Does moral realism entail moral verificationism?

First, I would like to restrict this discussion to duties or responsibilities, as opposed to good or bad states of affairs, for it seems plausible to me that states of affairs may be good or bad even if no one has a duty to bring them about or prevent their occurrence. For the purposes of this post, then, I will understand moral realism as the thesis that people really do have duties to each other.

Consider the following principle:

(1) Necessarily, if someone has a duty to do something, it is possible for them to find out or discover that they have a duty to do it.

(I say ‘find out or discover’ instead of ‘know’ to rule out externalist analyses of knowledge. This is because I think one can know one has a duty in an externalist sense even if one is unable to “tell from the inside” whether one has it. In my view this sort of knowledge of one’s duties is as good as none, for one cannot act on the basis of it.)

I think (1) is highly plausible. To see why I think so, consider what things would be like if (1) were false: If (1) were false, it would be possible for you to have a duty to do something and nevertheless not have even the slightest suspicion that this was so. And if, furthermore, you did not fulfill that duty, you would be morally responsible for violating it. Of course you would be completely ignorant of this—and so would everyone else, otherwise it would be possible for them to show you that you were in fact responsible (assuming the same evidence is available to all). No matter what you or anyone else did, you could never come any closer to discovering your duties than making a lucky guess.

I find this result intolerable, and I suspect many would agree. If the intuition supporting my view is correct, one’s duties must, in principle, be discoverable by one. From this it follows that moral skepticism—the idea that one could have duties that one could not discover one had—is incoherent; there cannot be any such thing as an undiscoverable duty. The only available options, then, are a form of moral verificationism and a form of moral nihilism: Either one has duties which are such that it is possible for one to find out that one has them, or one has no duties at all. So moral realism, understood as the thesis that people really do have duties to each other, entails that moral verificationism is true.

God, Explanation and Conditional Decrees

I think one of the deepest questions philosophy can ask is why nature exhibits the order and regularity it does, and one of the most fundamental divisions among philosophers is between those who think it capable of explanation and those who do not. In western philosophy, one of the most common explanations proposed in answer to this question has been that our world is the product of some kind of design or creative intention, usually on the part of some spiritual beings, such as the gods or God. In this post I want to (somewhat briefly) explore the theistic version of this answer.

If there is indeed a God Who is roughly that of traditional theism—that is, an omniscient, omnipotent, omnibenevolent (etc.) being—it would seem that we have, on the face of it, a good explanation for the existence of an ordered, law-governed, and relatively life-friendly universe such as we find ourselves in. As an omnibenevolent being, God would plausibly have the desire to create other, in some respects similar beings with whom God could share God’s love. And as an omniscient and omnipotent being, God would certainly have the knowledge of how to create them and the power to do so. But we must be careful here. For what sort of explanation could one offer for God’s infinitely many creative decisions? As Hume pointed out long ago in his Dialogues Concerning Natural Religion, it would seem no good to explain the order and regularity of the created world by appealing to a mirror image of that world in the Divine Mind, when this image is itself without explanation. Perhaps the answer is that God’s nature dictates that every world which God could create has some minimal amount of order. (I think Duns Scotus believed something like this, but unfortunately I have not yet found a reference.) If so, we would have an explanation for the fact that the universe is ordered without having an explanation for the particular order it has.

We can flesh out the above solution to this problem in terms of the notion of a conditional decree, my term for something which is nicely spelled out by Alexander Pruss in his post “Creation, Aseity, and Providence” over at the Prosblogion. Basically, conditional decrees are of the form “If p then q, and if not-p then r”, where God both permits p to be true and permits not-p to be true, leaving the outcome to chance. If this is so, God could accommodate libertarian free will by willing conditionals of the form “If Scott freely chooses A then x will follow, and if Scott freely chooses B then y will follow, and if Scott freely chooses C then z will follow…” In this way God can plan “for all possible contingencies”, as Pruss puts it, so that even though certain matters are left to chance—such as Scott’s choice between A, B, and C—something which God wants will occur in any case.

If this account of God’s creative plan is correct, we might suppose that God makes the same decrees, both conditional and unconditional, in all possible worlds where God exists. Thus God could decree unconditionally that some contingent things exist, that some of them are to be conscious and intelligent (etc.), while leaving their exact nature unspecified. God could then use conditional decrees to cover all the matters that are left unsettled by God’s unconditional decrees. On this supposition we do not have to explain how it comes about that God wills one thing when God might have willed something different, while at the same time holding that the existence of God is compatible with a wide variety of different possible worlds. We also wouldn’t have to worry about God’s decrees depending on God’s foreknowledge of what will actually happen. Thus God’s will—that is, the totality of God’s decrees—supervenes on God’s nature, for God’s nature does not vary from world to world. God’s will constrains reality without determining it in every detail, though nothing occurs without God’s permission. Thomas Aquinas once said that it does not follow from the fact that certain things change that God’s will changes, only that God wills that things should change (Summa Theologiae (A.k.a. Summa Theologica), Prima Pars, Question 19, Article 7). In much the same spirit, we can say that from the fact that certain things happen differently in different possible worlds, it does not follow that God’s will differs in different possible worlds, only that God wills that certain things should happen differently in different ones.

Rethinking the limits of dialetheism

In a previous post I tried to undercut one of the main motivations for believing in dialetheism by giving the following argument:

Consider for a moment (2):

(2) This statement has the same truth value as “0 = 1”.

Assume (2) is false. If so, it must have a different truth value than “0 = 1”, for what (2) says is that they have the same value. Since “0 = 1” is false, (2), if it has a different value, must be true. But if (2) is true, it has the same truth value as “0 = 1”, for that they have the same truth value is precisely what (2) says. Now if (2) is true, and it has the same truth value as “0 = 1”, then “0 = 1” must also be true, and hence we can conclude that 0 = 1!

We cannot give (2) a dialetheic treatment—holding that it is both true and false— for we can substitute any falsehood we like for “0 = 1” and use the paradox to show it must be true as well as false. We would then end up with trivialism—the view everything is both true and false! Since (2) cannot be solved by dialetheic means, it must have a different, consistent solution.

I now think this argument doesn’t work. A dialetheist can simply say that (2) is both true and false while “0 = 1” is false only, because it is the statements’ conjoint falsity which accounts for the truth of (2), and not their conjoint truth. After all, it would appear that any statement of the form “p has the same truth value as q”, where q is both true and false, is itself both true and false, but surely this does not entail that p is both true and false. For example, one can easily generate statements of this form by substituting a Liar statement for q and an arbitrary statement for p, but as long as one rejects explosion—the principle that contradictions entail everything—this gives us no reason at all to think that p must also be both true and false. It may have taken me a year, but at least I caught my own mistake. :-P

Is there more to life than being happy?

Suppose there are two men, Bob and Rob, whose mental lives are exactly similar. Both are very happy throughout the majority of their lives. There is, however, an important difference between them: Bob lives in the real world, while Rob lives alone in the Matrix, never to discover his predicament. None of Rob's family and friends are real.* His love is directed towards people who don't exist, and his accomplishments are appreciated by no one. No one shares in his joys or comforts him in his times of sorrow. Now, my question is this: would you rather live a life like Bob's or a life like Rob's? If you would rather live a life like Bob's, your choice cannot be based on any subjective difference between Bob and Rob, for they are exactly alike when it comes to their thoughts and feelings. So if you prefer a life like Bob's you want more for yourself than just being happy. What this “more” is is hard to characterize. Personally, I think it involves the notion that sharing one's life with others is intrinsically good, and that sharing one’s life in this way is something which is not desirable for the sake of any effect it has on our subjective well-being. But what primarily interests me here is what the reader has to say.

*I will stipulate that the simulations Rob encounters are not conscious. If one thinks such simulations must be conscious, imagine an equivalent scenario with a Cartesian demon running the show instead.

A note on God and unsurpassable worlds

Let us say that a possible world is unsurpassable if there is no possible world which is better than it. (This allows for the epistemic possibility that there may be more than one unsurpassable world, as opposed to the term “best” which is commonly understood to presuppose uniqueness.) Now, suppose for the sake of argument that (roughly) the God of traditional theism—an incorporeal, omniscient, omnipotent, omnibenevolent (etc.) being—exists. The question I want to examine is this: If God is infinitely good, not just in the sense of being omnibenevolent but also in the sense that God is of infinite value, is every possible world in which God exists an unsurpassable world? The answer depends on what we take into account in assessing the value of possible worlds. I see at least two ways of carrying out such an evaluation.

On the first way, we ignore any weight that might be assigned to the goodness of individuals and simply regard one possible world as being better than another if and only if the set of all good things which exist in the latter is a proper subset of the set of all good things which exist in the former. In this sense a possible world which contains God and one sentient being is—assuming all sentient beings possess at least some value--better than a world which contains God alone (not counting necessarily existent abstracta), and this is so quite irrespectively of the fact that God is infinitely good. It seems to me that there is no unsurpassable world in this sense, for given any possible world w_x there is always another world w_y such that the set of all good things which exist in w_x is a proper subset of the set of all good things which exist in w_y. On this view possible worlds can only be ranked according to their goodness, one cannot say how much better one world is than another.

According to the second way one should take into account not only the number of instances of goodness but also, so to speak, their intensity. For when we say that God is infinitely good we do not (or should not) mean that God has aleph-null (or some other transfinite cardinal) units of goodness, but rather that God’s goodness is “infinitely intense” or “unsurpassably intense”. We might characterize this by saying that in our moral considerations God’s goodness ought to be given an infinite and/or unsurpassable weight. Given that God’s goodness is infinitely or unsurpassably intense in all possible worlds where God exists, it appears that taking the “intensity” of something's goodness into account in determining the value of possible worlds yields the result that all possible worlds where God exists are unsurpassable.

So it seems that if God exists either none of the worlds which God can actualize are unsurpassable or that all of them are, and in neither case is there a unique "best" world that God can actualize. The interesting question is then, if that’s so, does it follow that God must choose a world to actualize at random?

Against Hacker on the Justifiability of Grammar

Over at Methods of Projection, in the comments section of a post about Wittgenstein on meaningfulness and language games, N. N. posted the following arguments by P. M. S. Hacker, which attempt to show that the rules of grammar cannot be justified:

Justifying grammar by reference to the facts leads to an infinite regress. Any attempt to justify grammatical rules by reference to how things are in reality must employ a language in giving that justification. The form of words that purports to justify a rule of grammar must itself have a grammar. If it has the same grammar as that which it purports to justify, the justification begs the question. If it has a different grammar, then (a) it determines different concepts and so cannot be about the same thing, hence is irrelevant; and (b) that grammar too will stand in need of justification. So any attempt at grounding grammar is reality will launch us upon an infinite regress of justifications.
[...]
No description of reality can justify grammar. Any attempt to justify grammar by reference to reality must take the form of a grammatically licit description of how things are. Such a description is given by a proposition with a sense. Consequently its negation too must make sense, for the negation of a proposition with sense, which describes how things are, is itself a proposition with sense. But for such a proposition to justify a grammatical rule which delimits the sense of sentences and excludes nonsensical forms of words, the negation of the justifying description would have to be nonsense, not a falsehood. This has two corollaries, both of which were discussed by Wittgenstein.
(a) If it were possible to justify grammatical rules by reference to reality, those rules would be superfluous. One cannot say that a grammatical rule is made necessary by certain properties of things: e.g. the rule that excludes the words 'transparent white' or 'flashing black' cannot be justified by saying that white is not transparent or that black is not radiant. For if one could say this, then it would make sense, even though it would be false, to say that this white glass is transparent or that the traffic lights flashed black. But then the grammatical rule would be superfluous, since what it does is precisely to exclude such forms of words as nonsense.
(b) Any justification of grammar by reference to reality requires the possibility of describing a reality that would not justifify that grammar. A justifcation of our grammar by reference to reality should, it seems, take the form of saying that since reality is thus-and-so, the rules of grammar must be such-and-such. But one must then also be able to say that if reality were otherwise, then the rules of grammar would have to be different. However, one cannot sensibly say how reality would have to be in order for a different grammar to be justified. For in order to describe such a different reality, one would have to use the very combinations of words which our existing grammar excludes, i.e. one would have to talk nonsense. But if something counts as nonsense in the grammar which is to be justified, it cannot at the same time pass for sense in the grammar of the propositions purporting to justify it.

To this I responded as follows:

Hi n.n.,

I disagree with Hacker's arguments for the unjustifiability of grammar for the following reasons: First, it seems to me his regress argument works, if it works at all, only if we take sentences as the ultimate bearers of truth. If one believes in abstract propositions, as I'm inclined to do, one can hold that the justifications one gives for the grammar of some language, being abstract propositions which may be expressed in several languages each with a different grammar, don't have a grammar in the required sense. I'm sure Hacker would reject the existence of such propositions, but he would need to give some independent argument for doing so. Second, and more importantly, it seems to me that his arguments about nonsensicality vs. falsehood are self-referentially incoherent. Let us take, for example, the statement "No description of reality can justify grammar." Hacker takes this to be true. If it is true it certainly makes sense, but if it makes sense then (according to Hacker) so must its negation, namely "Some description of reality can justify grammar"; and if it makes sense Hacker can't rule it out a priori. On the other hand, if "Some description of reality can justify grammar" is nonsense, then (by Hacker's lights) so is the statement "No description of reality can justify grammar." Thus it appears that the conclusion Hacker wishes to establish is either false or nonsensical. Where does that leave us? One might think these considerations show that there are some statements which are meaningful but necessarily false. Personally, I think this is probably the correct conclusion. But there's another option which is often overlooked-- one could say that some meaningful statements simply don't have a meaningful negation at all.

The rest of the discussion is also quite interesting, so if you have the time by all means go check it out.

In Defense of Private Language: Part 2

Kripke’s theory of naming—though he refuses to call it that—is a reaction against the views of Gottlob Frege and Bertrand Russell. They had thought that the reference of a name is determined by a description which is associated with it in the mind of a speaker. Thus the reference of a name such as 'Aristotle' may be determined by a description such as “the most famous student of Plato.” Kripke makes several criticisms of this kind of account of names, which I cannot go into here. The important thing is the positive view that Kripke develops in response to it.

If the Frege-Russell view is wrong, how does it come about that people are able to use names to refer to objects? On Kripke’s theory, names are simply labels that we tag objects with. They can pick out their referents directly, without a need for any mediating description. In place of a description, Kripke envisions a causal chain stretching from current utterances of a given name all the way back to an initial “baptism” of its bearer. (Naming and Necessity, pp. 96-97) During a typical baptism a person will attend or point to an object which causally affects them in some way—perhaps by the light it reflects—and pronounce a word which, in the right circumstances[1], becomes the object’s name. Others hear the baptizer utter this name and come to use it themselves. Still others hear it from them and come to use it as well, etc. In this way the name can be passed on to an ever increasing number of speakers. So long as they intend to use the name to refer to the same thing the original baptizer used it to refer to, they too can use it to refer to that thing, even if they have never encountered it and know next to nothing about it. Indeed, they can successfully use the name to refer to it when most of their beliefs about it are false. These results are a great strength of Kripke’s theory, and one would do well to remember them, for they are crucial to understanding how the Private Language Argument goes wrong.

If Kripke’s account of naming is correct, we may say either that names refer but have no meaning, or that the meaning of a name just is its bearer. Either way, Wittgenstein’s view is in trouble, for the Private Language Argument rests on the assumption that names do have a kind of meaning, in the form of a rule which governs their correct application. Consider this excerpt from section 258 of PI : “A definition surely serves to establish the meaning of a sign.—Well, that is done precisely by the concentrating of my attention; for in this way I impress on myself the connexion between the sign and the sensation.—But “I impress it on myself” can only mean: this process brings it about that I remember the connexion right in the future. But in the present case I have no criterion of correctness.” (PI p. 92) But it is doubtful that such a conception of meaning applies to the sort of expressions being considered here. What, for instance, would the rule for the correct use of the name ‘Aristotle’ be? Would it be “Apply the name ‘Aristotle’ to Aristotle and nothing else”? If one does not already “understand” the name ‘Aristotle’ this rule is useless, and if one does understand it the rule is entirely superfluous. Note also how Wittgenstein quickly passes from saying that a definition[2] establishes the meaning of a sign to saying that one impresses a connection on oneself through an act of attention. The connection between a sign and a sensation is a relation of reference, and if one thinks of reference as Kripke does it will sound very odd to talk of “impressing” such a relation on oneself or of “remembering” it. What could it mean, on a view like Kripke’s, to impress on oneself the connection between the name ‘Aristotle’ and the man to whom it refers? For Kripke this connection is constituted by a certain series of causal relations, and it exists whether I remember it or not.

The truth is that, to use the name ‘Aristotle’ meaningfully—or “referentially,” if we hold names to be meaningless—one need only stand in certain causal relations to Aristotle and intend to use the name to refer to the same thing as those from whom one got it. Whether one also has certain beliefs about Aristotle, undertakes to “use” the name ‘Aristotle’ in a certain way, or is able to “remember” the referential link between the name and its bearer will not affect the meaning or reference of the name. Apart from this there is no criterion for its correct use. Names can be used significantly because they stand in certain relations to something in the world, not because of any rules we supply to govern their application. The same, I contend, goes for the terms of a private language.

In opposition to Wittgenstein, I propose the following Kripke-inspired picture of the meaningfulness of sensation words. Suppose I am a private linguist who wants to record occurrences of a private sensation—a toothache, for instance—in a calendar of the sort Wittgenstein mentions in section 258 of PI. On having the toothache I go over to the calendar and inscribe the sign ‘T’. Since I am trying to keep track of the recurrence of this sensation, I am evidently using ‘T’ a general term, not as a name for that particular toothache. The term ‘T’ is, when used in this way, a natural kind term. To establish its reference I simply attend to my toothache and think something like “Let this kind of pain be called ‘T’,” just as I can attend to a particular kind of substance and say “Let this kind of metal be called ‘gold’.” In order to establish a relation between my sign ‘T’ and this kind of pain I need not impress on myself any connection or give myself any rule for its use, for terms which are introduced in this way either have their referent as their meaning or have no meaning at all. The baptism itself is all that is needed for me to use the sign significantly. Once the reference of ‘T’ has been established, I can use the sign in the future to refer to the same class of pains simply by intending to use it in the same way I originally did, even if the initial baptism has long since been forgotten and I now apply the term ‘T’ (incorrectly) to pains which are not toothaches. The reference is passed on to my future selves much as the reference of proper names such as ‘Aristotle’ is passed on to subsequent speakers. Moreover, if others should stumble across my calendar they can also use the sign ‘T’ to refer to my toothaches, even if they have no means of discovering what ‘T’ stands for.

We have seen that if the Private Language Argument is sound, sensation words must have publicly accessible criteria for their correct application in order to be meaningful. If there is no such thing as a criterion for the correct use of words of this kind, Wittgenstein’s argument falls apart. The upshot of the foregoing considerations is that if Kripke’s theory of naming is right the notion of a private language may be intelligible after all, in which case it is Wittgenstein himself who has fallen victim to a conceptual confusion.

Bibliography

Kripke, Saul A. Naming and Necessity. Cambridge, Massachussetts: Harvard University Press, 1980.

Wittgenstein, Ludwig. Philosophical Investigations, 3^rd Edition. Trans. G.E.M.

Anscombe. Engelwood Cliffs, New Jersey: Prentice Hall, 1958.

---

[1] These circumstances may include such background conditions as that the object does not already have a name or that the baptizer is authorized to name this object.

[2] By which he means ostensive definition, as is made clear earlier in section 258.

In Defense of Private Language: Part 1

(The following is my final paper for the Philosophy of Language course I took last semester, lightly edited to improve grammar and clarity. I've also divided it into two parts so you don't have to read the whole thing in one sitting.)

Wittgenstein’s Philosophical Investigations (henceforth PI) is a deep and important book, densely packed with thought experiments and many insightful observations. One of the most significant themes running through this work can be found in a chain of related aphorisms containing Wittgenstein’s ruminations on the possibility of a private language—a language whose terms are intelligible only to its speaker. Collectively known as the Private Language Argument, they are designed to show that the notion of a private language is incoherent. This argument, if sound, would be of lasting significance to philosophy, for it has the potential to overthrow some deep-seated intuitions about the mind. In what follows I shall attempt to show that, even if such a language is impossible, the Private Language Argument does not give us a good reason for thinking it is.

The main thrust of Wittgenstein’s arguments concerning the possibility of a private language seems to be that a would-be private linguist has no means of telling whether they are using a sign which purportedly picks out one of their private sensations correctly or not. For a private linguist to use a sign for one of their sensations meaningfully there must be a distinction between correct and incorrect usage. But what could this distinction consist in for a term of a private language? Not in its agreement or disagreement with how the term is used by others in the private linguist’s community, for by hypothesis the meaning of the term is not determined by and cannot be inferred from anything that is publicly observable, including the private linguist’s behavior. Nor can its correctness consist in its conformity with the private linguist’s judgments regarding whether they are having the same sensation or a different one, for then the distinction between correct and incorrect usage would evaporate. For what we are after here are not merely the conditions under which, as a matter of fact, the term is correctly or incorrectly used, but rather what it is for the term to be used correctly or incorrectly. The issue at stake in the Private Language Argument is not the skeptical one of whether, given that there are private sensations, we can be sure that for the most part we are applying our sensation words to them correctly. The issue is instead whether talk of such things as private sensations is meaningful at all. So when Wittgenstein demands criteria for the correct use of words, what he wants is simply some means of distinguishing correct from incorrect use; how often our use is correct is immaterial. Now, if the criterion for the correct use of a term in a private language is its accordance with the judgments of the private linguist, it will be nonsense to speak of any possibility of error. As Wittgenstein puts it, “One would like to say: whatever is going to seem right to me is right. And that only means that here we can’t talk about ‘right’.” (Section 258; PI. p. 92) Yet if the correct or incorrect application of the term is established neither by public use nor private judgment, what else could establish it? I think there is another possibility, but we must critically examine Wittgenstein’s account of meaning as use, and its relation to naming, in order to see what it is.

On Wittgenstein’s view, the meaning of a term is its use in the language of which it is a part (PI section 43, pp. 20-21). It must be noted that Wittgenstein is not asserting the rather trivial thesis that a term—if one could even call it a term—would not be meaningful if no one ever spoke it or wrote it down or in any way employed it in communication. Nor is he maintaining the equally trivial thesis that a term’s meaning depends on the particular way it is used, so that it would have meant something different if it had been used differently. These theses are true of course, but Wittgenstein is making the far stronger claim that the meaning of a term consists in the way it is used to shape behavior, and in its role or utility in our lives.

Wittgenstein distinguishes the meaning of a name from the bearer of a name. (See PI sections 39-44, pp. 19-21.) The bearer of a name is the individual to whom it refers, while the meaning of a name is the set of rules which determine whether or not a name has been correctly applied to this individual. Wittgenstein thinks that the bearers of proper names have little to do with their names’ meaning because a proper name can be meaningful even when its bearer has ceased to exist. According to Wittgenstein, naming is preparatory for actual use. Names can refer to things, but they can do so only in the context of a language game: “Naming is so far not a move in the language-game—any more than putting a piece in its place on the board is a move in chess. We may say: nothing has so far been done, when a thing has been named. It has not even got a name except in the language game.” (PI section 49, p. 24) For Wittgenstein, then, naming—and hence reference—play but a minor role in the mechanics of language.

Given the account of meaning and reference sketched above, it is easy to understand why Wittgenstein, in attacking the notion of a private language, focuses his arguments on the notion of a “private ostensive definition”—on how the connection between the private linguist’s sign and the private linguist’s sensation is set up. In section 244 of PI Wittgenstein asks, “How do words refer to sensations?—There doesn't seem to be any problem here; don't we talk about sensations every day, and give them names? But how is the connexion between the name and the thing named set up? This question is the same as: how does a human being learn the meaning of the names of sensations?—of the word “pain” for example.” (PI p. 89) Notice that Wittgenstein here identifies the question of how sensation words come to refer with that of how one learns their meaning. It is this identification—a conflation, in my view—which vitiates the Private Language Argument. To see why, we must contrast Wittgenstein’s view of naming with that of Saul Kripke in Naming and Necessity.

Best posts that never got any comments

Well, finals are finally over and the summer break is here, which means--barring any laziness or procrastination on my part--that I'm going to start posting again soon on a somewhat regular basis. In the meantime, feel free to check out what are, in my opinion, the best of my posts that (so far) have never gotten any responses:

Sense Data and the Determinacy of Perception

Term Gaps: An Alternative to Term Limits

Relativity and Dualism

Cosmological Arguments and Abduction

The Case of the Self-Conscious Calvinist

Necessary Existence, Truthmakers, and Modal Solipsism

A follow up on Necessary Existence

A Presentation on Culture and Values

I hope you'll find them interesting. Have a great summer everyone!

Deflating Debates over Essential Properties

Suppose we have a debate as to the essential properties of something, or over whether some x is really an F. For example, let’s say there's a dispute between an epistemic internalist and an epistemic externalist as to what knowledge or justification essentially is. It seems to me that we can avoid debates such as this in the following way: Instead of arguing over whether knowledge requires accessibility or not, or whether a belief’s being the product of reliable cognitive faculties is sufficient to justify it or not, we could simply coin terms such as “knowledge_e” and “knowledge_i”, or “justification_e” and “justification_i”. Then we could say that knowledge_i requires accessibility but knowledge_e does not. And we could say, similarly, that being the product of reliable cognitive faculties is sufficient for justification_e but not for justification_i. So long as each of these notions is consistent, there is no a priori obstacle to their all having instances. We might, of course, be able to find evidence or devise arguments to show that, as a matter of fact, either knowledge_e or knowledge_i or both do not exist. And then again, we might not. What I want to know is why we should think there is some other thing, knowledge simpliciter, concerning which we are unsure of its essential properties. If there is no reason for supposing there is such a thing, we risk only the loss of much fruitless debate if we eliminate it from our ontology.

Does every proposition have a negation?

Some philosophers have held—as Wittgenstein seems to in the Tractatus—that if some (apparent) statement is meaningless then so is its “negation”, and conversely that if the negation of a statement is meaningful then the negated statement must be meaningful too. Thus some have held that, since statements such as “It is not the case that Jones is identical to himself” are (so they think) obviously meaningless, then “Jones is identical to himself” is likewise meaningless. On the other hand, some have supposed that since statements such as “Jones is identical to himself” are (so they think) obviously meaningful, then so is “It is not the case that Jones is identical to himself”; it’s just that the latter is necessarily false. What has never been questioned, so far as I know, is that every meaningful statement has a negation. I think one might reasonably maintain something like the following: Suppose you think the meaning of a declarative sentence is the proposition it expresses. In that case you could say that while a given declarative sentence, say “Jones is identical to himself”, expresses a proposition, the sentence which results from prefixing a negation operator to it, say “It is not the case that Jones is identical to himself”, expresses no proposition. One could thus maintain that there are necessary truths but no necessary falsehoods. I think many would see this as beneficial, since if we could grasp the meaning of a necessarily false statement—that is, if we could understand full well what things would be like if it were true—what would we mean by calling it necessarily false or impossible? On the other hand, since we would still believe in necessarily true propositions, we could (at least potentially) accept the existence of a priori knowledge. We could also avoid a major pitfall of theories which reject (apparently) necessary truths as pseudo-propositions, namely, that on such theories a statement like “Every genuine statement has its truth value contingently” would seem not have its truth value contingently.

Such, I think, are the merits of this view. But what do you think? Is this view tenable, or does it suffer from problems comparable to those of the rival views discussed above? I have my suspicions, but for now I’m just interested in your own opinion.

Dialetheism and Hume's Principle

Suppose the dialetheic treatment of the logical and / or semantic paradoxes is correct; in particular, that sentences of the liar family express propositions which are both true and false. Then consider the following list, which I will call List A:

(1) All whales are mammals.

(2) Nothing can escape a black hole.

(3) (3) is not true.

How many statements on List A are true? Well, both (1) and (2) are true, and under our assumption of dialetheism so is (3). Since these statements are all distinct from each other, it follows that there are three true statements on the list. But (3) is also false, so what it says is not true; hence it is also true that there are only two true statements on the list. So the number of true statements on List A is both two and three. By a parity of reasoning, we can conclude that the number of false statements on the list is both zero and one.

What if we bring Hume’s Principle to bear on this case? According to Hume’s Principle, the number of F’s equals the number of G’s if and only if there is a one-to-one correspondence between them. Suppose, now, that Jones has three books on his coffee table, which we will call Book A, Book B and Book C. Is the number of books on Jones’ coffee table the same as the number of true statements on List A? Invoking Hume’s principle tells us that the number of books is the same as the number of true statements if and only if each book can be paired off with exactly one true statement and vice versa. Can this be done? On the assumption of dialetheism, the answer is “Yes and no”: Book A can be paired off with (1) and Book B with (2), but can Book C be paired with (3)? Insofar as (3) is merely a statement Book C can indeed be paired with it. But in being paired with (3), is Book C paired with a true statement? Since (3) is both true and false, it follows that Book C both is and is not paired with a true statement. Because of this, while it is true that Book A, Book B and Book C are each paired with a different true statement in List A, it is also false that they are thus paired. Hence, if Hume’s Principle holds, we get the result that the number of books on Jones’ table both does and does not equal the number of true statements on List A. What follows from this? If the number of books on the table is three, and the number of books on the table both does and does not equal the number of true statements on List A, shouldn’t it follow that three does not equal three? After all, if there are three books on the table and the number of true statements on List A equals this, there must be three true statements on List A. If the number of true statements on List A is also not equal to three, how can it fail to hold that three, which does in fact number the true statements, is not equal to three? Now, as equality does not depend upon context, if three is not equal to three in this case, it is not equal to three in any case, and I take it that this would be a Very Bad Thing. However, a dialetheist need not embrace this result. Even though, on Hume’s Principle, the number of books on the table is both equal and not equal to three, it does not follow that “the number of books on the table” picks out some one thing that is not equal to itself. Instead, the dialetheist should hold that the phrases “the number of books on the table” and “the number of true statements on List A” are really descriptions which falsely presuppose uniqueness because they contain the definite article ‘the’. In truth, what’s going on here is that there is more than one number which exhaustively numbers the true statements on List A, and this in no way entails that there is some one number which is unequal to itself. All that follows is that the numbers involved are not equal to each other. Yet it remains true that there both is and is not a one-to-one mapping from the books on Jones’ table to the true statements on List A. From this, I think dialetheists should conclude that the number of F’s can be different from the number of G’s even if there is a one-to-one mapping between them, and can be the same even if there is not. They should hold that Hume’s Principle, in dialetheic contexts, is a biconditional which fails in both directions, and as such cannot be used to provide a criterion of identity for numbers.