Would the absence of universals not make it impossible to make and/or express judgments?

Question

Predication is an integral part of making a judgement, which is expressed in propositions (such as 'the sun is round'). Predication itself is possible because in some sense something can be said of something else. But this is only possible because something above or distinct in thought from any particular subject can come to be instantiated in a particular subject; that is to say, a universal, not being limited to any particular concrete instance, can be predicated of a subject(s). Thus in our example 'roundness' is predicated of the particular subject 'the sun'. Roundness is considered to be universal at least in some respect in that where the sun can only be said of thing (namely itself), roundness can be said of many.

If we reject such an argument, does this not alter our logic also? It might be best to clarify the question using our example of the sun. The traditional view of the proposition "the sun is round" is that the universal 'roundness' is being predicated of the particular subject 'the sun'. But rejecting the notion that 'roundness' is universal would thus seem to either result in rejecting that 'roundness' is said of many things (although granting that it is said of one thing) or to reject that there is a distinction between 'roundness' and 'the sun'. The first option seems very hard to uphold. For if we allow that some concept of roundness is said of one thing, why should we not hold that it is said of many things. It is by the same logic and inference that we arrive at the conclusion that roundness is said of one thing that we arrive at the conclusion that is said of any other thing it might be thought to be said of. This leaves the second option, which seems to be the far more ambitious but also the far more clear requirement for rejecting universals; that is to reject the distinction between 'roundness' and 'the sun'.

Accompanying this effort seems to be the evidence of perception; in perceiving the sun we do not perceive of its roundness independent of its own being. Instead, in our mental image of the sun, 'roundness' and 'the sun' are inseparable. Thus, our original statement might be converted from "the sun is round" to "the round sun". But in itself, this is not constituent of a judgement. It is only rather a subject, that does not inform us of its validity or truthfulness. One could attempt to formulate a new proposition by adding another predicate as follows: "the round sun is a fact". But this itself seems to face the same problems, namely that the predicate 'fact' would seem to be a universal, since 'the round sun' is not the only thing that can be factual. Furthermore, if the only predicate were 'fact' this seems to have the adverse effect of making propositions ambiguous. For example, in saying "the round sun is a fact" it is unclear what is being affirmed. This is perhaps more clear in negative propositions: "the round sun is not a fact". What is not a fact about such a proposition? That there is no sun or that there is no round sun?

In any case, it seems that universals are both unavoidable in terms of their necessity in making a judgement and in clarifying what is meant by a judgement. But is this correct? Does the absence of universals in some sense result inevitably in the impossibility of judgments?

Answer 1

Wittgenstein's notion of the language-game gives a credible alternative more in-line with the observed data. He characterizes informational interactions as a game, the rules of which are negotiated by the players and learned by new arrivals. We can agree the sun is round because we have learned what people mean by round, not because roundness is natural to human beings. Therefore it is not really universal, there may be tiny children somewhere whose notion of roundness is incompletely developed. They just have so little leverage on the game as a whole that we can ignore them until they adapt to the general experience and correct their notion of the label.

There are observations that are universal in an objective sense, and always remain that way, but that is only because the humans not holding them do not get purchase on the game. In your example of 'the round sun', the definition does not change, because learning it early and precisely pays off too well.

And even the game itself, or the notion of a game and how it is played, is not necessarily a universal. There are humans born who are too autistic to 'get' how to enter any existing game. But it is widespread enough that we simply declare those people defective and run civilization as if they did not exist.

(I don't think it is coincidental that descriptions of the people who give us the best models in this domain often suggest they are partially autistic. This includes Wittgenstein himself and also Alan Turing. People who are not a little 'Aspey' simply swim in the game as fish in water. They just don't ask 'What do you mean by an idea?' 'Why can one person make another person think something?' or 'What does it mean to figure something out?' without some prompting. They don't believe the game exists because they are used to thinking of it as reality.)

The other formulation of this same idea is Lacan's observation that 'master signifiers' are empty. Anything important to human beings is folded up into layers of references, and the references seem to point back to a single basis. But if you carefully unfold the references, you find that humans do not in fact really share what seems to be shared in the ultimate definition. We don't all really agree on exactly which more or less ovoid shapes are round. The place where each of us puts the cutoff differs, and in the end, the number of people who exactly agree on a precise and complete definition of roundness is going to be zero.

Both of these viewpoints lead us to a notion of logic that is less realist and more psychological. We can make and express judgements because the psychological effects on other people are well-predicted by their investment in the game (or in the hierarchy of signification.) And we can judge the physical world by seeing what psychological models of it do and don't lead to success.

We cannot actually make judgements, in the sense we would like, only predictions. There are no facts, only the power to safely presume which actions will be safe and effective. We all hold that power to different degrees, dependent upon our grasp of and leverage over the rules of the games we take part in, and we have an internal model that we leverage to do this, but it is not one that is ever completely shared outside ourselves. (Or, if we don't have a model, we lack leverage on the game, and we are not effective.)

Classical logic is a lovely model of what we (or at least those with the power to be 'we') wish language were like. By explicitly learning it, we can better negotiate the game. But it is an incomplete model with idealized elements that simply do not refer to anything. The gain is in the coordination of information exchange, and not in describing reality. Reality is better described in a piecemeal and fluid manner.

Answer 2

Roundness can be given a definition, so let’s be explicit. If, for any object, there is a (sufficient*) set of points at that object’s edge which all (1) lie equidistant from one point within the object, and (2) lie alongside one another, then with respect to that one point within the object, it exhibits roundness.

Now I first have to point out that the usual notion of judgment, while it would apply to the question of what counts as "sufficient*" in the definition of roundness, wouldn’t normally apply to any object which exhibits full sphericality like Sol does. It’s intrinsic to the definition that a perfect sphere exhibits roundness; by extension, it should be obvious that this applies to any elliptoid as well (as it must still be round in at least one plane). So most any object which obviously exhibits roundness in this manner does so via the definition of roundness. Perception alone is sufficient to tell us that the Sun is round with no judgement on our part. We would have to perceive a different object, or have a different definition for roundness, in order to be mistaken. Judgment traditionally allows that we can be mistaken, based on the facts we have available to us, not based upon the facts themselves. So the first issue here is captured by your first premise: we cannot confidently say that "predication is an integral part of making a judgment" insofar as your example goes. Can we find a better example, which supports this premise? Are there any counterexamples?

Let’s leave answering these to the side, for a moment, and address this concept of universals you’ve constructed. The language you’ve chosen is a bit confusing, because in symbolic logic, which goes well beyond propositional logic, ’universals’ are an operator, denoted by an upside-down uppercase A. They work by applying some simple predicate (such as ’round’, ’blue’, or ’guilty’) to a variable. A symbolic logic sentence such as ∀x(Px) means Px is true for all x. To say that ’roundness’ is a universal would thus normally indicate that ’all things are round’, despite that this clearly goes against your intentions.

Universals, (a.k.a. universal quantifiers) have their opposite number: the Existential operator, ∃. In contrast to the universal quantifier, a logic sentence ∃x(Px) means there is at least one x such that Px is true. Now this we can certainly say is true of ’roundness’ and the like. However, keep in mind that the way this works is because of the status of x as a variable, and the way that predicates are supposed to work. Predicates in logic are not facts, but descriptions; nor are they propositions in their own right. Variables are anything that can be described, but only if they are quantified universally. When quantified existentially, they are something which can be described.

If all this seems a little fast, apologies. I’m attempting to summarize two semesters of university logic (which I’d recommend, by the way) into two paragraphs. It hopefully hasn’t yet distracted from the point, which is that the concept of predication as you’ve expressed it in your question, is crippled by these assumptions: (1) that facts can be predicates; (2) that predicates can be propositions; and finally (3) that judgement requires the qualities expressed by a proposition to exist. That is to say with respect to 1, you equate "x is a fact" with a proposition, because it fits the syntactic form of a proposition despite having no quality to express. A fact is simply a propositional statement, or predicate statement which is true. So "x is a fact" is only true if "x" is indeed a fact. There is nothing which makes this true, outside of the statement itself, and so it actually expresses nothing. As a predicate however, this may be slightly informative: let Fx be "x is true". Then it is certainly not the case that F is a universal predicate— some statements are false. So 2 is as well a false assumption.

So back to the first point. Are there better examples than "roundness" or counterexamples? Try the proposition "unicorns are imaginary". If you take ’imaginary’ as predicative of unicorns, then it would be easier to apply this to judgment: given any example of a unicorn existing as it does in our imagination, the proposition would be false, making the truth of this statement subject to inductive judgment in the traditional sense. We judge that unicorns are imaginary because we have no facts available to contradict the claim, not because of the definition of the predicate.

I certainly can’t think of any counterexamples. But perhaps this is because what you’re asking answers itself. The way you’ve laid out your concept of "universals" in your question, is (apparently) the same as predicates in the way I’ve tried to define them here— as descriptions which beg for quantification over some set of objects.

Now, perhaps you mean something different than this. Yet this seems to be the only way to read you. So if I’ve understand you correctly, then the answer to your question is "yes". Predicates are descriptions, and fundamental to judgment is deciding whether some description applies to some object, event, concept, or person. In point of fact, that is all what judgment is. Were we to have no descriptions, then by definition we would be unable to form judgments.

Or any thoughts at all, for that matter.

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As a final point I note that you may be thinking in terms of descriptions as "existing" in their own right, and that what you’re really after, is whether the fact that we can form judgments at all is evidence that they do. That’s a litte beyond the scope of .SE, and it can be argued either way. It depends, I suppose, on what your definition of ’is’ is. You might start by asking whether numbers exist. It would be closely related to your question, and there is a wealth of debate on the subject.