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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?

Ameet Sharma
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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 https://youtu.be/bqGXdh6zb2k – CriglCragl Mar 03 '21 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](https://plato.stanford.edu/entries/nominalism-metaphysics/#NomAboUni) believe. – Conifold Mar 03 '21 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 06 '21 at 06:55
  • @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 06 '21 at 07:40
  • @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 06 '21 at 07:49
  • 3 separate points there. a good metaphor for the first: a null pointer is not the same as a pointer to a unaddressable memory address. The null pointer is not referring to any memory address, but the invalid pointer is referring to a memory address that isn't there. – causative Mar 06 '21 at 07:52
  • @causative "Referring to something that does not exist" strikes me as stretching "reference" along the lines of the same fallacy you mentioned, and even when it is done (e.g. by Meinong) one has to provide a non-referential interpretation to link it to the earth. Languages may well be meaningless, that is why one has to define meaning-relevant use, and in a way that does not involve "meaning" itself, or non-existent referents, like your proposal. Of course, "meaning is use" is just a motto, but IEP, SEP and loads of books elaborate on specifics at length. – Conifold Mar 06 '21 at 08:18
  • @Conifold The meaning of a noun can be considered a predicate; a function that maps an object to T or F depending on whether the object matches the condition implicit in the noun. This works regardless of whether any physically existent objects yield T for this predicate. The meaning of the noun is the function, not its argument. – causative Mar 06 '21 at 08:25
  • @Conifold the meaning of a proposition P has two sides. The upstream side is, "what would persuade us that P holds?" And the downstream side is, "what would we be persuaded of if we accept P?" For example, the meaning of "Dave is good at fishing," consists on the upstream side of whatever evidence we would accept as persuasive of Dave's fishing prowess, and on the downstream side, whatever conditions we'd believe as a result of his fishing ability. – causative Mar 06 '21 at 08:37
  • For rational people there ought to be some correspondence between the upstream meaning and the downstream meaning; we ought not make a distinction (upstream meaning) without a difference (downstream meaning). And if there is a difference (downstream meaning) we ought to make a distinction (upstream meaning). – causative Mar 06 '21 at 08:43
  • @causative Languages also have adjectives, verbs, adverbs and other parts of speech, and even referential meaning theories, like Frege's, resort to non-referential uses to cover them all. I have no objection to the upstream/downstream idea broadly speaking, it reminds me intension/extension or stereotype/reference in Putnam's vector theory of meaning (he has two more components). As long as "what we are persuaded of" is not restricted to some sort of referential correspondence to reality, otherwise large swaths of language would be left out. – Conifold Mar 07 '21 at 02:17
  • @Conifold I have given definitions only for nouns and propositions. It is possible to give similar definitions for other parts of speech and non-proposition sentences. Generally, the upstream meaning of any utterance, including a word within a sentence, consists of those beliefs, previously held, which led to the utterance. The downstream meaning corresponds to the consequences the speaker wished to result from his utterance. – causative Mar 07 '21 at 02:33
  • @Conifold the meaning of propositions is a special case of that general definition. It's easy to see how the upstream definitions correspond. For the downstream definitions, it is considered that by asserting P, the speaker wishes his listeners and himself also to believe consequences of P. Thus, the downstream definitions in both cases also match. – causative Mar 07 '21 at 02:45
  • Even for nouns your idea is problematic. A function needs a domain, if it only has existent objects then all predicates false on all of them will be indistinguishable. If you need predicates to explain the meaning of nouns you'll need higher order predicates to explain predicates, etc. I do not see why upstream definitions need to correspond since previously held beliefs need not correspond. Anyway, this comment thread is already too long. – Conifold Mar 07 '21 at 04:24

2 Answers2

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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...

Double Knot
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  • 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. https://www.webpages.uidaho.edu/ngier/309/universals.htm – Ameet Sharma Mar 03 '21 at 05:07
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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 03 '21 at 05:38
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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 ?

viuser
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armand
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  • 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 03 '21 at 08:14
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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 03 '21 at 08:27
  • Not all universally quantified mathematical statements are as simple as "all squares have 4 sides." Many theorems are quite deep and non-obvious. https://en.wikipedia.org/wiki/List_of_theorems . – causative Mar 03 '21 at 08:31
  • Thanks for porting this to our attention. Yet, it is not what we are talking about here. Have a nice day. – armand Mar 03 '21 at 08:34
  • Mathematical statements can and do say a lot about the real world, too; this is why engineers use math to determine the proportions of a bridge. They are on the one hand dealing with purely analytic truths about an idealized model or simulation of the bridge, truths which could be derived purely axiomatically from ZFC, but then they are able to convert these analytic truths to synthetic truths about how much cement to pour and so on. – causative Mar 03 '21 at 08:47
  • "the modeled bridge is stable under the modeled winds" is an analytic statement, and "the actual bridge is stable under the actual winds" is a synthetic statement, but there is certainly some relevance of the analytic statement to the synthetic one. – causative Mar 03 '21 at 08:54
  • You're right. I probably used a bad example. But I'm really more concerned with the universal itself rather than the truth-value of the statement or what the whole sentence is saying. What I'm getting at is nominalists, conceptualists etc. generally agree that the use of the word "quadrilateral" or "square" in sentences is fine, even if they don't believe in the existence of the universal "quadrilateral" or the universal "square". But as I mentioned in my reply to Double Knot, there are also "radical nominalists" that might disagree with their usage. – Ameet Sharma Mar 03 '21 at 09:06
  • @ameetsharma that's what I am pointing at here. Wether one believes in the absolute form, the platonic pure idea of The Square, or just consider the idea of square to be a generalization of vaguely square shapes we see in the real world, once you have defined squares to be figures with 4 equal sides and straight angles, your example is always true. It just *can't be false*, and anybody who disagrees with it is just confused about what the words in the statement mean. – armand Mar 03 '21 at 09:26
  • @causative every statement with numbers in it is not a mathematical statement. "The bridge is 100 meters long, 5 meters wide, 1 meter thick" tells us about the real world but is a synthetic statement with no mathematical value. "100*5*1=500" is analytical and tells us nothing about the world. With the two we can deduce that we need 500 m^3 of cement, but what tells us it is relevant to the bridge is the 1st statement, not the second. – armand Mar 03 '21 at 09:34
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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 03 '21 at 09:41
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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 03 '21 at 09:57
  • @causative: You should be careful in your use of analytic and synthetic. As soon as there is some real-world data involved that is specific to (or meant to model) a particular bridge, most uses I am aware of would state that the model itself is synthetic, even though it *obviously* allows for analytic statements that refer to (or derive their truth value from) the model and not necessarily *are*, but definitely *are meant to be* true for the actual bridge. That is what makes the difference between models of physics and models of engeneering: The former are derived from, but do not contain data – Philip Klöcking Mar 03 '21 at 11:32
  • @causative: Also, Quine did question the analytic-synthetic divide fundamentally. – Philip Klöcking Mar 03 '21 at 11:33
  • All those comment are wonderful, but without relation to the fact that "All squares are quadrilateral" is merely restating the definition of a square, which should not be controversial and was my point. – armand Mar 03 '21 at 11:37
  • @PhilipKlöcking "the real bridge is 100m long" is a synthetic statement. "In this model of the bridge, it is 100m long" is an analytic one, entirely dependent on the mathematical definition of "this model of the bridge," which may or may not have any relationship to the actual bridge, and the truth of the claim about the model does not depend on that relationship. – causative Mar 03 '21 at 22:24
  • @causative That may be your use. It is not the common one. – Philip Klöcking Mar 04 '21 at 05:55
  • @PhilipKlöcking yes it is. Analytic statements are those whose truth value does not depend on the material conditions of the world, only on the definition of the terms involved. "In this (mathematical, formal) model of the bridge, it is 100m long" does not depend on the material conditions of the world, only on the definition of the model. The actual bridge could be 200m long and the statement about the model would still be true. – causative Mar 04 '21 at 05:59
  • @causative You mix model and statement here. I said that if the model is based on real-world data, it is synthetic. Of course, synthetic models do allow for analytical statements. Like, per definition. – Philip Klöcking Mar 04 '21 at 07:41
  • @PhilipKlöcking merely being based in real-world data is neither necessary nor sufficient for a proposition to be synthetic. Use instead this definition: https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction "Analytic propositions are true or not true solely by virtue of their meaning, whereas synthetic propositions' truth, if any, derives from how their meaning relates to the world." – causative Mar 04 '21 at 07:51
  • @causative A model is not a statement. The third comment was misleading: What I was getting at is that a) **statements** are analytic/synthetic, not **models**, and b) this division is quite artificial on the bottom of it, see Quine's *Two dogmas of empiricism*. – Philip Klöcking Mar 04 '21 at 08:04