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>There are no Platonic truths, only preferred models. Yeah, I disagree, I think there's something mathematical truths reflect that are independent of the physi

>There are no Platonic truths, only preferred models. Yeah, I disagree, I think there's something mathematical truths reflect that are independent of the physical world. When we decide whether certain mathematical claims are true or not, say, Fermat's last theorem---we prove them mathematically, we don't want to appeal to their utility or lack thereof, right? My reasoning for not wanting to appeal to utility for the validity of sense-data is analogous. >That's what the word "true" means. I agree. >It just so happens that the actual state of affairs in objective reality has an impact on survival, so having a faithful reflection of it in your brain is handy. I agree. >That's the reason "truth" is a thing. Well, truth is a thing regardless of whether or not we evolved to be able to hold such a concept in our minds, no? >podcast Sure. Contact me at knightoffaith123@proton.me

lisper 2y ago
> When we decide whether certain mathematical claims are true or not, say, Fermat's last theorem---we prove them mathematically, we don't want to appeal to their utility or lack thereof, right? Well, sort of. We don't care about the utility of Fermat's last theorem per se, but the only reason we care about numbers, which is what Fermat's last theorem is about, is because numbers have utility. It turns out that, having invented numbers for their utility, they also make fun mental playthings. But they were invented to keep track of how many sheep you had. > Well, truth is a thing regardless of whether or not we evolved to be able to hold such a concept in our minds, no? No. Truth is a property of propositions, so it only makes sense to talk about truth in the context of something that can harbor a proposition. If such a thing does not exist then neither do propositions and hence neither does truth. It's kind of like talking about "the mass of an idea". Mass is a property of matter, so it doesn't make sense to apply it to something that isn't made of matter. The thing that encodes propositions doesn't have to be a human brain, of course. It could be an alien brain, or a computer, perhaps even a thermostat (that one is debatable). But it has to be something.
- knightoffaith 2y ago
  >Well, sort of All that's fine---but I think you would agree that Fermat's last theorem isn't true by virtue of its utility for counting sheep or anything like that. Similarly, I don't think that the fact the physical world exists in the manner suggested by sense-data is true by virtue of its utility for preventing us from dying. >The thing that encodes propositions doesn't have to be a human brain, of course. It could be an alien brain, or a computer, perhaps even a thermostat (that one is debatable). But it has to be something. Are you saying that if there were no humans (or anything capable of encoding propositions) to conceive of it, the proposition "the earth is round" wouldn't be true---in other words, it would not be true that the earth is round? That seems to defy common sense.
  - lisper 2y ago
    > I think you would agree that Fermat's last theorem isn't true by virtue of its utility for counting sheep or anything like that. Similarly, I don't think that the fact the physical world exists in the manner suggested by sense-data is true by virtue of its utility for preventing us from dying. I actually would not agree with either of those. > Are you saying that if there were no humans (or anything capable of encoding propositions) to conceive of it, the proposition "the earth is round" wouldn't be true---in other words, it would not be true that the earth is round? That seems to defy common sense. Yes, I get that. This is not an easy concept to wrap your brain around, and I totally understand if you think it sounds like I'm absolutely crazy. But nonetheless, it is the case that if there were no humans (or anything capable of encoding propositions) to conceive of it, the proposition "the earth is round" would not be true. The reason is that if there were nothing capable of encoding that proposition, that proposition could not exist. A non-existent thing cannot have any properties, and so a non-existent proposition cannot be true. Two important things to note: first, the proposition "the earth is round" would not be true in a world where there is nothing capable of encoding propositions, but neither would it be false. It would simply be non-existent. And second, despite the fact that the proposition "the earth is round" would be neither true nor false, the earth would still be round. But we can only make that observation because we live in a world where there are things capable of encoding propositions. It's really hard to imagine a world where that is not the case because we would not exist in such a world. Here is a thought experiment that might help: consider some proposition P that has never been conceived of and will never be conceived of by anything capable of encoding propositions. Such propositions must exist because there are an infinite number of propositions but we live in a finite universe, and so only a finite number of propositions can ever be encoded. In fact, there must be an infinite number of such propositions. Are those propositions true or are they false? This might help too: https://blog.rongarret.info/2023/01/an-intuitive-counterexample-to-axiom-of.html https://blog.rongarret.info/2023/01/an-intuitive-counterexam... It's not directly on point, but it describes a similar concept in math.

lisper 2y ago

> When we decide whether certain mathematical claims are true or not, say, Fermat's last theorem---we prove them mathematically, we don't want to appeal to their utility or lack thereof, right? Well, sort of. We don't care about the utility of Fermat's last theorem per se, but the only reason we care about numbers, which is what Fermat's last theorem is about, is because numbers have utility. It turns out that, having invented numbers for their utility, they also make fun mental playthings. But they were invented to keep track of how many sheep you had. > Well, truth is a thing regardless of whether or not we evolved to be able to hold such a concept in our minds, no? No. Truth is a property of propositions, so it only makes sense to talk about truth in the context of something that can harbor a proposition. If such a thing does not exist then neither do propositions and hence neither does truth. It's kind of like talking about "the mass of an idea". Mass is a property of matter, so it doesn't make sense to apply it to something that isn't made of matter. The thing that encodes propositions doesn't have to be a human brain, of course. It could be an alien brain, or a computer, perhaps even a thermostat (that one is debatable). But it has to be something.

knightoffaith 2y ago
>Well, sort of All that's fine---but I think you would agree that Fermat's last theorem isn't true by virtue of its utility for counting sheep or anything like that. Similarly, I don't think that the fact the physical world exists in the manner suggested by sense-data is true by virtue of its utility for preventing us from dying. >The thing that encodes propositions doesn't have to be a human brain, of course. It could be an alien brain, or a computer, perhaps even a thermostat (that one is debatable). But it has to be something. Are you saying that if there were no humans (or anything capable of encoding propositions) to conceive of it, the proposition "the earth is round" wouldn't be true---in other words, it would not be true that the earth is round? That seems to defy common sense.
- lisper 2y ago
  > I think you would agree that Fermat's last theorem isn't true by virtue of its utility for counting sheep or anything like that. Similarly, I don't think that the fact the physical world exists in the manner suggested by sense-data is true by virtue of its utility for preventing us from dying. I actually would not agree with either of those. > Are you saying that if there were no humans (or anything capable of encoding propositions) to conceive of it, the proposition "the earth is round" wouldn't be true---in other words, it would not be true that the earth is round? That seems to defy common sense. Yes, I get that. This is not an easy concept to wrap your brain around, and I totally understand if you think it sounds like I'm absolutely crazy. But nonetheless, it is the case that if there were no humans (or anything capable of encoding propositions) to conceive of it, the proposition "the earth is round" would not be true. The reason is that if there were nothing capable of encoding that proposition, that proposition could not exist. A non-existent thing cannot have any properties, and so a non-existent proposition cannot be true. Two important things to note: first, the proposition "the earth is round" would not be true in a world where there is nothing capable of encoding propositions, but neither would it be false. It would simply be non-existent. And second, despite the fact that the proposition "the earth is round" would be neither true nor false, the earth would still be round. But we can only make that observation because we live in a world where there are things capable of encoding propositions. It's really hard to imagine a world where that is not the case because we would not exist in such a world. Here is a thought experiment that might help: consider some proposition P that has never been conceived of and will never be conceived of by anything capable of encoding propositions. Such propositions must exist because there are an infinite number of propositions but we live in a finite universe, and so only a finite number of propositions can ever be encoded. In fact, there must be an infinite number of such propositions. Are those propositions true or are they false? This might help too: https://blog.rongarret.info/2023/01/an-intuitive-counterexample-to-axiom-of.html https://blog.rongarret.info/2023/01/an-intuitive-counterexam... It's not directly on point, but it describes a similar concept in math.