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Insomuch as abstract objects exist, do all things considered abstract therefore exist?

Specifically, does the concept of infinity exist as a real object, and if so, how would you respond to people like William Lane Craig who say that if infinity exists, his classical theism god must therefore exist?

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“Actual infinity” cannot exist (for it’s a contradiction), but the concept of it does, as a thought. I don’t follow Craig’s argument, but unless the omnipotence paradox is addressed, there cannot be an omnipotent god, as such a being would be a contradiction

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You predicted my objection and stated it better than I could. But I’m not sure you countered it.

“There cannot be thinking without a thought that becomes generated.”

Thinking is definitely happening. It is primitive. But what makes one thought separate from another? When they involve language, we could say some are complete and others incomplete. Is a thought like a sentence? A paragraph? An inspiration?

As I write this, I am sleepy and fiddling with my mustache. Plenty of thinking is happening, but not many thoughts. Then words come out.

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"Thoughts" can be broken down to whatever unit where they can still be produced by mind and conveyed to other minds (predicate, proposition, picture, etc.). A thought can be as basic as possible, so long as anyone else could still understand it.

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Your reply and the quote above cannot both be true. If that describes what a thought is, there can be thinking without thoughts.

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How would you have access to thoughts if you weren't thinking? The act of "thinking" is the only way we can come to know "thoughts."

Like how a subjective visual experience gives one the ability to see an objective world, a subjective thinking ability necessitates the ability to see objective thoughts.

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Unless you restrict thinking, so that when I am confused I am not thinking.

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