[lisper]

> 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]

>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]

> 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-counterexam...

It's not directly on point, but it describes a similar concept in math.

[knightoffaith]

>It's "X is a faithful reflection of the actual state of affairs in objective reality." That's what the word "true" means.

As you've said earlier. This sounds like a reasonable construal of the word true. But I don't see anything about propositions needing to be encoded in this definition. "The earth is round" is a faithful reflection of the actual state of affairs in objective reality. It was a faithful reflection of the actual state of affairs in objective reality even before anyone was around to conceptualize this as a proposition. You don't think so?

[lisper]

Did I point you to this already?

https://blog.rongarret.info/2015/02/31-flavors-of-ontology.h...

Did you read it? Do you accept it?

Propositions are ideas, i.e. they exist in a different ontological category than material objects like earth (note no quotation marks). The word "earth" (with quotes) is an idea, one that happens to refer to earth, i.e. the material object referred to by the word "earth", which happens to be round. The words "earth is round" (with quotes) is also an idea, one which refers to a particular property (roundness) of a particular material object (earth). That idea falls into a subset of the more general concept of ideas which we call "propositions" because they have a particular relationship to the states of material objects, i.e. "the earth is round" (with quotes) is true because the earth is round (no quotes).

Material objects are made of atoms; they cannot exist without the atoms that comprise them, but their existence is more than just the totality of the existence of their constituent atoms. All of the atoms that comprise the earth existed billions of years before the earth came into existence. Earth did not come into existence until the atoms that comprise it arranged themselves in a particular way.

Ideas are not made of atoms, they are made of information. Just like material objects, ideas do not come into existence until some information that encodes that idea arranges itself in a particular way, i.e. until they are thought of. A proposition that hasn't been thought of is like a poem that hasn't been written. Saying that an unthought-of proposition is true is like saying that an unwritten poem rhymes.

Consider the words "Darth Vader was Luke Skywalker's father." Do those words stand for a proposition? Is that proposition true? Was it true before 1977 (keeping in mind here that the Star Wars story ostensibly happened "a long time ago")? Would Rene Descartes be able to recognize it as a true proposition?

It's really hard to talk about ideas. With material object you can point at them, poke them, prod them, weight them, shine lights at them. You can't do any of those things with ideas. All you can do is refer to them using representations like "the earth is round" (with quotes) or "la terre est ronde" or "Die Erde ist rund" or "地球是圆的". It is the act of referring to them in a way that some being can recognize as referring to a proposition that causes the proposition to come into being, just as the act of composing a poem causes that poem to come into being. Unwritten poems do not rhyme, and they do not not-rhyme. They simply aren't. Likewise, unthought-of propositions are neither true nor false.

[knightoffaith]

>Did you read it? Do you accept it?

Accept what specifically?

Here's what I understand you to be saying, and you're free to reframe this.

1. Propositions are ideas. 2. Ideas can only exist if they are conceived. 3. "The earth is round" is a proposition. 4. Therefore, "the earth is round" can only exist if it is conceived. 5. Truth and falsity are properties of propositions. 6. If something does not exist, it cannot have any properties. 6. If it is not conceived, "the earth is round" cannot exist. 7. "The earth is round" cannot have any properties. 8. Truth and falsity are not properties of "the earth is round".

Sounds reasonable. But how do we square this with:

1. "The earth is round" reflects a state of affairs about objective reality. 2. If something reflects a state of affairs about objective reality, it is true. 3. "The earth is round" is true.

There's nothing here about "the earth is round" needing to be conceived by someone.

One issue I would raise is the first argument's 1 and 2. Propositions don't just exist insofar as they are conceived. Representations of propositions, sure, but not propositions themselves.

[lisper]

> Sounds reasonable.

Cool.

> There's nothing here about "the earth is round" needing to be conceived by someone.

Yes, there is. You can't talk about a proposition without conceiving of it. The instant you wrote “"The earth is round"” (note the nested quotes) you conceived of the proposition "the earth is round" and brought it into being. This is impossible to avoid. So this:

> There's nothing here about "the earth is round" needing to be conceived by someone.

is false.

> Propositions don't just exist insofar as they are conceived. Representations of propositions, sure, but not propositions themselves.

I already gave you the answer to this in the parent comment but you ignored it.

"Ideas are not made of atoms, they are made of information. Just like material objects, ideas do not come into existence until some information that encodes that idea arranges itself in a particular way, i.e. until they are thought of."

etc.

So that is (still) my answer: you are simply mistaken when you say that "Propositions don't just exist insofar as they are conceived."

(You're in good company. Plato got this wrong too, and he was no dummy. But he didn't have Alan Turing's shoulders to stand on.)

BTW, note that the converse is not true. You can conceive of an idea without rendering it into a representation. Indeed, you can conceive of an idea without even being able to render it into a representation. (This is actually quite common!) But what you can't do is produce a rendering of an idea into a representation without conceiving of the idea being represented. (BTW, that is not quite true. There is a tiny loophole, but I'm going to leave it as an exercise for you to figure out what it is.)