Wednesday, December 13, 2006

Abstract universals

“How do I even know what an abstract universal is? When do I know I have it? I can’t argue for them from first principles and they aren’t self-evident, and yet you claim it is incoherent not to just accept them. Incoherent by what measuring stick? If their necessity can’t be formally demonstrated, what other *objective* mode of knowledge informs me of their reality in the absence of *direct* knowledge? All that is left are subjective appeals, it seems to me.”

i) Perhaps we should begin with a description. By abstract objects I mean things like properties, propositions, logical laws, mathematical truths, and possible worlds.

ii) Now, maybe not all of these count as truth-conditions, but some of them do.

You certainly know what logic is, because you’re using logic to ask what logic is (or isn’t).

ii) You know when you have it by using it. It’s part of your consciousness.

iii) You’re operating within the framework of classical foundationalism. Even within that straightjacket, some abstract universals are self-evident, such as laws of logic.

iv) You don’t need to directly prove a truth-condition, for a truth-condition is a necessary precondition for proving anything else. And that, in turn, is an indirect way of proving a truth-condition. You can’t do without it.

v) Whether or not we enjoy direct knowledge of truth-conditions depends, I suppose, on our theory of knowledge. If you’re a radical empiricist, then it’s more difficult to get from here to there.

But I would say that we do enjoy direct knowledge of certain truth-conditions. We enjoy an innate knowledge of informal logic, counterfactuals (i.e. possible worlds), numerical relations, &c.

“All the arguments I’ve seen make appeals to human intuition. They aren’t formal demonstrations. A subjective element always creeps in, or propositions are merely asserted. That just doesn’t help me…. I have what I’d call intuition about universals too, but I’m holding out for something much more formal than what realist philosophers seem to offer.”

Formal demonstration is no substitute for intuition. Andrew Wiles can write a 200 page proof of Fermat’s Theorem, but at the end of the day his colleagues can only intuit that his proof his compelling.

Formal demonstration can’t go on forever. It still depends on bedrock intuition to perceive the soundness of the demonstration. However technical, it comes down to intuition.

“The problem is *objectively* showing the distinctions between objective and subjective aspects of human cognition. It hasn’t been done, as far as I’m concerned. Not saying it can’t, but if it can, it will be via strict formalism (that is the only way I can see, at least).”

No, it needn’t be by strict formalism (see above).

“I simply reject the notion that I can’t make a factual statement about my mental state. Knowledge of *my* mental state is my paradigm for certainty. I *know* I exist. I *know* I have objects of experience. I *know* logic works. Factuality is a notion that I, in a sense, bring to the table. Without the fact of *my* mental state already intact as absolutely true before even considering a statement like “you are in no position to make a factual statement about your mental states” I’d… well, I’d not exist (or at least I can’t imagine how I could).”

i) I don’t deny that it’s possible to make factual claims about your mental states. What I deny is that it’s coherent to do so if you deny or doubt the reality of abstract universals like logic.

ii) Logic cannot be normative it if is merely descriptive of your mental state. Hence, solipsism is self-refuting.

iii) Apart from logic, you cannot “know” your mental states, for true belief is a necessary condition of knowledge, but apart from logic, truth is meaningless.

iv) Even on its own level, the problem with the Cartesian cogito is that it only applies to your present state of mind. It doesn’t warrant the belief that you existed five minutes ago.

“I must have *subjective* access to unconceptualized reality (which is what abstract universals are). I’d consider it impossible by definition to have objective access. If we *can* have objective access, I’d like to know how (in that case I’d stop calling abstract universals unconceptualized).”

i) I deny that there is any such thing as unconceptualized reality. And I deny that this is what abstract universals are.

ii) I would say that all of reality is conceptualized by God. This extends to truths of fact as well as truths of reason.

iii) Truths of reason are constituted by the timeless mind of God.

iv) Truths of fact are constituted by the omnipotent will of God.

v) A true belief is true by virtue of its correspondence to a divine belief. That is what makes my belief true (or false, as the case may be).

vi) You continue to confuse the mode of knowledge with the object of knowledge. Your mode of knowledge is subjective. This doesn’t mean the object of knowledge must also be subjective.

The question is whether your subjective belief is a true belief. If true, it is true because it corresponds to an objective state of affairs.

We can make a partial exception for mental states, which are self-presenting states. There the distinction between subject and objective thins out—although God retains an objective knowledge of our mental states.

vii) Abstract universals are mental entities. Thoughts, concepts, ideas. They are extramental in relation to the human thinker, but they are mental properties of the divine thinker.

viii) At the same time, the human thinker can know them to some degree. Abstract objects are not ontologically dependent on human cognition, but their concrete exemplifications are, to some degree, dependent on human cognition.

I can have an idea of the Mandelbrot set. A finite concept which is accurate as far as it goes.

“Not *knowing* what is the case is not ‘global skepticism’, in my view. It is a statement of what is factual for me. This doesn’t preclude belief (in ‘abstract universals ‘, for instance) on my part; it just constrains how I’ll talk about my belief.”

Sorry, but if it doesn’t count as knowledge, then it doesn’t count as fact.

If belief invariably falls short of knowledge, then that’s a recipe for global scepticism.

“But you say belief can’t be justified axiomatically and then claim that not to believe as you do is incoherent. How can this be? Incoherence is a *formal* notion, but that will not work for you, by your own admission. So, again, what is left but to appeal to subjectivity?”

You’re confusing a premise with a truth-condition. Invalidity is a formal notion. But the possibility of invalidity is a truth-conditional notion, not a formal notion.

“Infinite regress is in play when talk of universal abstractions is encoded in a non universal framework, which is what ordinary language is. How can non universal descriptors arrive at a *universal* description of abstract universals? The statement “human minds (or the external world) concretely instance abstract universals” leads to infinite regress as soon as you attempt argue for its status as an *objective* truth versus being something you *believe* is true.”

i) The scope of the descriptor doesn’t have to be conterminous with the scope of the universal. It only needs to be accurate or consistent, without being exhaustive.

ii) I don’t believe that we *arrive* at abstract universals via a process abstraction. I don’t use *abstract* in the Aristotelian sense of a psychological process of learning.

You’re assuming a bottom-up procedure rather than a top-down procedure.

Unless we enjoyed an innate capacity to classify property-instances as natural kinds or concrete exempla, the process of forming generalities would never get off the ground.

iii) There’s also a major different between Platonic realism and Christian Platonism.

As Leibniz would say, God has a complete concept of every creature. Not a general idea which the creature merely approximates. So Christian Platonism doesn’t generate the Third Man problem, involving a hiatus between abstract universals and infimae species.

iv) More fundamentally, I reject your philosophical method. I respect the fact that you take philosophy seriously. And I respect your quest for certainty.

But I think you’re looking at the issue through the wrong end of the telescope. You’re approaching this from the criterion of Cartesian doubt. But I reject the presumption. And I’d draw some distinctions:

a) There are truth-conditions we cannot deny on pain of self-refutation.

b) There are also some beliefs like our belief in other minds, the external world, the reality of the past, &c. which we may or may not be able to prove—or prove directly.

These in turn, rest on perceptual beliefs or mnemonic beliefs. Is there a noncircular proof for the reliability of the senses? Or our memories?

But even if these beliefs are unprovable, they are also irrepressible. We may pretend to doubt them, but such doubts are paper doubts. We can’t help believing in other minds, the external world, the reality of the past, &c.

That being so, why should the onus be on you and me to prove something that no one can bring himself to disbelieve?

c) It may be a good question to ask why we believe it. Why such a belief is universal and irresistible. But it’s quite artificial to shift the burden of proof to the other side when there is no other side.

In this respect, I favor the Reidian point of departure over the Cartesian point of departure.

d) Likewise, I prefer to begin with knowledge rather than doubt, and work back from knowledge to its necessary truth-conditions.

Yes, you can start where Quine starts, with referential opacity or the indeterminacy of translation—but why start there? Quine couldn’t even communicate the thesis indeterminacy of translation or referential opacity unless successful communication were possible.

So it’s better to ask what makes successful communication possible rather than fretting over objections thereto.

Likewise, we can tie ourselves in knots over the paradox of analysis. But as a practical matter we are quite able to identify or differentiate natural kinds even if we have no conscious, exacting, ready-made, criterion for telling cats from dogs.

So instead of commencing with a theory of analogical predication, in which we insist on isolating a point of identity between A and B—without which the comparison degenerates into equivocation—why not begin with our successful identification of natural kinds, and work back from that to ask what makes it possible?

Therefore, I prefer a Reidian presumption along with a transcendental method.


  1. Thought provoking as always, Steve. Thank you.

    Rather than add yet another layer of qualifications and distinctions to my original thesis, I think I’ll let your’s be the last word. I’ll chew some more on what you’ve said then maybe read-up on Christian Platonism. I’d welcome your recommendations.



    Robert Adams, ‘God, Possibility, and Kant,’ Faith and Philosophy vol. 17, no. 4, October 2000, pp. 425-440.

    Brian Leftow, Divine Ideas, Cornell University Press, (forthcoming).

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