This is a great post. I think the presentation of the ideas is clearer and more engaging than the sequences, and the cartoons are really nice. Wild applause for the artist.
I have a few things to say about the status of these ideas in mainstream philosophy, since I’m somewhat familiar with the mainstream literature (although admittedly it’s not the area of my expertise). I’ll split up my individual points into separate comments.
Alfred Tarski is a famous mathematician whose theory of truth is widely known.
Summary of my point: Tarski’s biconditionals are not supposed to be a definition of truth. They are supposed to be a test of the adequacy of a proposed definition of truth. Proponents of many different theories claim that their theory passes this test of adequacy, so to identify Tarski’s criterion with the correspondence theory is incorrect, or at the very least, a highly controversial claim that requires defense. What follows is a detailed account of why the biconditionals can’t be an adequate definition of truth, and of what Tarski’s actual theory of truth is.
Describing Tarski’s biconditionals as a definition of truth or a theory of truth is misleading. The relevant paper is The Semantic Conception of Truth. Let’s call sentences of the form ‘p’ is true iff p T-sentences. Tarski’s claim in the paper is that the T-sentences constitute a criterion of adequacy for any proposed theory of truth. Specifically, a theory of truth is only adequate if all the T-sentences follow from it. This basically amounts to the claim that any adequate theory of truth must get the extension of the truth-predicate right—it must assign the truth-predicate to all and only those sentences that are in fact true.
I admit that the conjunction of all the T-sentences does in fact satisfy this criterion of adequacy. All the individual T-sentences do follow from this conjunction (assuming we’ve solved the subtle problem of dealing with infinitely long sentences). So if we are measuring by this criterion alone, I guess this conjunction would qualify as an adequate theory of truth. But there are other plausible criteria according to which it is inadequate. First, it’s a frickin’ infinite conjunction. We usually prefer our definitions to be shorter. More significantly, we usually demand more than mere extensional adequacy from our definitions. We also demand intensional adequacy.
If you ask someone for a definition of “Emperor of Rome” and she responds “X is an Emperor of Rome iff X is one of these...” and then proceeds to list every actual Emperor of Rome, I suspect you would find this definition inadequate. There are possible worlds in which Julius Caesar was an Emperor of Rome, even though he wasn’t in the actual world. If your friend is right, then those worlds are ruled out by definition. Surely that’s not satisfactory. The definition is extensionally adequate but not intensionally adequate. The T-sentence criterion only tests for extensional adequacy of a definition. It is satisfied by any theory that assigns the correct truth predicates in our world, whether or not that theory limns the account of truth in a way that is adequate for other possible worlds. Remember, the biconditionals here are material, not subjunctive. The T-sentences don’t tell us that an adequate theory would assign “Snow is green” as true if snow were green. But surely we want an adequate theory to do just that. If you regard the T-sentences themselves as the definition of truth, all that the definition gives us is a scheme for determining which truth ascriptions are true and false in our world. It tells us nothing about how to make these determinations in other possible worlds.
To make the problem more explicit, suppose I speak a language in which the sentence “Snow is white” means that grass is green. It will still be true that, for my language, “Snow is white” is true iff snow is white. Yet we don’t want to say this biconditional captures what it means for “Snow is white” to be true in my language. After all, in a possible world where snow remained white but grass was red, the sentence would be false.
Tarski was a smart guy, and I’m pretty sure he realized all this (or at least some of it). He constantly refers to the T-sentences as material criteria of adequacy for a definition of truth. He says (speaking about the T-sentences), ”… we shall call a definition of truth ‘adequate’ if all these equivalences follow from it.” (although this seems to ignore the fact that there are other important criteria of adequacy) When discussing a particular objection to his view late in the paper, he says, “The author of this objection mistakenly regards scheme (T)… as a definition of truth.” Unfortunately, he also says stuff that might lead one to think he does think of the conjunction of all T-sentences as a definition: “We can only say that every equivalence of the form (T)… may be considered a partial definition of truth, which explains wherein the truth of this one individual sentence consists. The general definition has to be, in a certain sense, a logical conjunction of all these partial definitions.”
I read the “in a certain sense” there as a subtle concession that we will need more than just a conjunction of the T-sentences for an adequate definition of truth. As support for my reading, I appeal to the fact that Tarski explicitly offers a definition of truth in his paper (in section 11), one that is more than just a conjunction of T-sentences. He defines truth in terms of satisfaction, which in turn is defined recursively using rules like: The objects a and b satisfy the sentential function “P(x, y) or Q(x, y)” iff they satisfy at least one of the functions “P(x, y)” or “Q(x, y)”. His definition of truth is basically that a sentence is true iff it is satisfied by all objects and false otherwise. This works because a sentence, unlike a general sentential function, has no free variables to which objects can be bound.
This definition is clearly distinct from the logical conjunction of all T-sentences. Tarski claims it entails all the T-sentences, and therefore satisfies his criterion of adequacy. Now, I think Tarski’s actual definition of truth isn’t all that helpful. He defines truth in terms of satisfaction, but satisfaction is hardly a more perspicuous concept. True, he provides a recursive procedure for determining satisfaction, but this only tells us when compound sentential functions are satisfied once we know when simple ones are satisfied. His account doesn’t explain what it means for a simple sentential function to be satisfied by an object. This is just left as a primitive in the theory. So, yeah, Tarski’s actual theory of truth kind of sucks.
His criterion of adequacy, though, has been very influential. But it is not a theory of truth, and that is not the way it is treated by philosophers. It is used as a test of adequacy, and proponents of most theories of truth (not just the correspondence theory) claim that their theory satisfies this test. So to identify Tarski’s definition/criterion/whatever with the correspondence theory misrepresents the state of play. There are, incidentally, a group of philosophers who do take the T-sentences to be a full definition of truth, or at least to be all that we can say about truth. But these are not correspondence theorists. They are deflationists.
I’ve slightly edited the OP to say that Tarski “described” rather than “defined” truth—I wish I could include more to reflect this valid point (indeed Tarski’s theorems on truth are a lot more complicated and so are surrounding issues, no language can contain its own truth-predicate, etc.), but I think it might be a distraction from the main text. Thank you for this comment though!
The latest Rationally Speaking post looks relevant: Ian Pollock describes aspects of Eliezer’s view as “minimalism” with a link to that same SEP article. He also mentions Simon Blackburn’s book, where Blackburn describes minimalists or quietists as making the same point Eliezer makes about collapsing “X is true” to “X” and a similar point about the usefulness of the term “truth” as a generalisation (though it seems that minimalists would say that this is only a linguistic convenience, whereas Eliezer seems to have a slightly difference concept of it in that he wants to talk in general about how we get accurate beliefs).
There are, incidentally, a group of philosophers who do take the T-sentences to be a full definition of truth, or at least to be all that we can say about truth. But these are not correspondence theorists. They are deflationists.
My gut instinct is deflationist, but I don’t see this view as being opposed to “correspondence”. The alleged conflict is dubious at best. Stanford Encyclopedia of Philosophy writes:
the correspondence intuition so understood would endorse:
(8) The proposition that snow is white is true because snow is white
Now, the problem with (8) is that, when we combine it with the deflationary theory-or at least with a necessary version of that theory-we can derive something that is plainly false. Someone who holds a necessary version of deflationism would clearly be committed to the necessary truth of:
(9) The proposition that snow is white is true iff snow is white.
And, since (9) is a necessary truth, it is very plausible to suppose that (8) and (9) together entail:
(10) Snow is white because snow is white.
Unfortunately, however, (10) is false. The reason is that the relation reported by ‘because’ in (8) and (10) is a causal or explanatory relation, and such relations must obtain between distinct relata.
Emphasis added: the italicized premise is false. Explanation is a cognitive feat, and the same fact (even if the identity is a necessary one) can be cognized in different ways. (Such explanations occur frequently enough in mathematics, I think.) The SEP author anticipates my objection and writes:
If ‘because’ creates an opaque context, then it would be illegitimate to suppose that (8) and (9) entail (10). This too is a possibility; however, it is not clear that ‘because’ creates opaque context of the right kind. In general we can distinguish two kinds of opaque context: intensional contexts, which allow the substitution of necessarily co-referring expressions but not contingently co-referring expressions; and hyper-intensional contexts, which do not even allow the substitution of necessarily co-referring expressions. If the inference from (8) and (9) to (10) is to be successfully blocked, it is necessary that ‘because’ creates a hyper-intensional context. However, it is open to a friend of the correspondence objection to argue that, while ‘because’ creates an intensional context, it does not create a hyper-intensional context.
It is open to them to argue that “because” does not create a hyper-intensional context, but it is much more plausible that it does. So until a good argument comes along, mark me down as a correspondence deflationist.
It’s vogue to defend correspondence because 1) it sounds like common sense and 2) it signals rejection of largely discredited instrumentalism. But surely a correspondence theorist should have a theory of the nature of the correspondence. How does a proposition or a verbal string correspond to a state of reality? By virtue of what is it a correct description? We can state a metalinguistic relationship about “Snow is white,” but how does this locution hook onto the actual world?
Correspondence theorists think this is a task for a philosophical theory of reference. (Such as in an account where “torekp” refers to you by virtue of the “christening event” of your creating the account and causal connections therefrom.) Deflationists are apt to say it is ultimately a technical problem in the psychology of language.
Interesting. I am inclined to replicate my compatibility claim at this level too; i.e., the technical solution in the psychology of language will be a philosophical theory of reference (as much as one needs) as well. I’d be interested in references to any of the deflationist discussions of reference you have in mind.
This is a great post. I think the presentation of the ideas is clearer and more engaging than the sequences, and the cartoons are really nice. Wild applause for the artist.
I have a few things to say about the status of these ideas in mainstream philosophy, since I’m somewhat familiar with the mainstream literature (although admittedly it’s not the area of my expertise). I’ll split up my individual points into separate comments.
Summary of my point: Tarski’s biconditionals are not supposed to be a definition of truth. They are supposed to be a test of the adequacy of a proposed definition of truth. Proponents of many different theories claim that their theory passes this test of adequacy, so to identify Tarski’s criterion with the correspondence theory is incorrect, or at the very least, a highly controversial claim that requires defense. What follows is a detailed account of why the biconditionals can’t be an adequate definition of truth, and of what Tarski’s actual theory of truth is.
Describing Tarski’s biconditionals as a definition of truth or a theory of truth is misleading. The relevant paper is The Semantic Conception of Truth. Let’s call sentences of the form ‘p’ is true iff p T-sentences. Tarski’s claim in the paper is that the T-sentences constitute a criterion of adequacy for any proposed theory of truth. Specifically, a theory of truth is only adequate if all the T-sentences follow from it. This basically amounts to the claim that any adequate theory of truth must get the extension of the truth-predicate right—it must assign the truth-predicate to all and only those sentences that are in fact true.
I admit that the conjunction of all the T-sentences does in fact satisfy this criterion of adequacy. All the individual T-sentences do follow from this conjunction (assuming we’ve solved the subtle problem of dealing with infinitely long sentences). So if we are measuring by this criterion alone, I guess this conjunction would qualify as an adequate theory of truth. But there are other plausible criteria according to which it is inadequate. First, it’s a frickin’ infinite conjunction. We usually prefer our definitions to be shorter. More significantly, we usually demand more than mere extensional adequacy from our definitions. We also demand intensional adequacy.
If you ask someone for a definition of “Emperor of Rome” and she responds “X is an Emperor of Rome iff X is one of these...” and then proceeds to list every actual Emperor of Rome, I suspect you would find this definition inadequate. There are possible worlds in which Julius Caesar was an Emperor of Rome, even though he wasn’t in the actual world. If your friend is right, then those worlds are ruled out by definition. Surely that’s not satisfactory. The definition is extensionally adequate but not intensionally adequate. The T-sentence criterion only tests for extensional adequacy of a definition. It is satisfied by any theory that assigns the correct truth predicates in our world, whether or not that theory limns the account of truth in a way that is adequate for other possible worlds. Remember, the biconditionals here are material, not subjunctive. The T-sentences don’t tell us that an adequate theory would assign “Snow is green” as true if snow were green. But surely we want an adequate theory to do just that. If you regard the T-sentences themselves as the definition of truth, all that the definition gives us is a scheme for determining which truth ascriptions are true and false in our world. It tells us nothing about how to make these determinations in other possible worlds.
To make the problem more explicit, suppose I speak a language in which the sentence “Snow is white” means that grass is green. It will still be true that, for my language, “Snow is white” is true iff snow is white. Yet we don’t want to say this biconditional captures what it means for “Snow is white” to be true in my language. After all, in a possible world where snow remained white but grass was red, the sentence would be false.
Tarski was a smart guy, and I’m pretty sure he realized all this (or at least some of it). He constantly refers to the T-sentences as material criteria of adequacy for a definition of truth. He says (speaking about the T-sentences), ”… we shall call a definition of truth ‘adequate’ if all these equivalences follow from it.” (although this seems to ignore the fact that there are other important criteria of adequacy) When discussing a particular objection to his view late in the paper, he says, “The author of this objection mistakenly regards scheme (T)… as a definition of truth.” Unfortunately, he also says stuff that might lead one to think he does think of the conjunction of all T-sentences as a definition: “We can only say that every equivalence of the form (T)… may be considered a partial definition of truth, which explains wherein the truth of this one individual sentence consists. The general definition has to be, in a certain sense, a logical conjunction of all these partial definitions.”
I read the “in a certain sense” there as a subtle concession that we will need more than just a conjunction of the T-sentences for an adequate definition of truth. As support for my reading, I appeal to the fact that Tarski explicitly offers a definition of truth in his paper (in section 11), one that is more than just a conjunction of T-sentences. He defines truth in terms of satisfaction, which in turn is defined recursively using rules like: The objects a and b satisfy the sentential function “P(x, y) or Q(x, y)” iff they satisfy at least one of the functions “P(x, y)” or “Q(x, y)”. His definition of truth is basically that a sentence is true iff it is satisfied by all objects and false otherwise. This works because a sentence, unlike a general sentential function, has no free variables to which objects can be bound.
This definition is clearly distinct from the logical conjunction of all T-sentences. Tarski claims it entails all the T-sentences, and therefore satisfies his criterion of adequacy. Now, I think Tarski’s actual definition of truth isn’t all that helpful. He defines truth in terms of satisfaction, but satisfaction is hardly a more perspicuous concept. True, he provides a recursive procedure for determining satisfaction, but this only tells us when compound sentential functions are satisfied once we know when simple ones are satisfied. His account doesn’t explain what it means for a simple sentential function to be satisfied by an object. This is just left as a primitive in the theory. So, yeah, Tarski’s actual theory of truth kind of sucks.
His criterion of adequacy, though, has been very influential. But it is not a theory of truth, and that is not the way it is treated by philosophers. It is used as a test of adequacy, and proponents of most theories of truth (not just the correspondence theory) claim that their theory satisfies this test. So to identify Tarski’s definition/criterion/whatever with the correspondence theory misrepresents the state of play. There are, incidentally, a group of philosophers who do take the T-sentences to be a full definition of truth, or at least to be all that we can say about truth. But these are not correspondence theorists. They are deflationists.
I’ve slightly edited the OP to say that Tarski “described” rather than “defined” truth—I wish I could include more to reflect this valid point (indeed Tarski’s theorems on truth are a lot more complicated and so are surrounding issues, no language can contain its own truth-predicate, etc.), but I think it might be a distraction from the main text. Thank you for this comment though!
The latest Rationally Speaking post looks relevant: Ian Pollock describes aspects of Eliezer’s view as “minimalism” with a link to that same SEP article. He also mentions Simon Blackburn’s book, where Blackburn describes minimalists or quietists as making the same point Eliezer makes about collapsing “X is true” to “X” and a similar point about the usefulness of the term “truth” as a generalisation (though it seems that minimalists would say that this is only a linguistic convenience, whereas Eliezer seems to have a slightly difference concept of it in that he wants to talk in general about how we get accurate beliefs).
Thanks for this whole comment. In particular,
My gut instinct is deflationist, but I don’t see this view as being opposed to “correspondence”. The alleged conflict is dubious at best. Stanford Encyclopedia of Philosophy writes:
Emphasis added: the italicized premise is false. Explanation is a cognitive feat, and the same fact (even if the identity is a necessary one) can be cognized in different ways. (Such explanations occur frequently enough in mathematics, I think.) The SEP author anticipates my objection and writes:
It is open to them to argue that “because” does not create a hyper-intensional context, but it is much more plausible that it does. So until a good argument comes along, mark me down as a correspondence deflationist.
It’s vogue to defend correspondence because 1) it sounds like common sense and 2) it signals rejection of largely discredited instrumentalism. But surely a correspondence theorist should have a theory of the nature of the correspondence. How does a proposition or a verbal string correspond to a state of reality? By virtue of what is it a correct description? We can state a metalinguistic relationship about “Snow is white,” but how does this locution hook onto the actual world?
Correspondence theorists think this is a task for a philosophical theory of reference. (Such as in an account where “torekp” refers to you by virtue of the “christening event” of your creating the account and causal connections therefrom.) Deflationists are apt to say it is ultimately a technical problem in the psychology of language.
Interesting. I am inclined to replicate my compatibility claim at this level too; i.e., the technical solution in the psychology of language will be a philosophical theory of reference (as much as one needs) as well. I’d be interested in references to any of the deflationist discussions of reference you have in mind.