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?

  • Diogenes critique of Plato: existentialcomics.com/comic/219
    – CriglCragl
    Commented Apr 29, 2023 at 13:38
  • "most ethical principles and ideals have been shown to be human constructs" No, they haven't. Commented Apr 29, 2023 at 19:40
  • That ethical principles and ideals are human constructs is just one of modern positions, 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.
    – Conifold
    Commented Apr 29, 2023 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
    Commented May 1, 2023 at 19:43
  • 1
    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"
    – r0k1m
    Commented May 2, 2023 at 11:22

3 Answers 3


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?


One way to resolve your difficulty is to consider particulars to be real in a concrete sense and universals to represent attributes common to sets of particulars. Viewed that way, particulars are in no way dependent upon universals for their existence. Take the universal idea of a rectangle, for example. Viewed from certain directions, a brick, a laptop, an envelop etc all have in common the properties of having two pairs of parallel sides of equal length, with the members of each pair being right angles to the members of the other, ie to be rectangular. We can consider the universal idea of a rectangle to be the abstraction of those properties, which all kinds of rectangular objects have in common. The endless debates about whether rectangles 'exist' in a Platonic sense can be resolved by noting that they certainly do not exist in the way that bricks and laptops do, and therefore if you wish to attribute an 'existence' to them, then you are simply introducing a new use of the word exist, the meaning of which is the ontological status of numbers, shapes etc.


The question is a mix of multiple notions.

  1. Universals and particulars: although the idea has an historical value for the philosophical approach, it is not considered valid nowadays. The idea suggests that for an apple to exist, a sphere exists first, as a universal fact, independently of the human mind. But we know that a sphere is a geometrical fact, which is part of mathematics, which emerges as part of reason, which is the dynamic of thinking. Therefore, a sphere exists only in our heads, as a metaphysical object.

  2. "ethical principles and ideals have been shown to be human constructs", we can say this is correct: a) ideals are based on ideas, which are mental/rational judgements, and b) ethics -the study of morals, which is essentially the right behavior- (and so ethical principles) is necessarily a rational construct of judgements. However, in general, universals and particulars apply to objects, not to judgements.

  3. "universal truths lead[ing] to particular truths" implies a different problem: empirical induction. If a fact X has occurred in the past, it is not strictly proper to assume it will occur in the future (c.f. David Hume). According to C. D. Broads, Induction is the glory of science and the scandal of philosophy.

In any case, all rules are mental facts, not empirical facts (an apple falls down to the ground not due to gravity, but due to the huge, massive number of atomic/quantic interactions; gravity is our mental explanation of such phenomenon, but we don't really know the real facts out there).

Therefore, universal truths leading to particular truths is just a rational fact, which is essentially described by Logic. It has no relationship with platonic universals/particulars.

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