assertion: thinking is synonymous with computation (composed operations on symbolic systems).
computation is boolean algebra.
-> therefore, doing math is to think.
I'm not trying to be pedantic, I just don't think using intuitive associations with words helps clarifying things. If your definition for thought diverges here, please try to specify how exactly: what is thought, then? Semi-autonomous "pondering"? Because the closer I look at it, that, too, becomes boolean algebra, calling eval() on some semantic construct, which boils down to symbolic logic.
What you may mean is that "neural" networks are performing statistics instead of algebra, but that's not what the article is about, is it?
> I don't think using intuitive associations with words helps clarify things
Sincere question: do you think that "think using intuitive associations with words" can be safely translated to "compute using intuitive associations with words"?
I don't think so. Therefore, even if thinking is also computing, reducing thinking to boolean algebra is a form of reductionism that ignores a number of emergent properties of (human) thinking.
The intuitive model associated with some variable/word as a concept relates to other structures/models/systems that it interfaces with. Just because the operator that accesses these models with rather vague keys (words) has no clear picture of what exactly is being computed on the surface, doesn't mean that the totality of the process is not computation. It just means that the emergent properties are not mapped into the semantic space which the operator (our attention mechanisms) operates on. From my understanding, the totality I just referred to is a graph-space, it doesn't escape mathematics. Then again, I can't know or claim to do so.
> If your definition for thought diverges here, please try to specify how exactly: what is thought, then?
This is a burden-shifting reply of "so prove me wrong!" to anyone who feels that your assertion lacks sufficient justification for it to be taken as an axiom.
The original commenter also made a random assertion: "doing math is not thinking." The person you're responding to attempted to provide a definition of "thinking."
The original commenter's comment does not contain this claim. I suppose it could have been edited, though by the time I saw it, I believe the window for editing had closed.
Neither what lisper actually says nor what hans1729 replied with are random assertions, and, furthermore, they are each entitled to assert whatever axioms they like - but anyone wanting others to accept their axioms should be prepared to assume the burden of presenting reasons for others to do so.
computation is boolean algebra.
-> therefore, doing math is to think.
I'm not trying to be pedantic, I just don't think using intuitive associations with words helps clarifying things. If your definition for thought diverges here, please try to specify how exactly: what is thought, then? Semi-autonomous "pondering"? Because the closer I look at it, that, too, becomes boolean algebra, calling eval() on some semantic construct, which boils down to symbolic logic.
What you may mean is that "neural" networks are performing statistics instead of algebra, but that's not what the article is about, is it?