Is there a philosophy of the infinitely small?

Does anyone apply it to qualitative experience, and ask if that is divided up into instants?

It seems to me that the infinitely small could not be like something, but I can think of no conclusive reason to suppose that it cannot be like something.

  • Check this out. The question you asked is quite deep. plato.stanford.edu/entries/continuity – user4894 Aug 24 '14 at 1:27
  • is there an answer in all that :-) ? – user6917 Aug 24 '14 at 1:38
  • Nobody knows whether spacetime is ultimately discrete or continuous. It's an open question, and not likely to be resolved any time soon. There's a bounty of a Nobel prize for answering it! Here's another link I found. physics.stackexchange.com/questions/35674/is-time-continuous – user4894 Aug 24 '14 at 2:05
  • i mean the experience of time... points are probably invisible, is this provable PLUS time too? – user6917 Aug 24 '14 at 2:58
  • Why does it seem that way to you? What basis do you have for supposing that not being able to think of a reason implies that there is no reason? – ben rudgers Aug 24 '14 at 19:30

A brief philosophical analysis of the present moment is given by H.Bergson in Matter and Memory. He tried to prove that the infinitesimally small time moment of our internal life is rather an ideal construct, which does not correspond to the present that we experience. His objective was to demonstrate that the present is indivisibly entangled with the past and should be associated not with a time point but with a time interval.

One can argue, indeed, that in order to perceive a light, which is the wave with periods in space and time, our sensory receptors need some time span. If we see the color at one instant, this means that this instant is de facto an interval of time.

  • thanks !!! was bergson an immortalist ? AND any critical survey if he was right about time? – user6917 Aug 25 '14 at 22:39
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    There are some books on this subject, they discuss its influence; maybe they can be helpful. Jimena Canales, A tenth of a second. A history Milic Capek, Bergson And Modern Physics. A Reinterpretation And Re-Evaluation Jon E. Roeckelein, The Concept of Time in Psychology: A Resource Book and Annotated Bibliography As for the immortalism - perhaps, yes, it is so; however, he, apparently, could not argue satisfactorily in favor of this idea and spoke very carefully. There are some passages in his Mind-Energy. – Gelato di Cræma Aug 26 '14 at 23:40
  • Isn't this also related to Kants transcendental apperception? – Mozibur Ullah Aug 30 '14 at 13:13

In physics it's called Planck Time. It is theoretically the smallest possible measurement of time, since no change could possibly be observed beyond this measure.


However when it comes to length? Well, zoom in on the graph of a function, call it f(x), you could zoom in forever and never find a point where you couldn't zoom further. So for that reason, in math anyway, you examine something called a 'limit'. You can't just zoom in forever, or move x towards c forever, so you examine the limit as x->c.

There's also something called the Planck Length


Which is very very very small. So small that we couldn't even measure it. So we don't really know if it's possible to measure anything smaller. We do know however, at these sizes, the laws of physics get very weird. This is the world of the quantum. Interesting stuff!

  • That's true about the theories of physics. But you've said nothing about the true nature of reality. The Planck time is the shortest possible measurement. But that doesn't tell us whether time itself is continuous or discrete. You are mistaking the map for the territory. – user4894 Aug 24 '14 at 3:45
  • Well he asked about the unit, which would be the planck unit. If we want to wax about whether time is discrete or continuous? I would argue the later, and I would use my example of a mathematical function to support that argument. Good point though :D – Scuba Steve Aug 24 '14 at 3:48
  • And furthermore, whether or not there's a discrete 'unit', there isn't. However you can sorta fake it with limits, which is why math is awesome. – Scuba Steve Aug 24 '14 at 3:49
  • The Planck time is not infinitely small. It has a finite value, which you'll find in the linked Wikipedia article. – celtschk Aug 24 '14 at 9:48
  • After which point you cannot physically measure anything smaller because the light would appear to be in both places at once. – Scuba Steve Aug 24 '14 at 13:49

Democritus theorised atoms as the infinitely small & indivisible parts of matter; mathematically we tend to think them of points; physically not so; Aristotle agreed with this - he was against the possibility of the infinitely small being points; since points need to cohere somehow they must have extension; in mathematics where we do have points this cohesion is provided by topology.

Democritus claimed everything was made of atoms; but his theory of the perception of light strangely went against this dictum; he theorised infinitely thin films - eidolon - carry the image being seen and enter the eye; this sounds bizarre but isn't in fact far from wavefronts entering an eye; Newton when he read of Democritus's theory in Lucretious's De Rerum Natura corrected this discrepency by inventing the notion of light corpuscules.

In general, qualitative terms the atomic theory saturates the modern outlook in physics, mathematics, economics and the Anglo-American tradition of philosophy; where they go under the name of atomic theory of matter (classical) & the quanta of energy (Planck), the analytic theory of sets (Georg Cantor), the rational self-interested actor of classical economics (Adam Smith) and logical atomism (Wittgenstein); this side of modern thinking is also called reductonism.

Does anyone apply it to qualitative experience, and ask if that is divided up into instants?

All of the above isn't really applicable to qualitative experience; as experience requires the self; Kant, however, does have a theory how experience is synthesised from intuitions (qualia); though this isn't theorised as infinitely small - it is qualitively so - along the lines that de Craema pointed out.

It seems to me that the infinitely small could not be like something, but I can think of no conclusive reason to suppose that it cannot be like something.

If the infinitely small was also infinitesimal there are arguments first marshalled by Aristotle that this cannot be possible; cohesion is required, thus for a time like thing we need duration, and for a spacelike thing we need extension; though it is perhaps a little strange it is possible to have an infinitely small, but not infinitesimal 'object'; and this can be demonstrated quite rigourously by whats called synthetic geometry.

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