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Are physical and logical truths distinct and, if so, how are they related? Is one more fundamental than the other?
By ‘physical truth’ I mean something true in virtue of the laws of physics, such as ‘masses attract other masses’ (gravity) and by ‘logical truth’ I mean something true in virtue of logical or mathematical principles, like ‘2 + 2 = 4’.
Could there be a world where some of the physical truths of our world were false but all of the logical truths of our world were true? That is, a world where masses always repelled other masses but 2 + 2 = 4?
Conversely, could there be a world where some of the logical truths of our world were false but all of the physical truths of our world remained true? That is, a world where 2 + 2 = 5 but where, as in our world, masses attract other masses?
[We’ve been discussing this hours and feel in desperate need of professional guidance - please help!]

One of the things usually taken to be distinctive of mathematical and logical truth is that such truths are in some very strong sense necessary, i.e., they could not have been false. Assuming that it is in fact true that 2 + 2 = 4, how could that have failed to be true? (Or, to take a logical example: How could it fail to be true that, if Goldbach's conjecture is true and the twin prime conjuecture is also true, then Goldbach's conjecture is true?) Presumably, the answer to this question depends upon what, precisely, one thinks "2 + 2 = 4" means, but it is hard to see how one could accept the statement that 2 + 2 = 4 as both meaningful and true and think that it might not have been true. It's important to be clear that this statement does not say anything about how actual objects behave, e.g., that if you put two oranges on a table with two apples and no other pieces of fruit, then you'll have four pieces of fruit. Weird things might happen in some worlds, but that would not make it false in that world that 2 + 2 = 4. It might make it uninteresting or irrelevant, but that is all. It's also important to be clear that we are not talking about whether the sentence "2 + 2 = 4" might have been false. Of course it could have been false, since "4" could have meant what "5" means, and then "2 + 2 = 4" would have meant what "2 + 2 = 5" does mean and so would have been false.

Precisely what makes the statement that 2 + 2 = 4 true is not a question I'm prepared to answer here, however. (I'm not sure I'm prepared to answer it anywhere.)

The question about physical law is less clear. Some people have entertained the view that the most fundamental physical laws are, like mathematical laws, necessary, i.e., that there could not have been a world in which they were false. Sometimes this view seems to be tied up with some idea of the form: The laws are what tell us what mass, force, etc, are, and so if those laws did not hold, there wouldn't be masses, forces, etc. (Thomas Kuhn held a view of this sort at some times.) But most people seem not to care for this view and so regard the laws of physics as contingent, i.e., not necessary. That is just to say that the laws might have been otherwise. As has been noted by Hawking, among many others, universes in which the laws were different probably would not support life, or even be very stable. Our universe seems to be "just right", as Goldilocks famously said. But that does not mean there could not have been such universes, and some physicists, like Hawking, again, actually think there are all those other universes. (For what it's worth, however, and while we're on the topic, I think Hawking's recent remarks on the relevance of all of this to the question whether there is a divine being are not worthy of a man of his intelligence.)

By the way, you will sometimes see people talk about something called "physical necessity". This is a "relative" form of necessity, and it means: necessary, given the laws of physics. But what is physically necessary need not be necessary in some stronger sense: what could not have been otherwise, period, and not relative to anything else.

So, what do we have? Logical and mathematical truths are necessary. Physical truths are not (assuming we do not take the other view). So the laws of physics could have been otherwise, whereas the laws of logic and mathematics could not.

In response to a recent question about philosophy (http://www.askphilosophers.org/question/3529/), Oliver Leaman made the claim that, "there are no facts in philosophy." Briefly reviewing the definition of "fact" I see "something that actually exists; reality; truth." Can it really be that there is no truth in philosophy? It seems like the respondent has made an assumption that it very broad, fundamental, and contestable.

I think you are over-reading Oliver Leaman's point. He was contrasting philosophers to historians, pointing out that the latter can rely on a wealth of facts while the former cannot. So I believe he was referring to empirical facts ascertainable by observation, such as facts about bullets and bodies found underground beneath a Civil War battlefield. Such empirical facts constrain disagreement among historians (preventing historians from arguing that the battle was fought with swords and spears, for example). No such empirical facts constrain disagreements among philosophers - or so Leaman may plausibly be taken to have opined.

This claim is less sweeping and fully compatible with your suggestions that there are truths in philosophy. This suggestion seems right to me. Some philosophical arguments are sound, others unsound. Some philosophical positions are coherent, others incoherent. Some philosophical objections are decisive, others fail. It would be quite natural to say that such truths express facts: the fact that philosophical argument X is sound, the fact that philosophical position Y is incoherent, the fact that philosophical objection Z is decisive. But these were just not the kind of facts Leaman had in mind.

Is Leaman right to claim that there are no narrowly empirical facts in philosophy? I find even this more limited claim highly doubtful. It has been disputed in many areas of philosophy. An excellent example is W.V.O. Quine's seminal account of epistemology as continuous with empirical inquiries about mental processes like thought and perception - "epistemology naturalized." Quine's account has been influential also in the philosophy of science. Another example is ordinary language philosophy, which centrally draws on facts about ordinary language. Relatedly, Wittgenstein's later work depicts philosophical problems as arising from problematic uses of language and seeks to resolve such problems by paying close attention to how we actually use crucial words and expressions in our "language games." Further, in moral philosophy there is Rawls's view that principles of justice are formulated on the presupposition of, and in this sense depend upon, certain empirical facts - such as the "circumstances of justice" and various facts about human beings and their dispositions. To be sure, all these views have had their critics. For example, I have been involved in an exciting debate with the late Jerry Cohen who felt obliged to "rescue justice" from Rawls's understanding of it as fact-dependent. So I would not want to claim that there is as yet a settled agreement in any area of philosophy that empirical facts play a fundamental role there (as opposed to a role confined to the mere application of fact-independent philosophical methods and principles). But if empirical facts play such a fundamental role in just one area of philosophy, then Leaman's casual claim is incorrect.

Has there been much work done on the notion of approximate truth, for example under what rules of inference approximate truth is preserved, or what kind of metric one could use to say that proposition X1 is 'truer than' proposition X2?

Yes, there's quite a good deal of work on this kind of thing. It tends to go under the name "fuzzy logic" or "degree theoretic logic". The Stanford Encyclopedia entry is a good place to start. There's a fairly recent paper by Brian Weatherson called "True, Truer, Truest", if I remember right, that does some work on the philosophical foundations, which have always been a bit unclear.

Perhaps it is worth taking continuing the conversation just a bit further.

The idea that a proposition (statement, belief) is true if and only if it "corresponds to reality" is -- as I'm sure William would agree -- not entirely transparent. What does it commit us to, exactly?

The deflationist about truth of course says that the proposition that snow is white is true if and only if reality is such that snow is white -- i.e. just if snow is white. So if the correspondence theorist is to be distinctively saying more than that, she needs to spell out what "correspondence" here comes to, over and above what the weak kind of correspondence that is already built into the deflationist view.

Now, there are indeed metaphysicians who do claim to have an "industrial strength" version of the correspondence theory, who postulate the existence of facts as ingredients of the world, factswhichare truth-makers whose existence is required to make propositions true (where the worldly constituents of truth-makers are e.g. objects and universals).1 But it is far from clear that in saying something is true it is part of what we mean that there are such metaphysically weighty truth-makers as ingredients of the world.

For example, in our everyday truth-talk, outside the philosophy classroom, we are as ready to respond "that's true" to the claim that Angelina is beautiful or that slavery is wrong, as to the claim that snow is white. But are we really committed by this everyday way of talking to the existence of facts out there in the world which make true our aesthetic or moral judgments? Arguably not!

In other words, arguably not all everyday true propositions -- such as that Angelina is beautiful or that slavery is wrong (if you don't think they are true, choose your own examples) -- are made true by metaphysically heavy-weight facts, out there in the world. If that's right, then while the "industrial strength" correspondence theory might very well be part of the story about what makes some claims true, it isn't an account of the general meaning of 'true' across the board (indeed, there being or not being corresponding metaphysically weighty facts may be just what distinguishes some classes of truths from other classes).

As to the coherence theory as described by William, that sounds more like an account of how we tell (fallibly, no doubt) what is true, not an account of what it means to say that something, e.g. a theory, is true. Coherence of a theory with observation might well incline us, very reasonably, to think that it is true: but as skeptics love to point out, there seems to be no logical inconsistency in supposing that a theory is coherent but false.

1. Fine print: strictly this kind of truth-maker theory isn't a correspondence theory in the traditional sense, for it will deny that there is a one-one correspondence between truths and their truth-makers. For example, the same truth-maker, the fact that snow is white, makes true both "snow is white" and "either snow is white or grass is green"; and the fact that grass is green is another, different, truth-maker for the second proposition.

Some talk about facts is just a stylistic variant of truth-talk. For example, in ordinary discourse, to say 'It's a fact that the fast train to London from Cambridge takes less than an hour' is to say no more than that 'It is true that the fast train to London from Cambridge takes less than an hour'. And, arguably, both those in turn say no more than that the fast train to London to Cambridge does take less than an hour.

However there is also a more substantive notion of fact that has a long history in philosophy and has in recent years made something of a comeback -- this is the notion of facts as not truths but truth-makers. The proposition that the fast train to London from Cambridge takes less than an hour is true. And there is, plausibly, something worldly that makes it true, something that has to exist if the proposition is to be true, a truth-maker in short. And what kind of thing is a truth-maker? It isn't enough for London, Cambridge and trains to exist. And adding in the property of being a fast train and the property of taking less than an hour into your catalogue of existent things isn't enough either. No, the objects and the properties have to be put together in the right way to constitute the right fact to make it true that the fast train to London from Cambridge takes less than an hour.

So on this metaphysical view, there are facts (worldly items) which make propositions true. And of course, such a view has to distinguish facts, in the sense of truth-makers, from truths, meaning true propositions.

I recently had an argument in an epistemology class about the relationship between facts and human minds. I argued that a fact cannot exist until a human mind knows it. Most of the rest of the class (and the professor) argued that facts can exist independently of human minds. My professor's example: Every human being believes that the world is flat, when it is in fact round. I argued that the fact that the world is round did not exist until someone thought it. Can a fact exist without a human mind?

You are adopting a pretty radical position, for it seems like common sense for us to recognize as facts (or truths or as actual states of affairs) all sorts of things quite independent of human minds. Most of us would want to say (for example) that it was true that there was life long before there was intelligent life here on earth. Your professor's example is a little odd, partly because very few people have ever believed the earth is flat. (There is a good book on the myth of believing in a flat earth). But you might be able to defend your position as part of a philosophy of language, contending that facts are what correspond to or are referred to as sentences and simply hold the line about not recognizing facts until you have language-users. I believe Fred Stoutland holds that position, and Richard Rorty expresses something like that in The Mirror of Nature. Still, you are not in an enviable position in terms of arguments, as most of us would want to recognize that it is a fact that before there was language there was no language.

Are there philosophers who maintain a distinction between what is "true" and what is "useful"? It seems that much of analytical philosophy and higher mathematics is true without being of much use, even to scientists. Scientists and engineers, on the other had, come up with many useful ideas whose truth values may be doubted by the abstract thinkers.
In other words, does anyone in philosophy speak of useful untruths or useless truths?

Isn't it the other way about? Only a small number of philosophers would not maintain the distinction! For as you remark, lots of truths aren't useful in any ordinary sense (e.g. there is a fact of the matter about whether the number of grains in the rice jar yesterday was odd or even -- but the truth one way or the other is no use now to man or beast); and lots of claims which are strictly false can be useful (quick and dirty approximations that do us well enough.

So to tie the ideas of what is true and what is useful together will need, for a start, bending the idea of the useful into something fairly remote from its common-or-garden sense, and we will also probably have to be pretty revisionary about what counts as true, in a way that few philosophers will be happy with.

I'm not sure what the worry is here. I think it's clear that there are some philosophical views that are plainly wrong. There may be some truth in them somewhere, but research over the years has shown that the view is wrong. (Examples: Plato's theory of forms; Hobbes's theory of government.) So who says they're wrong? Well, the people who have done the research mentioned. This is no different from science. There are scientific theories that are wrong, and the people who say so are the scientists who do the work.

What is there to say/suggest that truth is nothing more than an agreed common perception of reality?
I would really appreciate any type of response to this question, whether it be a reply, some suggested reading material on the matter or whatever it may be.
Thank You,
Christopher

If you wanted to say something in favor of this view, you might point to the absence of observed discrepancies between what we all believe and the truth. But, on reflection, this isn't a strong argument because there are observed discrepancies between what is commonly believed now and what was commonly believed at some earlier time. At the earlier time, p was commonly believed. Now not-p is commonly believed. If what's commonly believed were true, then both p and not-p would be true. But p and not-p cannot both be true. Therefore it is not the case that whatever is commonly believed is true.

Now you might say that what you mean is that truth is nothing more that what's commonly believed throughout the ages, the future included. So here is an argument against this revised view. There are lots of propositions about which there is no common belief shared throughout the ages: neither p nor not-p have been commonly believed. Does it follow that neither p nor not-p are true? For example, it has not been commonly believed throughout the ages that the sun is larger than the moon. Nor has it been commonly believed throughout the ages that the sun is not larger than the moon. Would you then want to conclude that neither belief is true: it is not true that the sun is larger than the moon and also not true that the sun is not larger than the moon?

I have been reading the recent discussion about whether "facts" can be "rational" or "irrational" http://www.askphilosophers.org/question/2829). Professor Rapaport suggests that philosophers use facts differently than most non-philosophers. Facts, he says, "simply 'are'". They are not like beliefs, which are more like sentences. His statements have left me very confused.
The Earth is round. Is that a fact?
We all die. Is that a fact? Seems to me that it is. And it's simultaneously a sentence. I don't see how a fact can be anything but a sentence.
But suppose facts are not sentences. They are situations. One big fact would be the way the world is, I suppose. A smaller fact might be the way my room is right now. Fine, why can't situations be "rational" or "irrational"? I think very often we come upon a situation and say things like "This situation is totally crazy", by which we mean, it is irrational. As the questioner said, dictionary.com defines "rational" as "agreeable to reason". ...

I'm happy to try to clarify: I don't think that philosophers use facts differently from most non-philosophers. Rather, I think that philosophers use the word 'fact' differently from the way most non-philosophers use it. I think that most non-philosophers use it to mean more or less the same as the expressions 'true sentence', or 'true proposition', or 'true belief'. I think that most philosophers use it to mean more or less the same as the word 'situation' or the phrase 'state of affairs', i.e., a bunch of objects having properties or standing in relations. Used in this way, I don't think it makes sense to call a fact "rational" or "irrational", any more than it makes sense to call, say, the number 3 "beautiful" or to call, say, the color red "odd" (in the sense of not evenly divisible by 2).

In this sense, the sentence 'The Earth is round' is true. And the reason that it is true is that there is a fact that corresponds to it, namely, the fact consisting of the object that is the Earth having the property of being round. The sentence might be considered "rational" or "irrational", but the corresponding fact simply "obtains" or "holds".

What might it mean for that sentence to be "rational"? I don't think that there's a standardly accepted definition of "rational" in this sense, but here's one plausible possibility: A sentence is rational if it coheres with other true (or believed) sentences, and it is irrational otherwise. So, given the usually accepted claims of science, the sentence 'The Earth is flat' -- or, better, the belief that the Earth is flat -- might be considered irrational.

The sentence 'We all die' is true. That we all die is a fact. The sentence is not simultaneously a fact. Rather, there is a fact that corresponds to that sentence.

You say that you don't see how a fact can be anything but a sentence. I agree that in the usual non-philosopher's use of the word 'fact', it is usually used in the same way that the word 'sentence' is. But my understanding of the original question and Allen Stairs's original reply was that there was a confusion about how philosophers use the word. If you think that we use it in a strange way, so be it, but there is a distinction to be made between sentences and situations (or whatever you want to call them), and reserving the word 'fact' for the latter is the way some philosophers speak when they're wearing their professional philosopher's hats.

I do agree that the way the world is is one big fact and that the way your room is right now is a smaller fact (which is part of the bigger one). But as I said above, I don't see how such things can be "rational" or "irrational".

How are you using the word "irrational" to apply to situations? Do you mean that the situation doesn't "cohere" with other situations? But what would that mean? A person's actions might be irrational, I suppose. But an action isn't a fact.

I'm not quite sure what dictionary.com's "agreeable to reason" means, but if it means something like what I suggested above, namely, cohering with other true sentences, then it can't apply to facts considered as situations. (By the way, "agreeable to reason" doesn't mean that a reasonable person likes it or finds it "agreeable". A person could like a fact, but that's not what's meant in that definition.)