual’s willingness to tell the truth.

For example, a Marxist might say that what the bourgeoisie say depends on what their master (the market) wants. Someone may be less likely to speak the truth if they believe that doing so could result in a loss of income, resources, social status, etc.

According to Lenin, politics is concerned with the question of “who, whom?” (Trotsky, 1925; Bell, 1958; Suvin, 2006). Following the formula, we can always break down abstract political statements into statements about specific people doing specific things to specific others (Geuss, 2008, pp. 23-4). The discussion above, however, suggests that Lenin’s formula is incomplete. We must ask an additional question.

This other question is: “for whom?” When thinking about politics, we must consider agency, power, interests, and the relations between these. Who benefits from telling the truth? Who benefits from lying? How do material conditions influence whether telling the truth is in this person’s/group’s interest? These are the questions we must always keep in mind.

References

Bell, D. (1958). Ten Theories in Search of Reality: The Prediction of Soviet Behavior in the Social Sciences. World Politics, 10(3), 327–365. https://doi.org/10.2307/2009491

Geuss, R. (2008). Philosophy and real politics. Princeton University Press. https://books.google.ge/books?id=_lNcnK1XvB0C

Sophocles, & Segal, C. (1994). The Theban Plays: Introduction by Charles Segal (J. P. Hogan, Ed.; D. Grene, Trans.). Everyman’s Library.

Suvin, D. (2006). Terms of power, today: An essay in political epistemology. Critical Quarterly, 48(3), 38–62. https://doi.org/10.1111/j.1467-8705.2006.00720.x

Trotsky, L. (1925). Towards Capitalism or Towards Socialism? The Labour Monthly. https://www.marxists.org/archive/trotsky/1925/11/towards.htm
Doubting Skepticism

January 3rd, 2023
‘So, Pyrrho, you are dead?

— I beg to doubt it.’

‘Uncertain still?’

— ‘Hmph! certainly I scout it.’

‘This tomb, friend Pyrrho, leaves no doubt about it.’
– Julianus Ægyptius, Prefect of Egypt, translated by John Sampson (Quarrie, 2020, p. 166)

Introduction

Julianus Ægyptius’ epigram is not a refutation of Pyrrhonian skepticism, but it expresses one of its pitfalls: it is just too counter-intuitive. Pyrrhonian skepticism is a school of philosophical thought that originated in ancient Greece with the philosopher Pyrrho of Elis (Bett, 2022; Vogt, 2022). Most of what we know about it comes not from Pyrrho but from Sextus Empiricus’ Outlines of Pyrrhonism.

According to Pyrrhonian skepticism, the suspension of judgment is the only justified attitude concerning any proposition (including this one). While this approach to philosophy has had a significant influence on Western thought, it is not without its critics.

In this essay, I will first examine the claim that Pyrrhonian skepticism is circular or self-refuting. Then, I will discuss the idea that the suspension of judgment is itself a judgment and hence genuine skepticism is impossible. I will finally discuss the tension between genuine doubt and living while suspending judgment on all propositions. I will conclude that it is nearly impossible for Pyrrhonian skeptics to be consistent in their beliefs and actions.
The Self-Refutation Argument

According to some, Pyrrhonian skepticism is flawed due to its reliance on circular reasoning. The skeptic posits that knowledge of the true nature of reality is unattainable and subsequently uses this assumption to suspend judgment on all matters of fact. However, the validity of this assumption cannot be established, as it is based on the premise that certainty is impossible. As a result, the skeptic assumes the truth of their position.

The Pyrrhonian skeptic is essentially saying that we cannot be certain of anything, including the claim that we cannot be certain of anything. This does not prove the self-defeating nature of Pyrrhonian skepticism, but it undermines its persuasiveness.

The problem with this argument is that it presents Pyrrhonian skepticism as an argument. Skeptics aren’t committed to the truth of the premises and conclusions of Pyrrhonian skepticism. The aim of Pyrrhonian skeptics is not and shouldn’t be to convince anyone of its truthfulness. So if we (non-Pyrrhonians) think that the claims of Pyrhonnian skepticism aren’t sound, we should investigate why.

Suspension is Judgment

Another common criticism of Pyrrhonian skepticism relies on the idea that there is no such thing as neutrality. More specifically, claiming that you’re suspending judgment about X is a judgment about X. For example, claiming that both sides are wrong on a given political issue commits one to a specific political point of view.

What is important is that when someone acts like a skeptic, they do so in a non-neutral way. Does this make skepticism self-refuting? No. All this does, as Ronald Dworkin pointed out, is refute certain arguments for skepticism.

Doubt and Behavior

Pyrrhonian skepticism is incompatible with everyday experience. This is because the skeptic is effectively saying that we cannot be certain of anything, including the most basic and mundane aspects of our lives. For example, we cannot be certain that the sun will rise tomorrow, that the floor will hold us up when we stand on it, or that the food we eat will nourish us. However, these are all things that we rely on and take for granted in our everyday lives, and to suggest that we cannot be certain of them is to reject the very foundations of our experience.

This does not prove the contradictory nature of skepticism or do anything to undermine its truth value, but it does render it problematic from a pragmatic perspective. According to Charles Sanders Peirce (1992, pp. 109-123), Descartes made a similar error when he advocated for the doubt of all things and the reliance on first principles. Merely expressing a proposition in the form of a question does not demonstrate the presence of genuine doubt.

True doubt is always accompanied by a feeling. It motivates us to investigate until we minimize or eradicate it. Our beliefs guide our actions. So if skepticism is to have any practical significance beyond being a philosophy one espouses to appear original at social events, it must have practical consequences. What would those consequences be? How would a genuine Pyrrhonian skeptic behave?

The answer to these questions is unclear. If such people exist, I’ve never seen them. It is even difficult to imagine them without engaging in fantasy. It might be that a genuine Pyrrhonian skeptic is a philosophical chimera that does not and can not exist, similar to a strict nihilist, moral relativist, or Übermensch.

The main problem with Pyrrhonian skepticism is not that it is contradictory or logically flawed. Nor that it is too permissive or tolerant of opposing views. In my view, skepticism commits the opposite error: it demands too much of truth without acknowledging less demanding alternatives. I agree with Pyrrho and Sextus Empiricus in that complete certainty is not possible, but it does not have to be. Suspension of judgment on all matters is too extreme of a conclusion to draw from all this.

That demand for certainty Nietzsche characterized (The Gay Science, §347) as arising from the instinct of weakness is not a necessary component of all belief systems outside of skepticism. One can reject the concept of certainty while still holding beliefs about certain propositions. I believe that most people who consider themselves to be Pyrrhonian skeptics engage in this type of belief formation, despite their claims to the contrary.

Conclusion

Pyrrhonian skepticism is not self-refuting, circular, logically contradictory, or anything of the sort. People who claim to be skeptics can and do exist. It is a valid philosophical position that individuals can adopt. The point I want to convey is that given my pragmatist way of thinking, theory of truth, and definitions of what constitutes a “genuine X,” I see no clear way a Pyrrhonian skeptic could consistently act and think like one.

References

Bett, R. (2022). Pyrrho. In E. N. Zalta & U. Nodelman (Eds.), The Stanford Encyclopedia of Philosophy (Fall 2022). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/fall2022/entries/pyrrho/

Nietzsche, F. (2001). Nietzsche: The Gay Science: With a Prelude in German Rhymes and an Appendix of Songs. Cambridge University Press.

Peirce, C. S. (1992). The Essential Peirce, Volume 1: Selected Philosophical Writings (1867–1893). Indiana University Press.

Quarrie, P. (2020). Poems from Greek Antiquity. Knopf Doubleday Publishing Group.

Sextus Empiricus. (1933). Outlines of Pyrrhonism (R. G. Bury, Trans.) [Data set]. Harvard University Press. https://doi.org/10.4159/DLCL.sextus_empiricus-outlines_pyrrhonism.1933

Vogt, K. (2022). Ancient Skepticism. In E. N. Zalta & U. Nodelman (Eds.), The Stanford Encyclopedia of Philosophy (Winter 2022). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/win2022/entries/skepticism-ancient/
Forget Forgetfulness

November 4th, 2022
Let no thought pass incognito, and keep your notebook as strictly as the authorities keep their register of aliens. (Benjamin, 1928/2016, p. 46)

For as long as I can remember, I’ve been obsessed with systems that can help me think. Even my desire to write is downstream of my desire to understand. I’m afraid of forgetting, so I keep switching and inventing new systems for taking notes. My long-term memory is pretty good, but I still need an external system that collects my thoughts and lets me communicate with them. So does almost everyone else: “I started the index card file for the simple reason that I have a poor memory” (Luhmann, 1987, p. 149). Taking notes is a way to transfer the burden of remembrance from your brain to something else. Writing something down gives a sense of security—Lethe is no longer threatening. You have no reason to trust your memory. Your working memory could be the best in the world, yet that still wouldn’t be good enough. Any effective system for taking notes should allow you to forget about forgetting. So here I want to lay out mine. I want to specify why I chose this system and why you may wish to apply it.

The practice of taking notes has a long history. Many prominent writers, philosophers, and scientists have their methods. Gottfried Wilhelm Leibniz, Georg Philipp Harsdörffer, Niklas Luhmann, Claude Lévi-Strauss, Roland Barthes, Vladimir Nabokov, Georg Wilhelm Friedrich Hegel, Walter Benjamin, Reinhart Koselleck, Paul Valéry, Heinrich Heine, Arno Schmidt, Jean Paul, and Ernst Jünger just to name a few. Would their accomplishments be the same without their collections of notes? If not, how come none of them realized they were wasting their time? Luhmann, for example, managed to produce over 50 books and 550 articles during his lifetime because of his sophisticated system for taking notes (Schmidt, 2016, p. 289). The systems differ. No system is perfect for everyone at all times. I know this well, yet the thought that my system could be just a bit better never abandons me.

I often buy notebooks and soon stop using them for the most superficial reasons. I obsess over the formatting of each and every note. I dismiss entire notebooks because of a small mistake. I download new note-taking apps and try them out, only to stop using them after a month or two. I’m never satisfied with my tools. I’m never really calm. I’m terrified of becoming so obsessed with productivity and finding the ‘perfect system’ that this inhibits rather than helps me think. I see all this as a problem I need to fix. If any of this applies to you, I hope this essay serves you well.

I will do the following: First, I will discuss why you might want to write notes. Then I will briefly outline the history of note-taking. Specifically, I will consider hypomnema, commonplace books, journals, Paul Valéry’s Cahiers, and Niklas Luhmann’s Zettelkasten. I will then outline how I intend to take notes, at least for the conceivable future. I hope to encourage you to start taking notes more seriously. I also want to force myself to stick with one of the methods I discuss here. Essentially, this essay is a form of “working with the garage door up“: I will write about my problems and try to work through them openly.

In his famous essay, Kommunikation mit Zettelkästen, Niklas Luhmann posits that it is impossible to think in a sophisticated or networked way without writing (Luhmann, 1992, pp. 53-61). Is he right? Could, for example, Grigori Perelman have proved the Poincaré conjecture all in his head? Could James Joyce have written Ulysses linearly in one go? Could Shakespeare have written his 154 sonnets without any editing or modifications? I think not. What Luhmann means by “sophisticated thinking” is the type of thinking required for the complex synthesis of previously unrelated material. Synthesizing diverse material through writing notes is a form of intellectual labor.

If you want to retain the intellectual labor you’ve already done and increase its quality—you must write. You must write to protect yourself from forgetfulness. You must write to think. You must write now so that you may write more later. Writing accretes. Your collection of notes becomes your communication partner. If you want to figure something out and can’t succeed through thinking independently, you should speak about it with someone (von Kleist, 1805/2001, p. 319). That ‘someone’ may be the previous you. The previous you that made all those notes so many years ago. You may have forgotten, but the ink is still there. When one writes, one reads what one has written. The letters act upon their author right when they are born, just as they act upon anyone who reads them later. In time, notes become sovereign machines capable of influencing their readers.

Any practice or idea that has lasted millennia has a good chance of being useful. Lasting for long is proof of usefulness. Concepts go through the process of natural selection. Time obliterates all that is useless. We should, therefore, expect that note-taking will have many precedents that stretch for thousands of years. This is exactly what we find. Even Leibniz, Harsdörffer, Heine, and Hegel are relatively recent examples. Countermeasures against forgetfulness have their roots in ancient Greece. Plato’s criticisms of writing in the Phaedrus rely on the idea that writing discourages the use of memory. That instead of an elixir of memory, writing is an elixir of reminding (Plato, Phaedrus, 275a).

There also existed a practice of writing what the Greeks called hypomnemata (ὑπομνήματα). These books, notebooks, or notes were not substitutes for memory. They were not narratives of oneself or intimate journals. They intended to capture what was already said (Foucault, 2005, p. 500). To collect what one heard, read, or came up with (Foucault, 1997, pp. 210-211). Hypomnemata made possible the establishment of a “relationship of oneself with oneself” by making one’s recollection of the fragmentary λόγος readily available.

Seneca stressed the importance of keeping a treasure store of reading. According to Seneca, going from book to book and not writing anything down puts one in danger of retaining nothing and forgetting oneself (Seneca the Younger, Epistles, p. 7). The writing process counteracts stultitia, i.e., mental agitation, distraction, and constant wavering between opinions. Reading for nourishing and refreshing the intellect and writing for fixing ideas are both essential (Seneca the Younger, Epistles, p. 277). Hypomnemata allow the psyche to detach itself from concerns about the future and direct itself toward the past.

The issue with hypomnemata or notebooks is that they are collections of heterogeneous fragments. The writer must establish links, similarities, and differences between them. Most notebooks are unfinished, underused, chaotic, and fragmented. For these notebooks to be helpful, it is necessary to organize and index them.

Let us take down one of those old notebooks which we have all, at one time or another, had a passion for beginning. Most of the pages are blank, it is true; but at the beginning we shall find a certain number very beautifully covered with a strikingly legible hand-writing. Here we have written down the names of great writers in their order of merit; here we have copied out fine passages from the classics; here are lists of books to be read; and here, most interesting of all, lists of books that have actually been read, as the reader testifies with some youthful vanity by a dash of red ink. (Woolf, 1958, p. 25)

Seneca had a solution. It was to run everything we have absorbed through our lens. To digest all thoughts gathered from reading. To put in all hypomnemata a unifying element: us. Only in this way will the material enter our reasoning rather than exclusively our memory. Other writers, for example, Umberto Eco, have stressed a similar point (Eco, 1977/2015, pp. 164-167). It is vital to write in your own words. To paraphrase rather than quote. Direct quotations don’t demonstrate how you understand what you’re quoting. Paraphrasing, by contrast, always involves interpretation. It transforms the original material into “tissue and blood” (Seneca the Younger, Epistles, p. 281). Interpretation is a transformative and creative act. The more effort one puts into thinking an idea through, the sharper it seems. I write ‘seems’ because whether or not it sharpens is a matter of debate. The important part is that you become more confident in your writing.

There are, of course, exceptions to this rule. Sometimes you want to analyze a poem. Paraphrasing it is almost always a bad idea. Sometimes you want to dissect how the author uses language in a given passage. Or the language is so powerful that you do not wish to change anything. Sometimes your interpretation is not as important because the meaning is unambiguous. Consider, for example, Shakespeare’s 7th sonnet (1609/1923):

Lo, in the orient when the gracious light
Lifts up his burning head, each under eye
Doth homage to his new-appearing sight,
Serving with looks his sacred majesty;
And having climb’d the steep-up heavenly hill,
Resembling strong youth in his middle age,
Yet mortal looks adore his beauty still,
Attending on his golden pilgrimage;
But when from highmost pitch, with weary car,
Like feeble age, he reeleth from the day,
The eyes, ’fore duteous, now converted are
From his low tract and look another way:
So thou, thyself out-going in thy noon,
Unlook’d on diest, unless thou get a son.

If I had the choice of paraphrasing or directly quoting the passage above, I think it’s clear why I would choose the latter. The language gives it more value than any interpretation could. I could paraphrase just the meaning, but so much would get lost. The reader wouldn’t see that although Shakespeare uses many metaphors to describe the sun, the word itself never comes up. And the sonnet, when you’re not expecting, ends with the word son. This and other such ingenuities would all get lost. Analyzing the way Shakespeare uses language in this sonnet would require a lot of work and would be a more worthy endeavor.

In producing art of any kind, be it writing, painting, or architecture, I find that the more effort I put into something, the more proud I am. If I don’t spend much time on, for example, an architectural project, I will inevitably think it’s not good enough. When people say that a lot of work went into creating an art piece, they usually mean it as a compliment. As if the work that went into creating something gives it more value (Zumthor, 1998/2010, p. 12). Whether or not this is true, it certainly seems like it is. And it is, therefore, worth it for me to spend more time with each note. Hence my preference for writing by hand before moving to a computer. It gives them more value.

I won’t exhaust the comparison of digital vs. analog tools for taking notes. You probably know most of the pros and cons of each already. I could cite research on how writing things down by hand makes it more likely for you to remember them or how reading on paper rather than on a screen has the same effect. I could discuss how digital notes have the advantage of being easily searchable. I could claim that you might not want to rely on a specific app or company to store all your writings. That discussion deserves a separate essay, but there isn’t much I can add that hasn’t already been said a thousand times. I think it ultimately boils down to personal preference. I use both.

So how do we organize our hypomnemata? With commonplace books like John Locke, John Milton, Francis Bacon, Ralph Waldo Emerson, and Henry David Thoreau? With notebooks like Friedrich Nietzsche, Martin Heidegger, Virginia Woolf, Walter Benjamin, and Paul Valéry? With slip boxes like Gottfried Wilhelm Leibniz, Vladimir Nabokov, Roland Barthes, Claude Lévi-Strauss, and Niklas Luhmann? The way I currently organize my notes is a combination of these, so I will explain what each means in turn.

Let’s begin with commonplace books. Commonplace books are notebooks used for collecting notes about books, articles, journals, and other media. “In their purest form, commonplace books were written in Latin by schoolboys who organized sententiae under topic headings” (Burke, 2013). They differ from diaries or writer’s journals because they are generally not introspective or chronological (Basbanes, 2006, p. 82). My issue with exclusively relying on commonplace books is that my ideas have to get mixed with reading notes, and I think those two deserve their own spaces. If you want to find some idea and the only thing you use is a commonplace book, you must remember what you were reading when that idea came to you to find it. And I don’t want that. I want to be able to find any note based on its address.

Reflective notebooks, like Nietzsche’s notebooks (Nietzsche, 2003 & Nietzsche, 2009), differ from commonplace books because you don’t fill them with notes about the books you’ve read. You fill your reflective notebooks with the ideas you develop. Paul Valéry, for example, devoted the early hours of each morning to writing in his Cahiers (Lawler, 1976, p. 346). I prefer combining this with a commonplace book. I split my notebooks in half: I use the first half for my ideas and the second half for reading notes. These two correspond to different types of slip cards in Niklas Luhmann’s system.

Now I will explain what the zettelkasten is. A zettelkasten (slip box) or card file consists of small paper slips arranged in an organic network and linked to one another. Many writers use slip cards to help them write, but I won’t explain each method separately. I believe Niklas Luhmann brought everything useful about a zettelkasten to near perfection. I will, therefore, focus only on that.

When working on his dissertation, Luhmann realized that the notes he took would be useful not just for one book but for a lifetime (Luhmann, 1987, p. 149). Filling the zettelkasten took more of his time than the writing process itself (Luhmann, 1987, p. 142). Yet the results speak for themselves: it was worth it. The card index helped rather than held back Luhmann from writing so much.

Although surprising for such a systematic thinker, Luhmann didn’t pedantically adhere to specific types of ink or paper. He used A6 size paper, but the backside was sometimes already written. He took some notes with a blue pen and some with a red one. Some are on thick paper, some on thin, and so on (Schmidt, 2016, p. 291). I wish I could do this too, but it bothers me too much. Maybe after some inconsistencies, one gets used to them. I hope I will too. Luhmann used these slips of paper to record all kinds of information: his theses and concepts, reading notes, questions, and bibliographical information.

He had three types of cards. We may call them permanent, bibliographic, and index cards. Permanent notes contained distilled ideas. Bibliographic cards contained brief reading notes. Index cards contained lists of keywords with several addresses per keyword. What are addresses? Since Luhman was using pen and paper, he had to find a way to find the slip cards whenever he wanted. So he would give an alpha-numeric address to each slip. Card 9 would go between cards 8 and 10. If Luhmann wanted to put a new card between cards 9 and 10, he would give it the address 9a. If he wanted to put a card between 9a and 10, he would give it the address 9a1, and so on. I prefer using a physical notebook for ephemeral notes and bibliographic cards, and I use my computer for permanent notes. I find physical index cards to be limiting, and I prefer carrying around a notebook to carrying around a bunch of A6 papers.

So my system consists of two things: a notebook for reading and ephemeral notes and a folder on my computer for my permanent notes. The reasons I keep a physical notebook are as follows: (1) writing things down makes you remember them, (2) a notebook is more portable than a laptop, (3) I don’t have to worry about formatting, searchability, etc., (4) writing by hand forces you to make your notes more concise, (5) I don’t get distracted by a computer while reading, and (6) aesthetics.

The reasons I prefer to have my permanent notes on my computer are as follows: (1) it is easier to lose pieces of paper than files if you use external drives, (2) I can copy the already written text directly, (3) I can copy citations which I have already generated, (4) I can edit the permanent notes if I have to, (5) I can search the notes, so there is no need for physical index cards, (6) There is no length limit to any single note, and (7) digital notes are more portable. The software doesn’t matter much. I use Obsidian, but there are many other options.

We began with a discussion of the history of fighting forgetfulness. Note-taking has a surprisingly long history: even the ancient Romans have much to say about it. We saw different methodologies for taking notes and arrived at my system. I tried to give reasons for choosing this system, but I admit that this subject gives me a lot of trouble. I’m not firm in my convictions. I hope this was useful for you too.

references
- Basbanes, N. A. (2006). Every book its reader: The power of the written word to stir the world. Perennial.
- Benjamin, W. (2016). One Way Street. Harvard University Press. (Original work published 1928)
- Burke, V. E. (2013). Recent Studies in Commonplace Books. English Literary Renaissance, 43(1), 153–177. https://doi.org/10.1111/1475-6757.12005
- Eco, U. (2015). How to Write a Thesis. The MIT Press. (Original work published 1977)
- Foucault, M. (1997). Ethics: Subjectivity and Truth. New Press.
- Foucault, M. (2005). The Hermeneutics of the Subject: Lectures at the Collège de France 1981–1982. Pan Macmillan.
- Krajewski, M. (2011). Paper Machines: About Cards & Catalogs, 1548-1929. The MIT Press.
- Krajewski, M. (2016). Note-Keeping: History, Theory, Practice of a Counter-Measurement Against Forgetting. In Cevolini, A. Forgetting Machines: Knowledge Management Evolution in Early Modern Europe. BRILL.
- Lawler, J. (1976). Valéry’s Cahiers. Books Abroad, 50(2), 346–349. https://doi.org/10.2307/40130439
- Luhmann, N. (1987). Biographie, Attitüden, Zettelkasten. In Luhmann, N. Archimedes und wir. Interviews. Merve Verlag. pp. 125–155.
- Luhmann, N. (1992). Universität als Milieu: Kleine Schriften. Haux.
- Nietzsche, F. W. (2003). Writings from the Late Notebooks. Cambridge University Press.
- Nietzsche, F. W. (2009). Writings from the Early Notebooks. Cambridge University Press.
- Plato. Phaedrus.
- Schmidt, J. F. K. (2016). Niklas Luhmann’s Card Index: Thinking Tool, Communication Partner, Publication Machine. In Cevolini, A. Forgetting Machines: Knowledge Management Evolution in Early Modern Europe. BRILL.
- Seneca the Younger. (1917). Epistles (R. M. Gummere, Trans.). Harvard University Press. https://doi.org/10.4159/DLCL.seneca_younger-epistles.1917
- Shakespeare, W. (1923). Shakespeare’s Sonnets. Yale University Press. (Original work published 1609)
- von Kleist, H. (2001). Sämtliche Werke und Brief. Volume 2. dtv Verlagsgesellschaft. (Original work published 1805)
- Woolf, V. (1958). Granite and Rainbow: Essays. Harcourt.
- Zumthor, P. (2010). Thinking Architecture. Birkhäuser Basel. (Original work published 1998)
Blame Machine

October 24th, 2022
What’s your most radical and controversial view about ethics? My answer: I don’t believe in moral responsibility. Believing in moral responsibility requires that you ascribe agency to human beings, and I don’t: if we’re all just cogs in the machine, blame is always inappropriate. I can’t blame you for something you couldn’t have helped doing. We’re all familiar with making choices. Categories like responsibility, blame, guilt, revenge, and consent presuppose human agency. But this doesn’t change the fact that “there is in the mind no volition” (Spinoza, 1677/1910, p. 75). You are a force that changes the universe, yes, but you don’t decide how you will do so. In this essay, I want to reexamine concepts like blame and moral responsibility in light of my firm conviction that human beings don’t have agency. I will discuss whether these concepts are harmful and propose arguments for why they are fictional.

People often use the repercussions of determinism regarding the justice system as a practical argument for free will. Yet this has nothing to do with its actual existence. So free will is thought of as a Platonic noble lie (Plato, Republic, Book III, 414c). But even the benefits of this illusion are questionable. Yes, we must radically reassess moral responsibility, blame, praise, guilt, revenge, and similar concepts in light of determinism, but do you see a convincing consequentialist case against doing so? The justice system doesn’t necessarily have to rest on the assumption that human beings have moral agency. Punishment with the aim of prevention is still fully compatible with strong determinism. All that needs to change is our view of the relationship between blame and causation.

Let’s take a famous example from 18th-century history: The execution of King Louis XVI at the hands of Charles-Henri Sanson. Now, we would all say that Sanson caused Louis XVI’s death. But the disagreement between determinists and non-determinists is about blame and responsibility, not causation. So a determinist would say that even though Sanson caused the king’s death, he is not to blame, i.e., he is not responsible. All this sounds too radical, but here’s my reasoning: If the executioner is just as much a machine as the guillotine, then blaming him is as absurd as blaming the guillotine. The guillotine is just as much a cause of Louis XVI’s death as Sanson is, but it’s not responsible because it has no agency. I can’t blame the killer or the bullet. And if I can’t blame killers, I can’t punish them for punishment’s sake.

When I was in high school, I remember having a discussion with one of my teachers about the death penalty. We were analyzing a specific scenario: imagine that there is a prisoner so dangerous that the only options we have are life imprisonment and execution. If the prisoner prefers execution, should we administer it? My teacher’s answer was no. Her answer was not necessarily problematic, but her reasoning was: She said that we shouldn’t administer the death penalty because that wouldn’t be severe enough. All this sounds so evil to me because I don’t recognize punishment for punishment’s sake as anything other than madness. In a deterministic world, such ‘justice’ makes no sense. The conclusion that punishment of this kind is unjust follows from the premise that free will doesn’t exist.

If humans have no agency, a murderer doesn’t choose to kill. An amalgamation of forces moves the murderer toward that action. No one can claim to know all of those in any specific case, but that’s not necessary for the soundness of my argument. As for punishment, it doesn’t matter whether the murderer had the choice to kill or not. What matters is that we can reasonably expect similar behavior from the murderer in the future, so we must do what we can to prevent it. I don’t want to defend utilitarianism, but it is also compatible with strong determinism. If a utilitarian claims that the pleasure gained by the offended, for example, outweighs the pain inflicted upon the offender and, therefore, punishment is justified, then determinism has nothing to say for or against doing so. So we see that even if we remove blame from the equation, we can still use the concept of justice.

As a case study of how a deterministic moral framework could function, we may consult the Odyssey. In Homeric Greece, the problems of voluntary/involuntary action and the riddles concerning free will do not arise. There was no concept of will, so the moral vocabulary looked quite different. It doesn’t matter whether you could’ve acted courageously or the circumstances made it impossible for you to do so. You still wouldn’t be considered courageous. Odysseus can blame the suitors for having false beliefs (Homer, Odyssey, Book XXII) even though we would today think of having a false belief as an involuntary error. As MacIntyre explains, “it is not that Homer thinks that beliefs are voluntary; he is engaged in an assessment to which what the agent could or could not have done otherwise is irrelevant” (MacIntyre, 1966/2017, p. 7).

Almost any tragedy from Ancient Greece, and most famously Oedipus Rex, implicitly confronts us with the problem of free will. We see Oedipus try to avoid his destiny and achieve the exact opposite. While Sophocles had no concept of free will, he would probably have agreed that usually, we don’t see the true causes behind our actions, even when we think we’re acting freely. Even when we are the cause, we don’t choose to be.

After considering Homer and Sophocles, we can also look at Aristotle’s case. He expounds on a theory of voluntary and involuntary actions that obsoletes the concept of free will. He divides actions into voluntary and involuntary ones based on their causes. Actions that are caused by chance or necessity are involuntary, while those caused by one’s own wants and habits are voluntary. Note that each kind of action still has a cause that we don’t “control”:

Now, all human actions are either the result of man’s efforts or not. Of the latter some are due to chance, others to necessity. Of those due to necessity, some are to be attributed to compulsion, others to nature, so that the things which men do not do of themselves are all the result of chance, nature, or compulsion. As for those which they do of themselves and of which they are the cause, some are the result of habit, others of longing, and of the latter some are due to rational, others to irrational longing. Now wish is a rational longing for good, for no one wishes for anything unless he thinks it is good; irrational longings are anger and desire. Thus all the actions of men must necessarily be referred to seven causes: chance, nature, compulsion, habit, reason, anger, and desire. (Aristotle, Rhetoric, Book I, Chapter 10, Sections 7-8)

We cannot control our appetites, anger, reasoning, and habits. All this is because we cannot control who we are and what we think. To understand this, consider the following question: How do your thoughts arise? Not through any conscious decision on your part. Could it even be possible to decide what and when to think? No. The succession of thoughts always is and can only be unplanned.

Imagine the opposite: a thought, X, arises because of a preceding decision. I decide to think about X. But for this to be voluntary, I would have to decide to decide what to think. I would have to decide: I am going to decide whether to think X or something else. Even if this happened, I am in an infinite regress. At a certain point, the cause of my thoughts will necessarily be outside of my control. Furthermore, at any point in this chain, the decision is determined.

In the form in which it comes, a thought is a sign with many meanings, requiring interpretation or, more precisely, an arbitrary narrowing and restriction before it finally becomes clear. It arises in me – where from? How? I don’t know. It comes, independently of my will, usually circled about and clouded by a crowd of feelings, desires, aversions, and by other thoughts, often enough scarcely distinguishable from a ‘willing’ or ‘feeling’. It is drawn out of this crowd, cleaned, set on its feet, watched as it stands there, moves about, all this at an amazing speed yet without any sense of haste. Who does all this I don’t know, and I am certainly more observer than author of the process. Then its case is tried, the question posed: ‘What does it mean? What is it allowed to mean? Is it right or wrong?’ – the help of other thoughts is called on, it is compared. In this way thinking proves to be almost a kind of exercise and act of justice, where there is a judge, an opposing party, even an examination of the witnesses which I am permitted to observe for a while – only a while, to be sure: most of the process, it seems, escapes me. – That every thought first arrives many-meaninged and floating, really only as the occasion for attempts to interpret or for arbitrarily fixing it, that a multitude of persons seem to participate in all thinking – this is not particularly easy to observe: fundamentally, we are trained the opposite way, not to think about thinking as we think. The origin of the thought remains hidden; in all probability it is only the symptom of a much more comprehensive state; the fact that it, and not another, is the one to come, that it comes with precisely this greater or lesser luminosity, sometimes sure and imperious, sometimes weak and in need of support, as a whole always exciting, questioning – because every thought acts as a stimulus to consciousness – in all of this, something of our total state expresses itself in sign form. (Nietzsche, 2003, pp. 34-35)

So the ‘I’ that thinks is itself a construction of thinking. The conjunction ‘I think’ is a grammatical convention that might not correspond to reality. Nietzsche’s claim that “something can be a condition of life and nevertheless be false” (Nietzsche, 2003, p. 21) applies equally well to the thinking ‘I’ and to free will. You are not the thinking I. The ‘I’ feels, observes, and experiences. It doesn’t decide. If all this follows from determinism, then it is understandable why people often consider it a nihilistic worldview. Despite my belief that true nihilists don’t exist, this is a fair objection and merits a response.

I think the objection arises out of a different understanding of the relationship between being a cog in the machine and being coerced. I do not claim that we are just acted upon by outside forces, making all actions coercive. And, of course, no one likes being coerced all the time. But the nonexistence of free will doesn’t imply that all we do, we do reluctantly or against our will. “The absolute necessity of everything that happens contains no element of compulsion” (Nietzsche, 2003, p. 62). I claim that we also partially comprise those forces. You can influence the life of someone in good or bad ways. You can be the cause of someone’s happiness or pain. The fact that your behavior is determined doesn’t change this. You can’t be blamed or credited for who you are and what you do, but you can still be honest or dishonest, courageous or cowardly, proud or humble, and so on. There is no element of unpleasant compulsion in any of this. No one compels you to act against your will. It’s just the way the machine operates.

The offence taken at the doctrine ‘of the unfreedom of the will’ is that it seems to assert ‘you do what you do not voluntarily but unwillingly, i.e., under coercion’. Now, everyone knows how it feels to do something unwillingly, that is, reluctantly, ‘against your will’ – and one doesn’t concede that, because one does many things, in particular many ‘moral’ things, gladly. One thus understands ‘unfree will’ as meaning ‘a will coerced by an alien will’, as if the assertion were: ‘Everything you do, you do under coercion by somebody else’s will’. Obedience to one’s own will is not called coercion, for there is pleasure in it. That you command yourself, that is ‘freedom of will’. (Nietzsche, 2003, p. 57)

Free will may not exist, but the distinction between free men and slaves, like the distinction between voluntary and involuntary actions in Aristotle’s theory, remains. You may still know which actions are good for you and perform those, hence being free. Alternatively, being ignorant of your good coerces you to act in a way that is contrary to your actual will.

We shall easily see what is the difference between a man who is led by opinion or emotion and one who is led by reason. The former, whether he will or not, performs things of which he is entirely ignorant; the latter is subordinate to no one, and only does those things which he knows to be of primary importance in his life, and which on that account he desires the most; and therefore I call the former a slave, but the latter free. (Spinoza, 1677/1910, pp. 186-187)

Augustine needed the concept of free will to explain the problem of evil. God is all-good and all-powerful, so why do atrocities happen? Because God preferred to give us free will rather than make us slaves to destiny. This belief has persisted even among atheists due to inertia and its intuitiveness. So what is the practical significance of refuting responsibility and blame? Why go against everyday experience and common sense?

My issue with the concept of free will, when it comes to politics, is the notion of just desert that comes with it. If there is no free will, no one is inherently more deserving than anyone else. And the only reasons for permitting inequalities would be practical ones (Studebaker, 2013). So, for example, in a determinist world, the only reason to pay a neurosurgeon more than one pays an architect would be that being a neurosurgeon requires more years of training and is a more difficult job. Consequently, we need to give them a stronger incentive so that the profession does not die out. We would never pay doctors more because they are inherently more deserving or meritorious.

The other reason for problematizing moral responsibility, blame, and guilt are their usefulness to the oppressors. The concept of punishment for the sake of punishment that I wrote about in the beginning would not exist if not for the invention of free will:

Today we have no sympathy anymore for the concept of “free will”: we know only too well what it is—the most disreputable of all the theologians’ tricks, designed to make humanity “responsible” in the theologians’ sense, that is, to make it dependent on them . . . Here I am simply offering the psychology of all making-responsible.—Wherever responsibilities are sought, what tends to be doing the seeking is the instinct of wanting to punish and rule. One has stripped becoming of its innocence when some state of being-such-and-such is traced back to will, to intentions, to acts: the doctrine of the will was essentially invented for purposes of punishment, that is, for purposes of wanting to find people guilty. (Nietzsche, 1889/1997, p. 35)

Blame is, therefore, a machine for oppression. Thought up by the powerful to satisfy the desire to punish and suppress. Blaming the people is like blaming the bullets. What we can do and what we cause are not up to us. Like impersonal forces that have no agency, we make things happen. Whether we like it or not, what we want and when we want it is not for us or anyone else to decide. It’s just how we are and always will be. As Luther would say: “Hier stehe ich, ich kann nicht anders.” I know this vision doesn’t sound all that attractive. You may agree with Nietzsche and say that “truth is terrible” (Nietzsche, 1908/2018, p. 84.). I might not be able to change your mind. It is not my intention to convince as many people as possible. I’m no missionary. In my personal experience, I’ve found that people seem very keen on denying these claims, so I wouldn’t expect an essay to succeed. But here, I tried at least to make you consider these questions, even if they seem so contrary to what you currently believe.

references
- Aristotle (1926). Rhetoric. In Aristotle in 23 Volumes, Vol. 22. Harvard University Press. http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0060
- Homer. Odyssey. http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0136
- MacIntyre, A. (2017). A Short History of Ethics: A History of Moral Philosophy from the Homeric Age to the Twentieth Century, Second Edition. University of Notre Dame Pess. (Original work published 1966)
- Nietzsche, F. (1997). Twilight of the Idols, Or, How to Philosophize with the Hammer. Hackett Pub. (Original work published 1889)
- Nietzsche, F. (2003). Nietzsche: Writings from the Late Notebooks. Cambridge University Press.
- Nietzsche, F. (2018). Ecce Homo: How One Becomes What One Is. Immortal Books. (Original work published 1908)
- Plato. Republic. http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0168
- Sophocles. Oedipus Rex. http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0192
- Spinoza. (1910). Ethics. http://archive.org/details/in.ernet.dli.2015.263056 (Original work published 1677)
- Studebaker, B. (2013, May 2). Leftism and Determinism Part I. https://benjaminstudebaker.com/2013/05/02/leftism-and-determinism-part-i/
St. Borges of Canterbury

October 13th, 2022
In El Hacedor (1960), known in English as Dreamtigers, Jorge Luis Borges includes an ironic ontological argument for the existence of God. The intention might have been ironic, but whether the proof succeeds has nothing to do with the original intentions. So in this essay, I want to analyze whether that argument is valid and whether it is sound. Here is the original Spanish and its translation:

Cierro los ojos y veo una bandada de pájaros. La visión dura un segundo o acaso menos; no sé cuántos pájaros vi. ¿Era definido o indefinido, su número? El problema involucra el de la existencia de Dios. Si Dios existe, el número es definido, porque Dios sabe cuántos pájaros vi. Si Dios no existe, el número es indefinido, porque nadie pudo llevar la cuenta. En tal caso, vi menos de diez pájaros (digamos) y más de uno, pero no vi nueve, ocho, siete, seis, cinco, cuatro, tres o dos pájaros. Vi un número entre diez y uno, que no es nueve, ocho, siete, seis, cinco, etcétera. Ese número entero es inconcebible; ergo, Dios existe. (Borges, 1960/1972, p. 27)

I close my eyes and see a flock of birds. The vision lasts a second or perhaps less; I don’t know how many birds I saw. Were they a definite or an indefinite number? This problem involves the question of the existence of God. If God exists, the number is definite, because how many birds I saw is known to God. If God does not exist, the number is indefinite, because nobody was able to take count. In this case, I saw fewer than ten birds (let’s say) and more than one; but I did not see nine, eight, seven, six, five, four, three, or two birds. I saw a number between ten and one, but not nine, eight, seven, six, five, etc. That number, as a whole number, is inconceivable; ergo, God exists. (Borges, 1970, p. 29)

Fragment of # 1171, 1987-2018 by Yamamoto Masao

Before I discuss the validity and soundness of the paragraph, I want to specify what each of those means. An argument is formally valid if it is impossible that the premises are true and the conclusion is false. So validity doesn’t guarantee the truth of the conclusion. It just means that if the premises are true, so is the conclusion. The soundness of an argument is the real test of its truth value. If the argument is sound, it is both valid and true.

If we break down the paragraph into sections, we get the following:
1. “I close my eyes and see a flock of birds.“
In this section, Borges parodies René Descartes’ third meditation but doesn’t follow him in effacing all images of corporeal things from his mind:

Claudam nunc oculos, aures obturabo, avocabo omnes sensus, imagines etiam rerum corporalium omnes vel ex cogitatione mea delebo, vel certe, quia hoc fieri vix potest, illas ut inanes et falsas nihili pendam, meque solum alloquendo, et penitius inspiciendo, meipsum paulatim mihi magis notum et familiarem reddere conabor.

I will now close my eyes, I will stop my ears, I will turn away my senses from their objects, I will even efface from my consciousness all the images of corporeal things; or at least, because this can hardly be accomplished, I will consider them as empty and false; and thus, holding converse only with myself, and closely examining my nature, I will endeavour to obtain by degrees a more intimate and familiar knowledge of myself. (Descartes, 1641/1912, p. 95)

The image is, of course, unique to Borges. No one can have the same mental image of a flock of birds. But the concept has universal resonance because anyone who engages in the argument imagines a unique flock of birds. And the validity of the proof doesn’t depend on the characteristics of some specific flock of birds. This part is a novelty for ontological arguments. St. Anselm of Canterbury, the inventor of the first and most famous ontological argument, used definitions and concepts to make his argument, not mental images (Anselm, 1078/1903).
1. “The vision lasts a second or perhaps less; I don’t know how many birds I saw.“
Borges knows that he saw several birds but doesn’t know how many. His argument is, therefore, at odds with other ontological arguments. Anselm, Descartes, Leibniz, and others don’t have space for uncertainties. The part about how long the vision lasts is crucial because there cannot be enough time to count all the birds.
1. “Were they a definite or an indefinite number?“
We know that the number of birds Borges or we as readers saw cannot be indefinite. There was a specific image we saw. If only we had that image fixed somewhere, we could look at it again and count the number. So the number of birds must have been finite.
1. “This problem involves the question of the existence of God. If God exists, the number is definite, because how many birds I saw is known to God. If God does not exist, the number is indefinite, because nobody was able to take count.“
Here we have the main argument. It assumes that the number could have been definite if and only if (iff) some sentient creature knows it. But this isn’t very convincing. No one knows about the existence of some planets, but this doesn’t mean they can’t exist. And we may find later that they exist. Similarly, maybe in 300 years, we will invent a way to go back and rewatch every thought of every human being that ever lived. Of course, if we find out that the flock Borges imagined consisted of 9 birds, this would prove that the number was always definite.
1. “In this case, I saw fewer than ten birds (let’s say) and more than one; but I did not see nine, eight, seven, six, five, four, three, or two birds. I saw a number between ten and one, but not nine, eight, seven, six, five, etc. That number, as a whole number, is inconceivable; ergo, God exists.“
Borges claims that he saw an indefinite number of birds if no one could count them. Therefore, God must exist because indefinite whole numbers between 1 and 10 cannot exist. But again, the main issue is the assumption that if no one knows how many birds I saw, then the number must be indefinite.

If we turn all this into syllogisms, we get:
- P1. If the number of birds is definite, God exists.
- P2. The number of birds is definite.
- ∴ God exists.
- P1′. If God doesn’t exist, the number of birds is indefinite.
- P2′. The number of birds cannot be indefinite.
- ∴ God exists.
The first argument is an example of affirming the antecedent (modus ponens). The second is an example of denying the consequent (modus tollens). So both are deductively valid. Here’s a formalized version to prove their validity:
- P1. p→q (if p, then q)
- P2. p
- ∴ q (therefore q)
- P1′. ¬q→¬p (if not q, then not p)
- P2′. p
- ∴ q (therefore q)
So the arguments are valid, but are they sound? It is almost always impossible to decisively prove the soundness of a philosophical argument, but I believe these arguments aren’t. And Borges would probably agree. They are not sound because premises P1 and P1′ are very dubious. As I already mentioned, the number can be definite even if no one knows it. Criticisms like this one, however, cannot be applied to the ontological arguments proposed by Anselm, Descartes, Leibniz, Gödel, Plantinga, or others because this ironic paragraph by Borges has neither the same intentions nor the same form.

References
- Anselm, St. (1903). Proslogium; Monologium: An Appendix In Behalf Of The Fool By Gaunilo; And Cur Deus Homo. (Sidney Norton Deane Trans.). The Open Court Publishing Company. https://sourcebooks.fordham.edu/basis/anselm-proslogium.asp (Original work published 1078)
- Borges, J. L. (1970). Dreamtigers. E. P. Dutton & Co., Inc.
- Borges, J. L. (1972). El hacedor. Alianza Editorial. (Original work published 1960)
- Descartes, R. (1912). A discourse on method ; Meditations on the first philosophy ; Principles of philosophy. London : Dent ; New York : Dutton. http://archive.org/details/discourseonmetho1912desc (Original work published 1641)
Flux & Paradox

October 2nd, 2022
Once in my childhood, I remember doing a quiz named “Which philosopher are you?” For whatever reason, I got Heraclitus. I tried again because, at the time, I didn’t know who he was. I wanted to get someone more famous, but I got Heraclitus again. Since then, I’ve often used “Heraclitus” as a pseudonym on various sites. Partly because of this special relationship and partly because of my continuing fascination with obscurity, this essay will be about the obscure sage of Ephesus. More specifically, I want to explore Heraclitus’ idea of flux and its relation to the Ship of Theseus.

By changing it rests. (Heraclitus, Fragment LXXXIII)

You’re probably familiar with the Ship of Theseus, but for convenience, I’ll explain the main idea: Imagine a ship restored by gradually replacing each of its constituent parts. According to Plutarch, the philosophers later debated whether the resulting ship was still the original one. Thomas Hobbes later added another difficulty to the experiment: imagine that from the old parts, we assemble another ship (Hobbes, 1656, p. 100). The two are certainly not the same, yet you could reasonably claim that either of these is the original ship. One ship is the same as the original by one set of criteria. Another one is the same as the original ship by another set of criteria. So the main questions are: At what point does the ship lose its identity? What criteria should we use for determining whether X is still X after experiencing changes? Which ship, if either, can correctly be called the same as the original one?

The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same. (Plutarch, Life of Theseus)

The Naiku building of the Ise Grand Shrine is rebuilt every 20 years.

Now let’s consider Heraclitus. His thoughts come to us, unfortunately, only in the form of fragments. But it’s common to assume that there was a coherent, continuous text in the beginning. Nietzsche questioned this assumption, but I’ll leave that debate aside. It is, therefore, the job of philosophers and historians to construct a coherent picture of Heraclitus’ doctrine. This is an extremely difficult, if not impossible, task. Primarily because of the epigrammatic and enigmatic nature of the fragments. He was often called “the obscure” for this exact reason (Brémond, 2019). His legacy is the opposite of La Bruyère’s. Where La Bruyère is today mostly ignored because of his clearness and moderation (Barthes, 1964/1972, p. 222), Heraclitus continues to arouse interest, not despite but because of his cryptic language.

Generally speaking, that which is written should be easy to read or easy to utter, which is the same thing. Now, this is not the case when there is a number of connecting particles, or when the punctuation is hard, as in the writings of Heraclitus. For it is hard, since it is uncertain to which word another belongs, whether to that which follows or that which precedes; for instance, at the beginning of his composition he says: “Of this reason [Logos] which exists always men are ignorant,” where it is uncertain whether “always” should go with “which exists” or with “are ignorant.” (Aristotle, Rhetoric, Book III, chapter 5, section 6)

At the beginning of his book, which is quoted above by Aristotle, Heraclitus speaks of the Logos (λόγος) and later tells us that in the book, he will explain how everything relates to everything else, distinguishing each thing from others. But in what follows, Heraclitus tells us, again and again, that everything is the same. So from the beginning, Heraclitus speaks paradoxically.

Today, Heraclitus is primarily known for three doctrines: (1) universal flux, (2) the unity of opposites, and (3) fire as the primary material of the world (Graham, 2021). The latter doesn’t concern me here. I will therefore focus on the former two. The interpretations of those first two doctrines are, as with any obscure writer, controversial and open to debate.

Heraclitus (1630) by Johannes Moreelse

You could not step twice into the same rivers; for other waters are ever flowing on to you. (Heraclitus, Fragment XLI)

For Heraclitus, the river has an identity even if the flowing water is always different. The Ship of Theseus retains its identity even when it is constantly changed. You are the same person you were a year ago, no matter how dramatically you’ve changed. Heraclitus makes Logos responsible for this strange harmony behind the flux and makes understanding this Logos the primary aim of his inquiry. As Hans-Georg Gadamer claims, Heraclitus didn’t just believe in flux. He was more interested in the paradox of something changing yet retaining its identity.

… the pieces, the substances, the materials change, to the point where the object is periodically new, and yet the name, i.e., the being of this object, remains always the same; it is therefore a question of systems rather than of objects … (Barthes, 1964/1972, p. 153)

Merely stating that the river has a certain unity is no proof of said unity. One way we could interpret this is to say that Heraclitus believes that the name determines identity. So if we still call it the Ship of Theseus, that’s what it is. If others see you as the same person, then you are. I suspect Wittgenstein would subscribe to this view. He would claim that there is no objective identity of things. It’s only a matter of how we use language. But it’s not clear to me whether this is what Heraclitus believes.

Into the same rivers we step and do not step; we are and we are not. (Heraclitus, Fragment LXXXI)

Heraclitus is pointing out the paradox. He’s not interested in providing a clear solution. As with any philosophical question, no one can give a conclusive answer. Expecting to find one is naive. That is not the point of Heraclitus’ book. And it’s not the point of this essay. The Ship of Theseus is still a puzzle on which philosophers don’t universally agree. Some think spatio-temporal continuity should be privileged over the concept of identity retention through change, thereby claiming that the ship assembled from the original parts has a stronger claim to being the original one. Others think the opposite. There are many elaborate arguments involving possible worlds, but I won’t get into that here (e.g., Kripke, 1980).

Let’s consider another relevant fragment from Heraclitus about the ancient Greek drink called the posset. It is a mixture of “wine, barley groats, cheese, and herbs or drugs which remain suspended only if they are continuously stirred” (MacKenzie, 1986). If you stop stirring, the solids will sink to the bottom. What you will drink won’t be the posset. So for the posset to retain its identity, it must move. Change and motion can, therefore, be a necessary condition of identity, not a hindrance to it.

The posset too separates if it be not stirred. (Heraclitus, Fragment LXXXIV)

My aim was not to provide a solution to the problem of the Ship of Theseus but to infer how Heraclitus would have answered. And I believe we can formulate the general idea in the following way: The reassembled ship is still the original one because not considering it the original ship would undermine the way we ordinarily use language. We can also claim that the newly assembled one is the original ship. Yet we must understand that even those original parts constantly change due to being in different spatio-temporal circumstances. It, therefore, makes less sense to privilege the original parts over the new ones because those have also changed. So even if we didn’t replace any parts of the ship, that ship’s identity would still be questionable. Yet, for Heraclitus, it would be the same ship, and the fact of change would not touch the question of identity.

REFERENCES
- Aristotle. (1926). Rhetoric. In Aristotle in 23 Volumes, Vol. 22 (J. H. Freese. Trans.) Harvard University Press. http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0060
- Barthes, R. (1972). Critical Essays. Northwestern University Press. (Original work published 1964)
- Brémond, M. (2019). Les Présocratiques (A). dans Maxime Kristanek (Dir.), l’Encyclopédie Philosophique. https://encyclo-philo.fr/item/190
- Graham, D. W. (2021). Heraclitus. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2021). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/sum2021/entries/heraclitus/
- Heraclitus. (1931). On the Universe (W. H. S. Jones, Trans.). Harvard University Press. https://doi.org/10.4159/DLCL.heracleitus_philospher-universe.1931
- Hobbes, T. (1656). Elements of philosophy, the first section, concerning body. London : Printed by R & W Leybourn, for Andrew Crocke, at the Green Dragon in Pauls Church-yard. http://archive.org/details/b30335838
- Kripke, S. A. (1980). Naming and Necessity. Harvard University Press.
- MacKenzie, M. M. (1986). The Moving Posset Stands Still: Heraclitus Fr. 125. The American Journal of Philology, 107(4), 542–551. https://doi.org/10.2307/295102
- Plutarch. (n.d.). Life of Theseus (John Dryden, Trans.). http://classics.mit.edu/Plutarch/theseus.html