On an alleged counterexample to Leibniz’s Law – Part 2 (Dale)

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In his comment on my previous post, Brandon points out that he doesn’t assert the case described there to be a counterexample. Rather, he was wondering why it isn’t a counterexample; he was probing to see my response.

Fair enough. I’ve left the title of the post as is just for continuity with part 1.

The case Brandon described, was an omniscient God, who is both subject and object of knowledge of himself. God as knower is subject of knowledge but not object. But God as object is what is known, and not the subject of knowledge. So, don’t we here have something which is and isn’t intrinsically some way (being self-knowing) at a time? If so, the principle is false.

My response is that there is no reason to think this is a counterexample. At best, it just assumes the principle to be false, but doesn’t give us any reason to agree. “God as knower” just is “God as object” – of course, any self-knower just is that which is known by himself.

In Brandon’s original description of the case, he said, that

itself as object can’t have all intrinsic modes in common with itself as subject, because the intrinsic properties of objecthood and subjecthood themselves are different

I want to say that the concepts being an object of knowledge and being a subject of knowledge are different. Yet, it is obvious that one being may simultaneously satisfy both. Now if one satisfies the latter concept, this is because one presently has a certain mode, a certain mental state. But if one is an object of knowledge, this means that someone or other is knowing you, but it needn’t be the case that this is you. But when it is you, when you know yourself, what makes it true that you satisfy the concept of being an object of knowledge is that same mode that makes it true that you’re a subject of knowledge (of you). One could, I think confusingly, describe this as you-as-knower “intensionally differing from” you-as-known. But this is no difference in you, but only in how we refer to or think about you.

Finally, Brandon makes an interesting point:

x=y -> (Fx < -> Fy),

in other words, is only problematic in the cases you’re trying to work around if in those cases it really does matter (for whether F can apply to something) whether you are plugging something into x or plugging it into y. Since, ex hypothesi, we are plugging the same thing into x and y, that means that x and y must be taking the same value in different ways (i.e., they are intensionally different). The original only needs to be reformulated if intensional descriptions, like temporal or epistemic modalities, already can make a difference; if they don’t, your reformulated principle is unnecessary.

It may be unnecessary to get around “intensional descriptions” cases. For example,

1. Bob believes that Meat Loaf rocks.
2. But Bob doesn’t believe that Michael Lee Aday rocks.
3. Therefore, Meat Loaf isn’t Aday.

I think it is enough to point out that Bob does believe, of Aday, that he rocks. He doesn’t believe that the sentence “Michael Lee Aday rocks” is true. If read all de re (concerning the thing itself) 2 is false. If read read de dicto (concerning the sentence) then 3 doesn’t follow. If you read one premise de re and the other de dicto, 3 doesn’t follow.

I am more worried about intrinsic change. A cruder Leibniz’s Law seems to rule this out.

But the main reason I like my narrower principle is that it is sufficient to make my theological point, and by focusing on modes/intrinsic properties people (or most people!) easily see it to be true.

I think I neglected to answer Brandon’s question in a comment, whether or not I consider all modes to be non-relational. Well, I don’t think that any are relations, which as it were “obtain between” things. But a mode may be directed towards something, itself, or something else, even something unreal. Still, a mode is, as it were, within the boundaries of its owner; but like a vector, it may point in a direction. A mode can be “relational” in that it is part of what makes some statement with a relation-term true. e.g. This basketball is bigger than this golfball. What makes this true is that basketball’s mode of being, e.g. 12 inches in diameter, and the golf ball’s mode of being 1.5 inches in diameter.

Bonus video: