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Tuesday, December 12, 2006

Abstract objects

“I think it would help if you explained how you distinguish between ‘objective’ and ‘subjective’. You don’t possess, for instance, cognitive access to ‘transcendental universals’, do you?”

Yes, I do possess cognitive access to abstract universals. So do you.

“You believe in them because you have faith, not because you can prove them (as logically necessary) or even define them completely, right?”

i)No, I don’t believe them because I have faith. I believe them because abstract objects supply certain truth-conditions, without which reason would be impossible.

ii)It also depends on what you mean by “proof.” The proof would consist in the fact that:

a)We couldn’t reason apart from abstract universals.

b)There is no alternative to abstract universals.

There are sophisticated arguments for this position, viz.

Bob Hale, Abstract Objects (Oxford: Blackwell, 1987).

Jerrold Katz, Realistic Rationalism (MIT Press, 1998).

Crispin Wright, Frege’s Conception of Numbers as Objects (Aberdeen University Press, 1983).

“Your access to them, like anyone’s, is limited by your finiteness.”

Limited access and inaccessibility are two different things. You’re confusing a mode of knowledge with a mode of subsistence. The fact that abstract universals subsist apart from human cognition doesn’t mean they can’t be exemplified in nature or the mind of man, as objects of knowledge.

“This actually makes sense to me and I believe it is very mainstream among Christians.”

I doubt that most Christians have given serious consideration to the issue.

“You wouldn’t say you KNOW “transcendental universals” are true. You’d say you BELIEVE they are true, right?”

Wrong.

“If you KNOW they are true, then faith would be superfluous.”

Superfluous for what? What do you think is the function of faith?

In Scripture, faith does not stand in contrast to knowledge. Rather:

i)Faith is contrasted with works,

and:

ii)Faith is contrasted with sight.

In Scripture, the distinction between faith and sight is the difference between knowledge by description and knowledge by acquaintance.

A Christian has faith in divine revelation. But revelation is a source of knowledge.

“To my mind, if you are absolutely certain that they are true, but you can’t prove it, then something subjective is in play.”

The question at issue is not whether there is a subjective dimension to human cognition, but whether all of human cognition is purely subjective.

“First, why is it a slippery slope to relativism to say we are all, Christian or not, subjective in our most basic beliefs?”

Unless our beliefs correspond to a factual state of affairs, we are condemned to sheer relativism.

“What I can offer is a description of MY state of mind, and not KNOWING that certain things (universals) are objectively out there IS my state of mind.”

In this very statement you are asserting something to be the case—with respect to your own mental states. This is a truth-claim.

But a truth-claim is predicated on certain truth-conditions. Without certain extramental abstract objects (like logic), which are exemplified in the human mind, and supply the objective standard of logical or illogical reasoning, you are in no position to make a factual statement about your mental states.

“Faith is the only way to bridge the gap.”

In Scripture, faith is not a makeweight or stopgap.

“And when faith happens, I don’t expect to be able to give a full accounting for it; hence, the appeal to subjectivity.”

True, but irrelevant to arguments for the existence of abstract universals or their ontological dependence on God.

Faith has an indispensable role in Christian theology and experience, but you are assigning it the wrong role.

“Any presumed alternative (outside formal demonstration) will sneak subjectivity in through the back door.”

One of your tacit assumptions here is that human reasoning is an autonomous process. But if God created the human mind, and designed our minds to be preadapted to the external world, then it’s a mistake to set up a dichotomy between subjectivity and objectivity.

If you deny that, then you are, indeed, condemned to global scepticism. But since that is self-refuting, the nugatory consequence is, itself, a reason to believe in divine creation.

“If you’re claiming that you have an objective basis for your beliefs but arguing for that position with water tight, mathematical rigor is out of the question, then in what are you grounding your claim to objectivity that can, itself, be objectively grounded? How do you avoid infinite regress?”

How would an exemplar/exemplum relation lead to an infinite regress? That’s a two-term relation.

To say that human minds (or the external world) concretely instance abstract universals doesn’t automatically generate an infinite regress, does it?

6 comments:

  1. Realism is one alternative of many to "account for" abstract universals (which must be reworded by some theories, viz tropes).

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  2. Interesting post, Steve.

    This series of threads touch on moral and epistemic relativism here and there, but I'm wondering if you have any articles that address relativism directly? I ask because it can sometimes be a more complex view than people assume.

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  3. TURN OR BURN, HERETIC SCUM!!!

    "He is the Reason for the Season!"

    - Calvin

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  4. "Anonymous said...
    TURN OR BURN, HERETIC SCUM!!!"


    I can just imagine you sitting there in your tweed jacket, wearing a trilby, and guffawing into your beard:

    HAW HAW HAW HAW HAW HAW

    Every now and then slapping your knee in joy at your achievement:

    HAW HAW HAW HAW HAW HAW HAW HAW
    HAW HAW HAW HAW HAW HAW HAW
    HAW HAW HAW HAW HAW HAW HAW HAW
    HAW HAW HAW HAW HAW HAW HAW

    "I'm a comedy genius -guffaw- I'm on fire today -hawww- I need a glass of water I've been laughing so hard" You pour yourself a drink and wipe your face with one of your hairy hands. "Haw Haw, wait till I tell someone about this -hee hee haw haw- I'm the greatest man who has ever lived HAW HAW"

    A bit too close to the bone?

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  5. Steve,

    Out with it then! Is faith a subjective exercise or not?

    -Touchstone

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  6. ---
    Yes, I do possess cognitive access to abstract universals. So do you.
    ---

    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.

    ---
    There are sophisticated arguments for this position
    ---

    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.

    ---
    The question at issue is not whether there is a subjective dimension to human cognition, but whether all of human cognition is purely subjective.
    ---

    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).

    ---
    But a truth-claim is predicated on certain truth-conditions. Without certain extramental abstract objects (like logic), which are exemplified in the human mind, and supply the objective standard of logical or illogical reasoning, you are in no position to make a factual statement about your mental states.
    ---

    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).

    ---
    One of your tacit assumptions here is that human reasoning is an autonomous process. But if God created the human mind, and designed our minds to be preadapted to the external world, then it’s a mistake to set up a dichotomy between subjectivity and objectivity.
    ---

    The Christian has faith in something he considers to be the case (objectively true). The Muslim, in contrast, has faith in something the Christian believes is not the case. The believer isn’t denying what is objectively true by claiming his orientation to it is subjective.

    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).

    ---
    If you deny that, then you are, indeed, condemned to global scepticism. But since that is self-refuting, the nugatory consequence is, itself, a reason to believe in divine creation.
    ---

    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. 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?

    ---
    How would an exemplar/exemplum relation lead to an infinite regress? That’s a two-term relation.

    To say that human minds (or the external world) concretely instance abstract universals doesn’t automatically generate an infinite regress, does it?
    ---

    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.

    Andrew

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