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Disclaimer: I have not read philosophy outside of limited Greek works

So, Plato theorized that there was a world of "universals" and "particulars", the world of general principles (mathematical and philosophical) which are not limited by time and space, and the specific, which is subject to changes and place. However, most ethical principles and ideals have been shown to be human constructs. The only true "forms" left behind seem to be mathematical truths and general logical principles (such as that of noncontradiction). These are less "objects" and more relationships, with no specific subject mentioned. This makes sense, as it would seem to me that any universal object would be indistinguishable from a relationship, as it would be universal across all time and space, so we would not have anything to compare it to; we would not be able to extract the "object" and see only the universal relations proceeding from it.

This seems to lead to a paradox. How can the "specific" exist when any universal objects said to justify it are indistinguishable from relations?

Ludwig V
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Dusty574
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  • Diogenes critique of Plato: https://existentialcomics.com/comic/219 – CriglCragl Apr 29 '23 at 13:38
  • "most ethical principles and ideals have been shown to be human constructs" No, they haven't. – David Gudeman Apr 29 '23 at 19:40
  • That ethical principles and ideals are human constructs is just one of modern positions, [moral realism](https://plato.stanford.edu/entries/moral-realism/) is opposed to it and quite popular. But if one is a constructivist it is strange to try to reconcile that with universal platonism. Why not just treat mathematical relations as human constructs as well? And even if one is accepting *mathematical* platonism, they are free to treat the rest of ontology independently. This said, philosophers do propose relational ontologies, e.g. [Benjamin's](https://www.jstor.org/stable/26563906). – Conifold Apr 29 '23 at 21:11
  • Relations can be objects. In ancient Greek geometry, line segments or the edges of geometrical shapes were not strictly numbers, but rather taken as ratios and proportions, which are about relations. In Medieval Arabic mathematics, side lengths and ratios were shown to be expressible as numbers. (I know this sounds like it conflicts with the Pythagorean Theorem known the Greeks or Pythag's "all is number" but their geometry was dominated by ratio and proportion). This development in mathematics might provide wider philosophical insight – J Kusin May 01 '23 at 19:43
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    Just in general, universal truths such as "all green things are coloured" lead to particular truths such as "this green ball is coloured" since the premiss "this green ball is green" combined with the universal premiss "all green things are coloured" produced the particular conclusion that "this green ball is coloured" – Richard Bamford May 02 '23 at 11:22

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What you are asking is the medieval problem of universals, see also SEP, IEP. And there is still very much a live debate in philosophy descended from it, about the status of mathematics, with modern Mathematical-Platonists like Max Tegmark arguing that math is 'more real' than ordinary existing things, in his book The Mathematical Universe.

But this is metaphysics, and most scientists just refuse to engage in this topic, seeing it as basically meaningless. You can interpret the 'transferability' of mathematical truths, their apparent universality, as like the way a piece of computer code is independent of specific microchips, yet still requires microchips to be run; that is, the code has 'substrate independence'. From a physicalist-materialist perspective, it comes down to what you can observe, and universals seperate from instantiation, cannot be observed, so are not part of science.

We can understand abstraction, finding what things have in common, as being about organising our experiences so that we can make simple enough models of the world that they can run on the lump of meat in our heads.

Some related discusions:

Plato's Forms and Determinism

Seeking Help on Cartesian Dualism and the Mind-Body Relationship

The Unreasonable Ineffectiveness of Mathematics in most sciences

According to the major theories of concepts, where do meanings come from?

CriglCragl
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