I think this may have been answered earlier. They are a set of ways you think a certain class of problem works. They’re very much an element of your mental model of reality.
In other words, math (or logical axioms) are what adding two pebbles and three pebbles has in common with adding two apples and three apples.
Uhm, not really. I’m not entirely sure what you mean by “math relies on things doing math”. Math isn’t about the thinking apparatus doing math. It’s a way of systematically reducing the complexity of your mental models—it replaces adding pebbles and adding apples with just adding.
If you imagine a universe with 4 particles in it, then 2+3 is still 5.
Right, which explains his position: math is real and 2+3 really is 5, but he does not know what that means, or where that is true.
You are right though, it isn’t a fully fleshed out account. All I said is that it explains his position clearly, not that his position itself is perfectly clear.
I think this question is somewhat ambiguous; you’ve gotten two correct answers that say “contradicting” (different) things and apparently answer different questions.
When you say math, are you talking about the way apples and stones interact and the states of the universe afterwards when the universe performs “operations” on them? If so, then math is agent-independent, as the world-state of 2+3 apples will be five apples regardless of the existence of some agent performing “2+3=5″ in that universe.
If you’re talking about the existence of the “rules of mathematics”, our study of things and of counting, along with the knowledge and models that said abstract study implies, then it does rely on agents having 2+3=5 models, because otherwise there’s just a worldstate with two blobs of particles somewhere, three blobs of particles elsewhere, and then a worldstate that brings the blobs together and there’s a final worldstate that doesn’t need “2+3=5″ to exist, but requires an agent looking at the apples and performing “mathematics” on their model of those blobs of particles in order to establish the model that two and three apples will be five apples.
In other words, what-we-know-as “mathematics” would not have been invented if there were no agent using a model to represent reality, as mathematics are abstract methods of description. However, the universe would continue to behave in the same manner whether we invented mathematics or not, and as such the behaviors implied by mathematics when we say “2+3 apples = 5 apples” are independent of agents.
So when an agent or computing device performs an operation on real numbers, say division of 1200 by 7, that result is real, even though the instance of this division requires the agent to do it? The answer IS the only answer, but without an agent, there would not be a question in the first place?
That result is logically valid and consistent, but does not have any new physical real-ness that it didn’t already have—that is, its correlation and systematic consistency with the rules of how the universe works.
I think this may have been answered earlier. They are a set of ways you think a certain class of problem works. They’re very much an element of your mental model of reality.
In other words, math (or logical axioms) are what adding two pebbles and three pebbles has in common with adding two apples and three apples.
Thank you. In that case, does math rely on at least one particular agent or computer having some [true] model that 2+3 = 5?
Uhm, not really. I’m not entirely sure what you mean by “math relies on things doing math”. Math isn’t about the thinking apparatus doing math. It’s a way of systematically reducing the complexity of your mental models—it replaces adding pebbles and adding apples with just adding.
If you imagine a universe with 4 particles in it, then 2+3 is still 5.
I found Eliezer’s post “Math is Subjectively Objective” which explains his position very clearly. Thanks for your help.
No it doesn’t, since it ends “Damned if I know.”
Right, which explains his position: math is real and 2+3 really is 5, but he does not know what that means, or where that is true.
You are right though, it isn’t a fully fleshed out account. All I said is that it explains his position clearly, not that his position itself is perfectly clear.
I don’t think it even makes it clear that math is real, just that mathematical truth is objective and timeless.
Yes (show me one atom containing the Peano axioms, containing math, etc.).
Like you already implied, though, the statement “2+3 = 5” is “true” with respect to the Peano axioms whether an agent takes the time to look or not.
I think this question is somewhat ambiguous; you’ve gotten two correct answers that say “contradicting” (different) things and apparently answer different questions.
When you say math, are you talking about the way apples and stones interact and the states of the universe afterwards when the universe performs “operations” on them? If so, then math is agent-independent, as the world-state of 2+3 apples will be five apples regardless of the existence of some agent performing “2+3=5″ in that universe.
If you’re talking about the existence of the “rules of mathematics”, our study of things and of counting, along with the knowledge and models that said abstract study implies, then it does rely on agents having 2+3=5 models, because otherwise there’s just a worldstate with two blobs of particles somewhere, three blobs of particles elsewhere, and then a worldstate that brings the blobs together and there’s a final worldstate that doesn’t need “2+3=5″ to exist, but requires an agent looking at the apples and performing “mathematics” on their model of those blobs of particles in order to establish the model that two and three apples will be five apples.
In other words, what-we-know-as “mathematics” would not have been invented if there were no agent using a model to represent reality, as mathematics are abstract methods of description. However, the universe would continue to behave in the same manner whether we invented mathematics or not, and as such the behaviors implied by mathematics when we say “2+3 apples = 5 apples” are independent of agents.
So when an agent or computing device performs an operation on real numbers, say division of 1200 by 7, that result is real, even though the instance of this division requires the agent to do it? The answer IS the only answer, but without an agent, there would not be a question in the first place?
That result is logically valid and consistent, but does not have any new physical real-ness that it didn’t already have—that is, its correlation and systematic consistency with the rules of how the universe works.
Otherwise, yes, exactly.