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This is my first post on philosophy stack exchange, so I apologize in advance if this question is not well-defined or if it happens to be a duplicate. If so, feel free to link the corresponding post(s) you believe best answers my questions, and then close the current one.

Broadly speaking, my inquiries can be summarized by the following set of soft questions:

  1. How can the philosophy of time inform us about the philosophy of number and vice versa?
  2. What are some ontological / epistemological consequences which follow if one accepts there is a meaningful relationship between number and time?
  3. Are there any case studies in cognitive science, psychology, etc. which might support one set of philosophical perspectives and paradigms as more viable than others? [I understand this is a little "out-of-bounds", but it'd be interesting to know if a non-trivial intersection exists between what you might refer to as numerical cognition and that of philosophy.]

Loosely, my questions are motivated by the following:

  1. Insofar as I am aware, it appears to be an innate inclination for one to associate numbers with time. For instance, we use numbers to model time in the form of analogue and digital clocks. I don't feel like such natural associations exist by accident, but am unsure how to unite the cognitive science and philosophy in a way which addresses why this might be the case.
  2. That numbers and time are intimately related is not a new idea. From what little I understand, Kant held that our intuition of time is arithmetic. I cannot seem the find the exact quote I wished to reference, but hopefully what I stated is suggestive enough.
  3. Similarly, intuitionists hold that there is a significant relationship between time and the construction of the ordinal numbers. Quoting Brouwer:

"However weak the position of intuitionism seemed to be after this period of mathematical development, it has recovered by abandoning Kant's apriority of space but adhering the more resolutely to the apriority of time. This neo-intuitionism considers the falling apart of moments of life into qualitatively different parts, to be reunited only while remaining separated by time as the fundamental phenomenon of the human intellect, passing by abstracting from its emotional content into the fundamental phenomenon of mathematical thinking, the intuition of the bare two-oneness. This intuition of two-oneness, the basal intuition of mathematics, creates not only the numbers one and two, but also all finite ordinal numbers, inasmuch as one of the elements of the two-oneness may be thought of as a new two-oneness, which process may be repeated indefinitely; this gives rise still further to the smallest infinite ordinal number."

Any commentary, insight, or further resources / references you are able to provide would be most appreciated.

John Smith
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  • I'll try to write an answer if I get the time, but for now: (1) I'm pretty sure you are misremembering what Kant said, (2) numbers are associated with measurement, so they get indirectly associated with time when we try to measure time, and (3) There are various philosophers who insist that if you imagine a set of steps, you have to imagine them happening in time, which strikes me as simply a failure of abstract thinking on their part. – David Gudeman Nov 14 '23 at 01:34
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    What Kant says is, "Thus, number is nothing else than the unity of the synthesis of the manifold in a homogeneous intuition, by means of my generating time itself in my apprehension of the intuition." This is not quite arithmetic (and where is zero?), although the eventual theory that addition and multiplication could be reduced to compounded succession suggests that conclusion somewhat (but consider subtraction and division as part of arithmetic, of course, and matters become unclear again, here). – Kristian Berry Nov 14 '23 at 02:21
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    for 1) you should check out Brouwer and mathematical intuitionism "As did Kant, Brouwer founds mathematics on a pure intuition of time (but Brouwer rejects pure intuition of space)." https://plato.stanford.edu/entries/brouwer/#Bri – J Kusin Nov 14 '23 at 02:44
  • Numbers are one to one with the dots placed on the real line. In reality, numbers are fatter (wider. Perhaps, even wiser. Numbers, become, in one to one corrispondence to faces. Thus – Joselin Jocklingson Nov 14 '23 at 03:56
  • Thus a face has a Trinity. The number, the face, and the face. If you see the other face as a separate face, they are three. Otherwise they are two. With the Trinity they are four. – Joselin Jocklingson Nov 14 '23 at 03:57
  • No, paradigms are not there to be viable. They are there, to release: dopamine, and stress a mine – Joselin Jocklingson Nov 14 '23 at 04:00
  • I am really sorry, but the second set of 1. 2. and 3., seems to be doing something else. – Joselin Jocklingson Nov 14 '23 at 04:01
  • You might like this answer on mathematics as derived from our shared experiences of continuous symmetries: 'The Unreasonable Ineffectiveness of Mathematics in most sciences' https://philosophy.stackexchange.com/questions/92058/the-unreasonable-ineffectiveness-of-mathematics-in-most-sciences/92064#92064 Have a look in to Noether's theorem, which shows is that translational symmetry of an object through time is directly equivalent to stating, that momentum is conserved. – CriglCragl Nov 14 '23 at 12:05
  • Further to Kristian's quote: "... by means of my generating time itself in my apprehension of the intuition." This is further elucidated here : "because the self originally and in its innermost essence is time itself." Kant and the Problem of Metaphysics page 201. – Chris Degnen Feb 26 '24 at 12:04

3 Answers3

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Time is what a clock measures. A clock is a machine that does the same process over and over and moves a pointer from one entry in an ordered set without an upper bound to the next entry in the set every time it does the process. Number is useful for measurement because the set of whole numbers is an ordered set without an upper bound that can be expressed concisely, and because (expanding from the set of whole numbers to the set of real numbers) number can easily represent iterations on one clock in terms of iteration on any other clock. But in principle any ordered set without an upper bound would do.

g s
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Your question reminds me of the broader one that is often mentioned on this site, asking why the Universe can be modelled by mathematics at all. I will address point 1) in your list of motivations, as that seems, on my reading, to be the main issue underlying your question.

There are many aspects of the Universe- such as length, mass, temperature, toes, energy, direction- that have a particular property, namely that it is meaningful to quantify them. Leaving aside toes, which are a handy (excuse the pun) aid when teaching children to count, we use odometers to measure the lengths of journeys, thermometers to measure temperature, scales to measure mass, and so on. The outcomes of all of these measurements are numbers. Looking at numbers on a measuring device such as a clock is comparable to looking at them on an odometer, for example.

I would not expect, therefore, numbers to have a stronger affinity with time than with any other phenomenon with a small number of dimensions, such as space. Admittedly we check our watches more often in a day than we check our positions, but that is because our positions are immediately apparent from a quick view of our surroundings- I don't need GPS coordinates to tell me that I am at my desk. Of course, that is not always the case- on board a ship in a fog, numbers might be just as often used to answer the question 'where are we?' as 'what time is it?'.

Marco Ocram
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How can the philosophy of time inform us about the philosophy of number and vice versa?

I don't think it can: time as (the notion of) the purely dynamic, space as (the notion of) the purely static, are two orthogonal dimensions; and numbers, being "purely structural", can be said to be the most pure representative of the purely static.

Indeed, as to a properly philosophical research, just consider Heidegger's Being and Time: the problem of "time" is most fundamental and is certainly not the problem of "space". But even in Kant (whom you mention) space and time are both analytic apriori and are not the same thing.

More mundanely, Einsteinian relativity is commonly said to have put "time" on the same footing as "space", namely, to have made "time" into another "spatial dimension": but even that is debatable, as one thing is coordinate time, another is proper time...

Rather, all mathematical problems are spatial problems, indeed along the lines of numbers are "spatial", and so are all problems once mathematized.

Insofar as I am aware, it appears to be an innate inclination for one to associate numbers with time.

No, innate would be counting, which is about numbers: distinguishing then counting, e.g. sheep, or enemies... Counting (measuring) time comes quite later, and itself goes with the development of mathematics (and technology).

Julio Di Egidio -- inactive
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