I'm looking for a clarification. Do philosophers generally agree that the use of statements involving universals are meaningful, even if the specific ontological status of the universal is in dispute?

For example:

"Any square has four angles."

Regardless of whether or not there is a universal "square" that exists apart from the particulars or not... seems to me that it is pretty uncontroversial that this type of sentence is meaningful. For example nominalists, platonists, conceptualists would agree this is a perfectly meaningful sentence right?

So the "use" of universals in language is accepted as valid generally by all philosophers... it's just the detail of how/why/where the universal exists that is in contention?

Or are there philosophers that would say all use of universals is invalid? (I don't know if this even makes sense, but I'm taking it to mean something like eliminativism with regards to consciousness). In other words are there philosophers that would say, "Every square is a quadrilateral." does not really make any sense as a statement, but we just play some kind of game as if it does?

So generally... it seems like philosophers can agree whether a sentence is meaningful or not, even if we don't agree what specifically the terms in the sentence refer to? ie: platonists, conceptualists, nominalists may disagree on specifically what a "square" is, but there's no problem using it in language?

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    What about a square on the surface of a sphere? Then, what about the fact we live in curved Minkowski space..? Follow the history of the philosophy of mathematics, to understand how axioms shifted from being 'self evident' assumptions, to being recognised as essential framing - anything 'true by definition', depends on the definitions. This intro is good and concise youtu.be/bqGXdh6zb2k – CriglCragl Mar 3 at 10:39
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    Meaning is use, if we play some kind of game then words have "meaning" within it. On other theories of meaning they may not have it, as positivists claimed about metaphysics, but that just amounts to rephrasing. One could say that something is meaningless only when a play does not conform to the rules, but that presupposes the rules. "Eliminativism" would probably mean that universals can be paraphrased out of the language, which is, roughly, what nominalists believe. – Conifold Mar 3 at 10:42
  • @Conifold Meaning may be derived from use, but to have meaning we specifically need to be able to say what object/event/condition a word refers to. The meaning of a word is not the same as the set of all instances in which it is used. It is possible to imagine a use of language that lacks meaning - people babbling perhaps with syntactic regularity but no content or intent. – causative Mar 6 at 6:55
  • @causative "Object/event/condition a word refers to" seems to presuppose realism and some sort of referential semantics. But even metaphysical realists are anti-realists about some discourses (e.g. fictional ones), i.e. allow meaningful words with empty referents, so "meaning" is certainly broader than referential use. I think it is broader than inferential use as well (vs what inferentialists believe). But on most use theories specifically linguistic use is delimited by some role in coordinated interaction and/or communal practice, so babbling with syntactic regularity would not count anyway. – Conifold Mar 6 at 7:40
  • @Conifold a word may refer to an object/event/condition that does not exist; that's not the same as it not referring to anything. It seems like a no-true-scotsman fallacy to just define meaningless language as not language. Anyway, simply saying "meaning is use" does not actually let you answer the question "what does word X mean?" with any level of specificity. At best it can tell you where one might look to find the meaning of X. – causative Mar 6 at 7:49

Ignoring the logical analysis of a statement or a proposition with all its predicates and qualifiers, natural language with universal concept seems the only way to communicate some epistemological ideas corresponding to some perceived truth with fellow people. Since this may be the only possible way, I don't see any controversy to make use of universals in language.

Via correspondence of truth, Eliminativism (a form of pure extreme materialism as I understand) does seem the most likely to deny the real existence of the universal concepts such as "square", "four". Since there're no two exactly same leaves in this measurable physical world, Eliminativism may even deny the existence of pure ideal numbers such as "2", "4", or a perfect "square", all these universal concepts can be "eliminated" to illusory phenomena as the perceived world only has "likeness" without "exactness". However, the Platonist on the other spectrum end will probably regard ideal forms and numbers as true ontological existence, while imperfect material world is just an imitation and reflection phenomena from the universal ideals. In philosophy you'll find all kinds of schools fit in between this spectrum, such as panpsychic rational idealism sits in the middle way...

In summary, it all depends on your own philosophical position, science cannot prove which one is the ultimate truth as long as your philosophy explains the world in a logically coherent way...For my personal take, dragging real ontology to either end of the said spectrum sounds potentially absurd and inconsistent. For example, if we only admit particulars and likenesses without any universals and exactness, then how two persons holding intrinsically always different qualia can even share a same fact or idea? We can never have any exactness under this philosophy which some eliminativists may truly believe, but modern computer SaaS apps seems clearly against such doctrine...

  • Googling.. .there does seem to be something called "radical nominalism" which seems eliminativist with regards to any generalities. But I don't understand how one can ascribe any meaning to any statement with this position. It seems to lead to a radical skepticism. I assume very few hold this position. webpages.uidaho.edu/ngier/309/universals.htm – Ameet Sharma Mar 3 at 5:07
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    Agree, a particular object still can be reduced to its molecules, atom, particles...., this leads to total skepticism. There was an argument against "non-acceptance of everything" doctrine. Ask such a person "do u accept your own "non-acceptance of everything" belief? If they accept, it means they still accept something, thus their belief is not applicable in all cases. If they don't accept, it means they effectively despise their own doctrine. So I think we can use logic at least to show people you have to "specifically" believe something, not blindly reject or accept everything uncritically. – Double Knot Mar 3 at 5:38

Be careful that all "Any..." sentences are not created equal.

Because it stems from the definition of mathematical objects, your example is trivial. The definition of a square is to be a quadrilateral with all sides equal and all angles right (some might say "at least 1 right angle" because then all the others must be right too). So "Every square is a quadrilateral" really means "Every quadrilateral with all sides equal and all angles right is a quadrilateral" which is saying... nothing, really.

In the Tractatus Logico-Philosophicus, Wittgenstein qualifies such statements to be "senseless" (sinnlos). While they have value and are valid in a logical sense, they don't say much about the real world, because as we saw they can be reworked into sentence of the type "every quadrilatere is a quadrilatere". Such a sentence just can't be false.

Contrast with "Every duck has two wings". If we define a duck to be "an animal with 2 wings", then it is true but it raises a lot of practical questions. What if I take a duck and cut one of its wings ? Is it not a duck anymore ? What if I grab a pigeon, which has 2 wings ? Why is it not a duck ?

  • Mathematical truths can be very deep and hard to see. It's a gross oversimplification to say that they are simply a restatement of your axioms. Yes, mathematical facts are a restatement of the axioms, but no, that does not mean they convey no additional or surprising information to the reader. e.g. how is the Riemann hypothesis simply a restatement of the axioms? (assuming it's true, which we don't know). – causative Mar 3 at 8:14
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    @causative I suggest you say that to Wittgenstein. I am but the messenger here. Anyway, my point is, not withstanding more complicated maths, "all squares have 4 sides" is nothing but stating the definition of a square, and therefore not a universal statement subject to philosophical controversy like "all ducks have 2 wings". – armand Mar 3 at 8:27
  • Not all universally quantified mathematical statements are as simple as "all squares have 4 sides." Many theorems are quite deep and non-obvious. en.wikipedia.org/wiki/List_of_theorems . – causative Mar 3 at 8:31
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    @armand I established the difference between the engineer's mathematical model of the bridge (analytic) and the actual bridge (synthetic). Are you arguing that statements about the mathematical model of the bridge are not analytic, or are you arguing that the mathematical model of the bridge does not relate to the actual bridge? I can't unambiguously interpret your objection in relation to my claim. – causative Mar 3 at 9:41
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    Analytic statements are tools that we use, to assist us in reasoning about the world. This is why we invented mathematics. The engineer builds an analytic model and uses it as a tool to assist his reasoning about the actual bridge. – causative Mar 3 at 9:57

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