"There are none so blind as those who will not see." --

Wednesday, December 04, 2013

Ways Modality Could Be: Revised and Expanded

My article "Ways Modality Could Be: Revised and Expanded" is now up on Scholardarity.

Here's an excerpt:

1. Introduction
            In this paper I introduce the idea of a higher-order modal logic—not a modal logic for higher-order predicate logic, but rather a logic of higher-order modalities. “What is a higher-order modality?”, you might be wondering. Well, if a first-order modality is a way that some entity could have been—whether it is a mereological atom, or a mereological complex, or the universe as a whole—a higher-order modality is a way that a first-order modality could have been. First-order modality is modeled in terms of a space of possible worlds—a set of worlds structured by an accessibility relation, i.e., a relation of relative possibility—each world representing a way that the entire universe could have been. A second-order modality would be modeled in terms of a space of spaces of (first-order) possible worlds, each space representing a way that (first-order) possible worlds could have been. And just as there is a unique actual world which represents the way that things actually are, there is a unique actual space which represents the way that first-order modality actually is.
            One might wonder what the accessibility relation itself is like. Presumably, if it is logical or metaphysical modality that is being dealt with, it is reflexive; but is it also symmetric, or transitive? Especially in the case of metaphysical modality, the answer is not clear. And whichever of these properties it may or may not have, could that itself have been different? Could at least some rival modal logics represent different ways that first-order modality could have been?
            To be clear, the idea behind my proposal is not just that some things which are possible or necessary might not have been so at the first order, as determined by the actual accessibility relation, but also that the actual accessibility relation, and hence the nature or structure of actual modality, could have been different at some higher order of modality. Even if the accessibility relation is actually both symmetric and transitive, perhaps it could (second-order) have been otherwise: There is a (second-order) possible space of worlds in which it is different, where it fails to be symmetric, or transitive. We must, therefore, introduce the notion of a higher-order accessibility relation, one that in this case relates spaces of first-order worlds. The question then arises as to whether that relation is symmetric, or transitive. We can then consider third-order modalities, spaces of spaces of spaces of possible worlds, where the second-order accessibility relation differs from how it actually is. I can see no reason why there should be a limit to this hierarchy of higher-order modalities, any more than I can see a reason why there should be a limit to the hierarchy of higher-order properties. There will thus be an infinity of orders, one for each positive integer, and each order will have an accessibility relation of its own. To keep things as clear as possible, a space of first-order points (i.e., of possible worlds) shall be called a galaxy, a space of second-order points, a universe, and a space of any higher order, a cosmos. However, to keep things as simple as possible, in what follows I will deal with but a single cosmos at a time, and hence will not deal with modalities higher than the third order.
            The accessibility relation is not the only thing that might be thought to vary between spaces of worlds: Perhaps the contents of the spaces can vary as well. While I presume that the contents of the worlds themselves remain constant—it makes doubtful sense to suppose that in one space some entity e exists in a world w and in another space e doesn’t exist in that same world w—we may suppose that different spaces may differ as to which worlds they contain, just as different worlds may differ as to which objects they contain. Thus we might have a higher-order analogue of a variable-domain modal logic. There seem, then, to be three ways in which spaces can differ: First, as to the properties of the accessibility relation; second, as to which worlds the relation relates; and third, as to which worlds or spaces are parts of their domains.
            The paper will be structured as follows. In Section 2 I provide some reasons why one might want to pursue this kind of project in the first place. In Section 3 I outline the syntax and semantics of my proposed logic. Section 4 covers semantic tableaux for this system; and after giving the rules for their construction, I construct a few of them myself to establish some logical consequences of the system and give the reader a feel for how it works. In Section 5 I outline a potential application of my framework to the metalogic of modal logics. In Sections 6, 7 and 8 I explore some of  its potential philosophical implications for areas besides logic, namely the philosophy of language; metaphysics, including the metaphysics of modality, the philosophy of time, and laws of nature; and finally the philosophy of religion, before concluding the paper in Section 9.

Sunday, December 01, 2013

An idea regarding charitable giving

Today I had an idea regarding charitable giving that as far as I know hasn't been implemented, at least on a large scale: Why not have "charity cards", credit cards which automatically donate a certain percentage  of what you spend to charity whenever you make a purchase? For example, if you spend $100.00 on something and have a 2% threshold, that would automatically generate a corresponding $2 donation to a charity of your choice. I think that would be good because such "microdonations," which most of us wouldn't bother to make separately, would eventually ad up. They would also require no special effort, which I think is a great psychological  barrier to giving. If a lot of people ended up using charity cards, it could easily generate millions (or more) in donations.  So instead of getting "points" or filer miles, why not have cards that automatically generate microdonations?

Don’t Think of a Square Circle!

Don’t Think of a Square Circle!

Wittgensteinian Reflections on Imagining the Impossible

3.031 It used to be said that God could create anything except what would be contrary to the laws of logic. The truth is that we could not say what an 'illogical' world would look like. 

—Wittgenstein, Tractatus Logico-Philosophicus, trans. D. F. Pears and B. F. McGuinness (London: Routledge & Kegan Paul)

It has been noted (by George Lakoff, among others) that if someone tells you “Don’t think of an elephant!”, it’s pretty hard not to do it. Though it would take empirical research to fill in the details, the answer as to why this is so does not seem hard to discern: To understand the order—to understand what one is not supposed to think of—one must understand the term ‘elephant’, and thus come to think of one. I’d wager that in addition to thinking of one an image of an elephant popped into your head as well. This is probably because the concept of an elephant is an empirical concept—no crisp, abstract definition of an elephant comes readily to mind, so a stereotypical image is needed to make it intelligible. By contrast, if someone were to tell you “Don’t think of the number 2!” it is less likely that an image would come up, unless you confuse the numeral ‘2’ with the number 2—or, at least, that the image would be unlikely to be constant for different people, or for the same person at different times.

What, though, if someone were to tell you “Don’t think of a square circle!” Is it so hard to comply in this case?

Well, maybe it is: Do I really know what it is I’m not supposed to think of? If not, I’m not really complying with the order, because I fail to understand it. I’m merely doing what it says. Nevertheless, what interests me here is not our concept of compliance, but rather that of conceiving or imagining the impossible.

If one can imagine or conceive of something, what then could one mean by saying that one can’t understand how it could be the case? Could it be, for instance, that I can conceive that a square circle exists, but not that the existence of a square circle is possible? It would seem not: It is not more impossible that it is possible that a square circle exists than that a square circle exists; so if I can conceive the latter, I should be able to conceive the former as well. If however, I cannot conceive of the existence of a square circle, I cannot conceive of its possibility either. That seems fine, but one could ask: If I cannot conceive of a square circle, nor of its possibility, how could I still conceive of its impossibility? That is, if I truly cannot conceive of it, how can I say that it is that, and not something else, or nothing at all, of which I am unable to conceive? If someone tells me that I cannot eat or drink on the subway, I know what it is that I am being forbidden to do. And if I am informed that no human being can run as fast as a cheetah, I know what is being declared to be impossible, and it is relatively easy to form an image of what the contrary would look like. But if someone tells me that it is impossible for a circle to be square, or identical to (i.e., the same thing as) a square, how am I to know what it is that is being said to not possibly be the case?  For if you were to be told that snorogs are impossible, you would have every right to ask your alleged informant what a snorog is. If no answer were forthcoming, the most you could conclude is that you cannot know whether they are possible or not if you have no idea what they are supposed to be. The same should hold just as much for “square circles”: If I simply don’t know what the term means I should conclude, not that they cannot exist, but rather that I have no idea whether they can or not, if the term is meaningful at all. And if I do understand it, it seems—as was said above—that I must also be able to understand the claim that square circles are possible, as the possibility of something cannot be any more impossible than the thing itself. If I nevertheless say that they or their possible existence is inconceivable, I cannot mean that I do not understand the claim that they exist, or that their existence is possible. What, then, can I mean? 

A natural answer would be something like: In virtue of understanding the term ‘square circle’, I “see” or “grasp” that they cannot exist. But what am I seeing here, and how do I see it?

The second question would involve us in the thorny details of epistemological debates surrounding a priori knowledge, which I will not enter into. By contrast, it might seem that an answer to the first question is trivial: I’m seeing that square circles cannot exist! But what we have said so far should make us suspicious of this answer. To be sure, it is a right answer to our question, if it’s true that I’m really seeing that, but it’s not the only possible answer, and certainly not the most helpful one. If someone were to tell you that they can see that snorogs cannot exist, and you were to ask them what exactly it is to see that, it would not be very informative to be told that it is simply to see that snorogs cannot exist! If you don’t know yourself what snorogs are, or what ‘cannot’ means in this context, such an answer won’t help you one bit. We have two problems: (1) If I am to “see that something cannot be the case” in virtue of understanding a term, ‘cannot’ should not mean: It is inconceivable that it is the case. What, then, does it mean? It must be more than mere nomic or physical impossibility, for one cannot tell something to be nomically or physically impossible merely in virtue of understanding a certain term. (2) How am I to tell whether I or someone else truly understands the term? For unless I have some means of doing so I am at a loss as to how to assess the claim of impossibility, and can make no progress.

I’ll leave the first question to one side (for now). As for the second, in all cases it should be possible to specify the meaning of a term somehow, to give some kind (not necessarily very exact and not necessarily very informative) of explanation or definition of what it is. In addition, for empirical terms it should be possible to imagine the corresponding entity or recognize it in experience.

Can one specify the meaning of ‘square circle’? It certainly seems so: One can define it as a circle that is also a square, or as a circle that is identical to (is the same thing as) a square. Alternatively, if the term ‘spherical cube’ is already understood, (as, e.g., a sphere that is also a cube, or a sphere that is identical to a cube) one could define a square circle as a 2-dimensional cross-section of a spherical cube that cuts through its center. Admittedly, these definitions are not very rigorous, but rigorous definitions cannot be given for most terms in ordinary use, and they are none the worse off for that.

One can note that as ‘square’ and ‘circle’ (or ‘sphere’ and ‘cube’) are empirical terms, ‘square circle’ should  be one too. But whereas it has appeared easy to define what a square circle would be, it seems much more difficult to imagine what one would look like. Supposing one were shown a drawing of a disc with a large square hole in it, or a square solid with a large circular hole in it, one would naturally reply that that isn’t what one means . But what then does one mean? It is not as though I have some (vague) image of a square circle to which they fail to conform, but rather that no image suggests itself. Is it that it would look like something, only I don’t know what? Or is it that there is no such thing as “what it would look like”?

Well, if the One True Logic is not paraconsistent (i.e., is not non-explosive), then contradictions entail everything. So if square circles are contradictory—and they seem to be, for squares are square and circles are not, while square circles are both squares and circles—then every counterfactual beginning “If there were square circles, they would look like…” is true. If Logic is not paraconsistent, then, nothing is easier than imaging what a square circle would look like: Take anything you please, such as a shoe, a ship, some sealing wax, a cabbage, or a king. If the One True Logic is paraconsistent, matters are less clear. But suppose some lover of paradoxes were to come to you, draw a square and a circle next to each other, and ask you whether a square circle would look like that.

“Like the square or the circle?”, you enquire.

“Like both,” he replies.

“Well,” you say, “a square circle is supposed to be a square that’s identical to a circle, but the figures you have drawn don’t look identical.”

“I grant that the figures I have drawn are not identical,” he replies, “but that’s the thing about representations: they need not share the properties of the things they represent. As for identity, I wasn’t aware that it looked like anything at all. If it did, one could tell by mere inspection whether properties are universals or tropes, by ostending different “instances” or “tokens” of the same type and checking to see—literally see—that the instances either do or do not have something numerically identical in common; and one could thus very easily settle that dispute. As things are this is not possible, so it seems safe to say we cannot perceptually experience relations of identity. So I think I can safely say that the circle and the square are depicted as being identical, even though the depicted square and the depicted circle don’t look identical.

“Identity may not look like anything,” you reply, “but difference certainly does, and the square depicted and the circle depicted look different.

“Naturally,” he replies, “for I have drawn a contradictory object, which is naturally both self identical and self-distinct. Since I have drawn a square which is identical to a circle, it differs even from itself, and it is this difference which you are picking up on.”

“Well,” you say, more hesitantly, “not only do they look different, they appear to be in different places. A square circle isn’t supposed to be a mereological sum of a square in one place and a circle in another, but one thing in one place which is both square and circular.”

“That,” he replies, “is merely a defect of the medium. I drew a square shape and a circular shape in different places, but they are intended to depict exactly the same location. And in any case, just as the depicted shape is both self-identical and self-distinct, the depicted location of the shape must also be both self-identical and self-distinct. The places of the shape(s) are thus both different and not different, and again it is the difference which you are picking up on.”

“But,” you sputter in exasperation, “I can see that the square and the circle are different from each other, and also that they are not different from themselves, but what I cannot see is that they are not different from each other!”

“But of course you can!” he replies, smiling, “for take the depicted square. You can surely see that it is not different from itself; that is, that the square is not different from the square. And since that square is identical to the depicted circle, it follows by Leibniz’s Law that the depicted circle looks not to be different from the depicted square!”

At this point I suspect you would give up, and let the lover of paradoxes go on his merry way. But who has won the hypothetical dispute? Why shouldn’t we say that his drawing of a square circle is a perfectly good one—that by looking at it we can now tell what one would look like? If we still insist, as I think most will, that his drawing isn’t a good one, I think the proper moral may well be a Wittgensteinian one: When we say that we cannot imagine a square circle, what we’re really doing (whether we realize it or not) is excluding any purported description of what one would look like from our language-game(s). We’re saying, in effect, “No matter what anything looks like, we refuse to call that ‘what a square circle looks like’, and no matter what anyone draws, we refuse to call it ‘a good drawing of a square circle.’ And this isn’t to say that there can’t be some strange looking drawings—one can simply look at a Penrose triangle or some of M.C. Escher’s works (or for a real life case, one can check out ‘the waterfall illusion’). One must get away from the idea that behind a grammatical rule there stands something that cannot be done—unless one only means that there is a norm that we shouldn’t speak in a certain way. Any image can be described in language in multiple ways, and what the case of the lover of paradoxes shows, if it shows anything, is that our current, actual language game forbids certain descriptions of certain phenomena. Perhaps, as in the case of the waterfall illusion, a language game which admits of inconsistent modes of description would be more appropriate (and note that I say more appropriate, for consistent modes of description are certainly also available). As with the description ‘the pitch of sweetness’, the (apparent) description ‘the look / appearance of a square circle’ has been denied a role in our language game. Just as ‘the pitch of sweetness’ is not something we fail to hear in any ordinary sense, ‘the look / appearance of a square circle’ is not something that we fail to see or imagine in any ordinary sense. Why such terms play no role in our language may be hard to say, but that they do not could be said to be shown by our reaction to the case of the lover of paradoxes: the simple fact is that we know how the investigation is to turn out before we begin to inquire. For it is not that the term ‘square circle’, like the term ‘snorog,’ simply calls up no image for us as a matter of fact—if someone were to introduce us to a community where things which were regularly called snorogs looked such-and-such a way, we would accept that easily—it is rather that we know in advance that we will refuse to apply the term ‘square circle’ to anything.

In this way we avoid the misleading idea of imagining the impossible as something that we are unable to do—that “our powers of imagination are unequal to the task” as Wittgenstein put it in the Investigations—as well as avoiding the equally misleading picture of logical or conceptual necessity whereby we in effect personify it as the bouncer at the door of Club Reality; of logical/conceptual necessity as a powerful force which keeps out the riffraff of impossibilia struggling to get in in order that they may exist. This, at any rate, is the best I think I can do to give content to Wittgenstein’s idea of logical/conceptual necessity as being basically linguistic.

Wednesday, November 27, 2013

On the Announcement of Pope Francis's first Apostolic Exhortation: Evangelii Gaudium

Has anyone else seen this? I don't consider myself Catholic, but it's pretty awesome.

"As we open our hearts, the Pope goes on, so the doors of our churches must always be open and the sacraments available to all. The Eucharist, he says pointedly, “is not a prize for the perfect, but a powerful medicine and nourishment for the weak” And he repeats his ideal of a Church that is “bruised, hurting and dirty because it has been out on the streets” rather than a Church that is caught up in a slavish preoccupation with liturgy and doctrine, procedure and prestige. “God save us,” he exclaims, “from a worldly Church with superficial spiritual and pastoral trappings!” Urging a greater role for the laity, the Pope warns of “excessive clericalism” and calls for “a more incisive female presence in the Church”, especially “where important decisions are made.” 
Looking beyond the Church, Pope Francis denounces the current economic system as “unjust at its root”, based on a tyranny of the marketplace, in which financial speculation, widespread corruption and tax evasion reign supreme. He also denounces attacks on religious freedom and new persecutions directed against Christians. Noting that secularization has eroded ethical values, producing a sense of disorientation and superficiality, the Pope highlights the importance of marriage and stable family relationships."

Text from page 
of the Vatican Radio website

The document itself can be found here.

Sunday, November 24, 2013

The Concept of a Zombie: A Philosophical Parody

The Concept of a Zombie

(Or: On the Postmortem Survival of Conceptual Analysis)

It goes without saying that the recent outbreak of brain-eating corpses has been injurious to social order. But in addition to inspiring fear and panic in the man on the street, zombies have proved to be a source of headache for philosophers. For them it is apparently not enough to threaten our lives; no, they must call our concept of life itself into question. (And we thought phenomenal zombies were bad!)
Four positions jointly exhaust the logical possibilities, and they have all found adherents in the literature. One could think that zombies are (1) alive, (2) dead, (3) both, or (4) neither. In the remainder of this survey I will canvass each of these possibilities, and present some of the considerations that have been adduced for and against them.

Bioticists hold that zombies are (only) alive. Admittedly, they are not paradigm examples of living things, but neither are tomatoes paradigm examples of fruit, and yet by any reasonable biological criterion that is exactly what they are.  Analogously, bioticists argue, zombies satisfy the biological criteria for life: They consume nutrients (neurons and glia; i.e. brains), they can move, they reproduce (asexually, through biting), giving rise to “fertile offspring” (zombies who originate through biting can themselves bite people and create other zombies), and some of their cells can multiply, so they can heal themselves to a limited extent—military research has shown that the glia zombies consume are integrated into their nervous systems, while the neurons provide the raw material to repair the zombies’ neurons, or even grow new ones.  Moreover, bioticists claim, it just seems intuitively obvious that zombies are alive—it’s hard to deny, when being chased by a walking, groaning, to some extent intelligent neurovore that one is being stalked by a living thing. And one can’t leave out the linguistic evidence: When we shoot one in the head, electrocute it, or burn it to ash, we do most often say that we’ve killed it. Now, bioticists will say, it is surely conceptually impossible to kill something that isn’t alive; so, since it is part of our folk theory of zombies that we can kill them, it must be part of our folk theory of zombies that they are alive. That zombies are alive is thus part of common sense—and while common sense cannot be a satisfactory place at which to stop, it can hardly be a bad place from which to start.

Abioticists—or “dead-heads,” as they affectionately refer to one another—maintain that zombies are (only) dead. Abioticists admit that there is some (slight) linguistic evidence to regard zombies as living, but insist that on the whole common sense and science are against the idea. They are quick to point out that all zombies have died at some point—a trait shared by all clear cases of dead things! The mere fact that they have regained some bodily functions is not enough to make them alive again. Also, many zombies—all but the freshest—are in various stages of decay, another trait shared by all clear cases of dead things. Furthermore, zombies do not need to breathe, and for many of them their circulatory systems don’t even work, neither of which holds for any clear case of a living being that has a circulatory system.

In addition, Abioticists question how well zombies really satisfy the biological criteria for life. Sure enough—and unfortunately enough!—they move and consume nutrients, but the multiplication of their cells is partial at best, being restricted almost entirely to the nervous system. But most importantly, dead-heads maintain, zombies do not truly reproduce—the zombies that they “sire” are not new organisms at all, but rather pre-existing ones who die and become zombies themselves. Even viruses, when they reproduce, generate new copies of themselves, and biologists do not regard them as being alive. Finally, while zombies do sire other zombies, there is nothing like the inheritance of traits trough genetics or their alteration through evolution that typifies all known living organisms, a point frequently glossed over by bioticists.  A hundred generations from now, zombies will not be any better at hunting for brains than their ancestors of today—and thank God for that!
For zombie dual-aspect theorists—“zombie dualists,” or “zualists” for short—the term ‘living dead’ is not the oxymoron it may appear to be. Zualists think they can have the best of both worlds—zombies share many features with living things, and also with dead ones; hence, they are best regarded as both alive and dead. Unlike bioticists and Abioticists, zualists think they can account for all of the intuitions that underwrite our folk theory of zombies: Zombies are alive, which explains how it is conceptually possible for them to be killed. Nevertheless, they are also dead, which explains how it is conceptually possible for them to have died and to exhibit different stages of decay. And the fact that they satisfy some of the biological criteria for life while ambiguously satisfying others fits well with the idea that zombies are both alive and dead. Finally, the very popularity of the term ‘living dead’ bears witness, they claim, to the fact that the folk do not regard the concepts of life and death as incompatible.

Bioticists and Abioticists alike greet zualism with a stare as incredulous as the one received by those who first reported that corpses were rising from their graves. It seems just obvious to them that life and death exclude each other, just as red and green or motion and rest do. (This is especially so for those who hold the increasingly popular deflationary theory of death—that to be dead is simply not to be alive.) And it is not as though we have biological criteria for being alive and biological criteria for being dead, and that zombies satisfy both. It seems rather that we have only biological criteria for being alive, and that it is unclear whether zombies satisfy them.  And the popularity of the term ‘living dead’ shows little, if anything—people often respond to questions with “yes and no,” but would anyone regard that as a good reason to think that the folk are committed to dialetheism, let alone that it is true?

Last, but not necessarily least, we have the undeadites, who regard zombies as neither living nor dead. Undeadites agree with dead-heads that zombies do not fit the criteria for being alive very well; and like both dead-heads and bioticists, they have the intuition that nothing could be both alive and dead. However, undeadites share the bioticists feeling that it seems somehow wrong to think that anything capable of chasing you, catching you and eating your brain could be dead in the usual sense. They accordingly propose to reject the deflationary theory of death and hold zombies to have a third status, which they call ‘undead’. Like logical theories that posit a third truth-value, this view has not found much acceptance among mainstream philosophers. If anything is neither alive nor dead, it would seem to be natural objects like rocks or man-made artifacts like toasters, but most would not think of them as being “undead.” Or, to put the point more neutrally, most would not place them in the same category as a zombie. The problem is that while rocks and toasters have no relevant features in common with living things or with dead ones, zombies seem to have some of both.

It is my hope that you now have a better appreciation for the various views on the concept of a zombie. The dispute between bioticists, dead-heads, zualists and undeadites remains as lively as ever (please forgive the pun!), and will not be adjudicated anytime soon. If the past century has taught us anything, it is that conceptual analysis is hard. Nonetheless, I remain hopeful that we will have made some progress in analyzing this concept before its tokens overrun us, should that fateful day ever come!

Dilbert Schmyle

Oxford, 11/24/2013.

Friday, November 15, 2013

Proof that Logic Can Be Fun

Proof that Logic Can Be Fun:

Premise 1. If you consider the sub-proof SP, you'll see that logic can be fun:

Premise 2. You consider SP:

       Sub-premise 1. All valid arguments which have a false conclusion have at least one false premise.
       Sub-premise 2. This argument has a false conclusion.
       Sub-premise 3. So, if this argument is valid, it has a false premise.
       Sub-premise 4. But this is a valid argument.
       Sub-Conclusion. Hence, this argument has at least one false premise.

(Lemma 1: You're probably thinking: WTF?! Just what kind of argument is SP supposed to be?!)

Conclusion: See? Logic can be fun!

Thursday, October 31, 2013

Deep Thought of the Day: Meinongianism

There are plenty of sound arguments against Meinongianism, the only question is whether they exist.

Sunday, October 27, 2013

A Counterexample to Social Externalism?

Suppose there are two linguistic communities of (roughly) equal size, dispersed throughout a large area. Both speak dialects of the same language. One community uses the term 'arthritis' to refer exclusively to a painful condition of the joints, the other uses it to refer to any painful condition in one's limbs. There is a certain smaller region in which members of both communities are to be found, and in (roughly) equal numbers. There is, however, no “overlap”: Each speaker fully adopts the convention of his or her community, they do not sometimes adopt one usage and sometimes another. The dialects are alike in every other respect. Along comes Wyman, who does not speak the language. Wyman, however, comes to learn it, and eventually speaks it, to all appearances, just as the two communities do. But he is nevertheless unaware of the difference in usage with respect to the term 'arthritis'. One day he tells his doctor, “I have a horrible case of arthritis in my thigh.” One community would judge that what Wyman said was false; and the other, that it was true. Both could not be right.

The question is: What did the term 'arthritis' mean on that occasion? Which of the two communities' incompatible usages could it have been that determined what 'arthritis' meant in Wyman's mouth? He was unaware of any difference between the two communities, both are equal in size and equally prevalent in his area, and he interacted just as much with both. To say that Wyman “really” counts as a member of one community rather than the other, and thus that the term “really” had one meaning rather than the other, seems arbitrary. And externalists cannot say that 'arthritis' had both meanings, for then what he said would have been both true and false. If externalists were to say that it was indeterminate which meaning it had, they must admit that some matters are indeterminate—which, though many may be happy to do, might not be coherent. That the statement had no meaning is something I can understand, though I find it implausible for this case; but could it really be that it's determinate that it had one or other of those meanings, but not determinate which? But however that may be, I'm interested to see what my readers think.

Tuesday, October 22, 2013

Truth-making and Reference-making: Appendix


Some may have noticed that on my account, as it stands, bivalence will fail for empty nouns or noun-phrases. A false-maker for a sentence is defined as a reference-maker for its subject term which is not a reference-maker for its predicate term. If the subject term is empty, it has no reference, so false-makers are not defined for sentences of this kind. Neither are truth-makers, for a truth-maker for a sentence is defined as a reference-maker for its subject term which is also a reference-maker for its predicate term, for these sentences their subject terms have no reference-makers. If we require that every true sentence has a truth-maker and that every false sentence has a false-maker, such sentences will come out as neither true nor false.

Many, I take it, will unhappy with this result. To reinstate bivalence, I'll introduce the concept of a negative reference-maker, in analogy with the concept of a false-maker for a sentence. A negative reference-maker is something that makes it the case that a term does not refer to anything. In the case of nouns and predicates, we could also call them empty-makers, for they make nouns and predicates empty.

I will now define this concept, calling what I have previously called reference-makers positive reference  makers. I say that a noun has the proper class V of all objects (excluding proper classes) as its negative reference-maker iff it has no positive reference-makers. Similarly for monadic predicates. For relations, I say that an n-ary relational has the proper class of all n-tuples as its reference maker if it has no n-tuple as a positive reference-maker.

We can now give revised definitions of false-makers for subject-predicate and relational sentences:

An object x is a false-maker for a subject-predicate sentence p iff x is a positive reference-maker for p's subject term but is is not a positive reference-maker for p's predicate term. The proper class V of all objects is a false-maker for a subject-predicate sentence p iff V is a negative reference-maker for p's subject term or p's predicate term (or both).

An ordered n-tuple o is a false-maker for an n-ary relational sentence p iff the objects ordered in o are each positive reference-makers for one of p's subject terms, but o is not a positive reference-maker for p's predicate term. A proper class C is a false-maker for an n-ary relational sentence p iff C is a negative reference-maker for one of p's subject terms, or for p's predicate term, or both.

With these definitions ready to hand, we can see that sentences containing empty nouns or empty predicates come out as false rather than truth-valueless. "Nessie [a.k.a. the Loch Ness Monster] exists" comes out as false because the term 'Nessie', being empty, has the proper class V of all objects as its negative reference-maker, and so "Nessie exists" has V as its false-maker. Moreover, since "Nessie exists" has V as its false-maker, "It's not the case that Nessie exists" has V as its truth-maker. On the other hand, "Nessie is non-existent" comes out as false--if we construe 'non-existent' as a real predicate, then since 'Nessie' has V as its negative reference-maker, "Nessie is non-existent" has V as its false-maker. To me this seems intuitively to be the correct result: 'Nessie' is empty, so nothing is true of its referent--not even that it is non-existent--for it has no referent, so there's no "it". Nothing could possibly be non-existent.

However, "It is not the case that Nessie is non-existent" is true--since "Nessie is non-existent" has V has its false-maker, "It is not the case that Nessie is non-existent"has V as its truth-maker. Yet though "It is not the case that Nessie is non-existent" is true, it does not follow that "Nessie exists" is true--given that 'Nessie' does not refer, "Nessie exists" cannot be true for reasons just explained. What this shows is that "x is non-F" and "it is not the case that x is F" are  not in general equivalent expressions, for the former entails the latter, but not conversely: In some situations where its not the case that x is F, "x is non-F" can nevertheless be false due to the fact that there is no such thing as x. We thus have the following three results:

1. 'Exists' is a meaningful predicate which is necessarily true of everything;
2. 'non-existent' is a meaningful predicate which is necessarily true of nothing; and
3. there can still be false positive existential sentences and true negative existential sentences.

Not bad results to get, if I do say so myself.

Truth-making and Reference-making: Part 3

Part 3: Philosophical Implications

I think my approach has the advantage that it can explain why necessary truths don't have everything as a truth-maker. Granted, "The Earth has exactly one moon --> the Earth has exactly one moon" is true no matter what, but it does not therefore have everything as a truth-maker. By my definitions, a truth-maker for that material conditional is either a false-maker for its antecedent or a truth-maker for its consequent. As the antecedent and consequent are the same in this case, and as it is in fact true, every truth-maker for "the Earth has exactly one moon" will be a truth-maker for our conditional, and nothing else will. Truth-making, on my account, is not trivial for necessary truths, not even for paradigm cases of tautologies. A different instance of the Law of Identity, say "Sacramento is the capitol of California --> Sacramento is the capitol of California", will have (a) different truth-maker(s) from the previous instance. We can call such sentences 'analytic' if we like, in the sense that their meaning fixes their truth value--they could not have the same meaning, but a different truth value--but on this view it would be wrong to say that they are true solely in virtue of meaning. They have truth-makers, and they are not trivially made true by everything, nor will even different logical truths of the same form necessarily have the same truth-makers.

Another advantage of my account is that it enables one to dispense with a primitive, cross-categorical relation between objects (including sets) and truths. We can, if we wish, instead define necessitation in terms of truth-making (which itself is defined in terms of reference-making): An object x necessitates p iff x is a truth-maker for p. I count this as an advantage because we can now explain why an object necessitates the truth of p via reference-making, which itself can be explained via meaning, which itself 
can be explained via the use and/or causal history of terms. On an account like that of D. M. Armstrong, it would appear to be brute that an object necessitates a truth-bearer. Brute facts are not always a bad thing--"Explanation comes to an end somewhere", as Wittgenstein said. But, first, it seems odd that there should not be an explanation for the obtaining of the necessitation relation, when we are trying to account for how the truth of truth-bearers is grounded in reality. To explain it in terms of necessitation by objects, and then offer no explanation as to why objects necessitate the truths they do, seems little better than taking truth to be a primitive property which just happens to attach to some truth-bearers and not others. Second, it also seems odd  that an account of why truth-bearers are true would say nothing about how their truth depends on the reference and structure of their components. My account is designed to do exactly that, and in virtue of doing that it can explain why objects make true the truth bearers they do--which, in my opinion, is perhaps the only kind of explanation of this that can be had, and perhaps also the only kind of explanation of it that we should desire. 

My account is neutral with respect to the existence of facts or states of affairs. Objects and sets are the only entities that it posits as truth-makers. If the relation of reference-making that holds between nouns or predicates and objects or sets counts as a fact, or a state of affairs, then of course my account will not work without such entities; but given them, it needs no others. All other predicational, relational, truth-functional and quantificational sentences can be accounted for in terms of my definitions. And if the reference-making relation does not count as a fact or state of affairs, then my needs none of them at all.

My account is also neutral with respect to the existence of properties, including relations, and for much the same reasons as just stated. If reference-making counts as a genuine relation, then of course my account needs genuine relations to work, but it will need no others for the purposes of explaining truth-making. One may need to posit genuine properties for other reasons, but they are not items that my account is committed to. My account, then, is metaphysically chaste: If it requires any potentially dubious entities, it requires only the least amount necessary to achieve its purposes. I hope it should thus  be acceptable to philosophers of a variety of metaphysical persuasions.

For some final thoughts on truth-makers for negative truths, please see the Appendix.

Sunday, October 13, 2013

Truth-making and Reference-making: Part 2

Part 2: A Quasi-Formal Account

I will now define truth-makers for truth-functional compounds and quantified sentences. To define truth-makers for them, we  will also require the notion of a false-maker: We say that x false-maker for a subject-predicate sentence p iff x is a reference-maker for p's subject term but is not a reference-maker for p's predicate term.  For relational sentences, an ordered n-tuple o is a false-maker for an n-ary relational sentence p iff the objects ordered in o are each reference-makers for one of p's subject terms but o is not a reference maker for p's predicate term. 

We then define:

1a) An object x is a truth-maker for ~p iff x is a false-maker for p. A set s is a truth-maker for ~p iff some member of s is a false-maker for p. 

1b) An object x is a false-maker for ~p iff x is a truth-maker for p. A set s is a false-maker for ~p iff some member of s is a truth-maker for p. 

2a) An object x is a truth-maker for p & q iff x is a truth-maker for p and for q. A set s is a truth-maker for p & q iff some member of s is a truth-maker for p and some member of s is a truth-maker for q. 

2b) An object x is a false-maker for p & q iff x is a false-maker for p or for q. A set s is a false-maker for p & q iff some member of s is a false-maker for p or if some member of s is a false-maker for q. 

3a) An object x is a truth-maker for p v q iff x is a truth-maker for p or for q. A set s is a truth-maker for p v q iff some member of s is a truth-maker for p or if some member of s is a truth-maker for q. 

3b) An object x is a false-maker for p v q iff x is a false-maker for p and for q. A set s is a false-maker for p v q iff some member of s is a false-maker for p and some member of s is a false-maker for q. 

4a) An object x is a truth-maker for p --> q iff x is a false-maker for p or a truth-maker for q. A set s is a truth-maker for p --> q iff some member of s is a false-maker for p or if some member of s is a truth-maker for q. 

4b) An object x is a false-maker for p --> q iff x is a truth-maker for p and a false-maker for q. A set s is a false-maker for p --> q iff some member of s is a truth-maker for p and some member of s is a false-maker for q. 

5a) An object x is a truth-maker for p <--> q iff x is a truth-maker for p and for q, or if x is a false-maker for p and a false-maker for q. A set s is a truth-maker for p <--> q iff some member of s is a truth-maker for p and some member of s is a truth-maker for q, or if some member of s is a false-maker for p and some member of s is a false-maker for q. 

5b) An object x is a false-maker for p <--> q iff x is a truth-maker for p and a false-maker for q, or if x is a false-maker for p and a truth-maker for q. A set s is a false-maker for p <--> q iff some member of s is a truth-maker for p and some member of s is a false-maker for q, or if some member of s is a false-maker for p and some member of s is a truth-maker for q. 

6a) For a given, restricted domain of discourse: An object x is a truth-maker for a universally quantified sentence iff x is the only object in the domain and x is a reference-maker for the open sentence bound by the quantifier (I take open sentences to be predicates, and thus covered by what was said above). A set s is a truth-maker for a universally quantified sentence iff every member of s is a reference-maker for the open sentence bound by the quantifier.

6b) For a given, restricted domain of discourse: An object x is a false-maker for a universally quantified sentence iff x is not a reference-maker for the open sentence bound by the quantifier. A set s is a false-maker for a universally quantified sentence iff some member of s is not a reference-maker for the open sentence bound by the quantifier.

7a) For a given, restricted domain of discourse: An object x is a truth-maker for an existentially quantified sentence iff x is a reference-maker for the open sentence bound by the quantifier. A set s is a truth-maker for an existentially quantified sentence iff some member of s is a reference-maker for the open sentence bound by the quantifier.

7b) For a given, restricted domain of discourse: An object x is a false-maker for an existentially quantified sentence iff x the only object in the domain and x is not a reference-maker for the open sentence bound by the quantifier. A set s is a false-maker for an existentially quantified sentence iff no member of s is a reference-maker for the open sentence bound by the quantifier.

There may be some additional complications concerning open sentences which are truth-functionally complex and/or which involve nested quantifiers, but I take it that they can be accounted for in much the same way as above. (And remember, I only said that this was a quasi-formal account.) In any case, this much should suffice for the purposes of Part 3

Truth-making and Reference-making: Part 1

Part 1: Introducing the Idea

In this post I introduce the idea of reference-making, which I take to be more-or-less undefined, and use it to account for the idea of truth-making for subject-predicate sentences. I take a truth-maker to be a reference-maker for a sentence. In Part 2 I'll give a quasi-formal account of how it can be applied to truth-functional compounds and quantified sentences, and in Part 3 I'll discuss some of its philosophical implications.

Let us say that the reference-maker for a noun or a noun-phrase is just what is ordinarily called its referent,  the thing that it "corresponds to" or '"picks out" in the world. Nothing interesting so far. For predicates, however, the idea is different: Just as sentences can  have many truth-makers--"Planets exist" being made true by each planet--on this view a predicate can have many reference-makers, without thereby becoming ambiguous (as nouns/noun-phrases would become if they had many reference-makers). This is a key difference between predicates and nouns/noun-phrases. We will therefore say that predicates have reference, but not that they have referents. We could say that every reference-maker for F is a referent of F, but that would be misleading in that it would suggest that F was ambiguous. (This is a terminological point introduced to prevent confusion. Nothing beyond that hangs on our choice of terms.) A reference-maker for a predicate is something that it is true of, or that satisfies it. Any red thing is a reference-maker for the predicate 'red' or 'is red'. In this 'red' and 'is red' differ from 'redness', whose reference maker, if any, is redness; i.e., the property of being red.

Since I take the relation of predicates to reality to be, in general, one-many, I think it would be a mistake to take the "referent" or the semantic value of a predicate to be its extension, the set of things of which it is true. On my view, any reference-maker for a predicate can be said to be a semantic value of the predicate. Still, most predicates of  a given language will have but one meaning.

What of relational predicates? Their reference-makers can indeed be taken to be sets, namely ordered n-tuples. Still, we will not identify "the" semantic value of a predicate with its extension (nor with the property, if any, that it expresses): A reference-maker for an n-ary predicate is any ordered n-tuple of which that predicate is true, not the set of all such n-tuples--unless that set is one of the things of which the predicate is true; but still it would only be only one reference maker among many.

We can now say what a truth-maker, which is a reference maker for a sentence, is for subject-predicate sentences. An object x ('object' being broadly construed as anything that exists) is a truth-maker for a subject-predicate sentence p iff x is a reference-maker for p's subject term and is also a reference-maker for p's predicate term. Similarly, for relational sentences: An ordered n-tuple o is a truth-maker for an n-ary relational sentence p iff the objects ordered in o are each reference makers for one of p's subject terms, and o is a reference-maker for p's predicate term. In Part 2, I'll extend this account to define truth-makers for truth-functional compounds and quantified sentences.

Monday, October 07, 2013

The Rational Man

The Rational Man


Jason Zarri

A rational man took a stroll one day, 
and chopped some logic along the way.
Quoth he: "What should a logician say?
Does the law of bivalence hold fast come what may?
How could my mind know it, assuming it's true,
when with such abstract facts it has nothing to do?"

Repeating to himself the words 'what' and 'why,' 
he took little notice of passers-by.
Some laughed, some sang, some played, some cried,
but all the while he tried and tried
to discern what might happen once one has died.

As the day wore on, the skies grew dim,
the path rose up, and the air grew thin,
while he wondered at the heavens and the moral law within.
In his thoughts faint memories stirred, yet were silenced by the din.
One thing too painful to ponder: the life that could have been.

Wednesday, September 11, 2013

A Problem for Hume's Problem of Induction

Could Hume consistently believe that his argument to the effect that inductive inferences are not justified is successful? In this post I put forward reasons to think the answer is "no."

Hume, very basically, argued that inductive inferences are not justified because there are only two ways that that they could be supported: Either through a priori reasoning, or through further inductive inferences. A priori reasoning cannot support inductive inferences, because there is no contradiction in the supposition that the course of nature may change, and hence it is possible that it could. Nor could inductive inferences rest on further inductive inferences for their support, for they all rest on the supposition that the course of nature will not change, and cannot support that supposition without begging the question. Hence, inductive inferences are not justified.

Let's see what happens when we apply Hume's Fork to the conclusion of Hume's argument. We get the following result:

           "Inductive inferences are not justified" states either a relation of ideas, or a matter of fact.

If we accept the first alternative, then, if it's true, it only states a relation between certain of our ideas--namely, our ideas of justification and inductive inference--and says nothing significant about matters of fact. It is no more informative, in any real sense, than "a = a". If we accept the second alternative, it states a matter of fact, which according to Hume's own principles could only be confirmed or refuted through induction. If inductive inferences are justified, or justified for the most part, it cannot establish that they are unjustified. And if they are unjustified, they cannot justifiably establish their own lack of justification. Thus it seems that even if inductive inferences are not justified, Hume cannot justifiably believe that they are not. If one is inclined to accept Hume's argument, one should reject Hume's Fork as a false dichotomy; conversely, if one is inclined to accept Hume's Fork, one should either reject Hume's argument as unsound, or conclude that it may be sound, but if so, we cannot know that its premises are true.

Friday, August 02, 2013

Towards A Kinder, Gentler Verificationism

Towards A Kinder, Gentler Verificationism 

A Sketch of a Research Project

Jason Zarri

It often happens, for various reasons, that philosophers defend radical views which, first, are too radical to be plausible, and second, are such that a less radical and more plausible view would satisfy the underlying motivations. Here is a historical example. The logical positivists famously sought to eliminate traditional metaphysics by arguing that the statements metaphysicians make are meaningless because of being unverifiable. Much of the ensuing discussion concerned whether verifiability is really necessary for meaningfulness. But clearly, even if the logical positivists were wrong about this, they could still have a strong case for the elimination of metaphysics. For already if they could establish that the statements made by metaphysicians are unverifiable, they could argue for the pointlessness of the enterprise. If we cannot obtain good evidence for or against the statements of metaphysics, surely metaphysics is a pointless enterprise.
—Matti Eklund, “Rejectionism About Truth”, p. 1,

            I think it may be advisable to follow a wise point that lies buried in Logical Positivism: Though it may very well be that unverifiable statements are meaningful, and so true or false, this does nothing to prove they are legitimate objects of inquiry. For the statements the positivists sought to ban are, after all, unverifiable, and where there is no possible method of verifying a statement, there is seemingly no means of resolving disputes concerning it. Save in those cases where our psychology compels our universal assent, such as, perhaps, our belief in the existence of other minds, there is, short of force, coercion or sheer coincidence, no way to reach a consensus with respect to unverifiable statements, and given this it appears unwise to argue over them. For if we do not aim to achieve consensus, to what purpose do we argue? However, it must be admitted that verifiability comes in degrees, and there are perhaps no statements which are conclusively verifiable. Still, one can say that the harder it is to verify or refute a given statement, the less reasonable it is to argue over it. And of course to say that we shouldn’t bother arguing over something is not to say that we cannot have our own, private opinion on the matter.
None of this is to say that the positivists were correct in determining which statements are verifiable and which are not, only that we should not try to assess the truth value of statements which are genuinely unverifiable. I differ from the positivists in my estimation of the scope of the unverifiable. I think there may be a great many metaphysical, religious, and ethical claims which are verifiable. Furthermore, the methods of verification employed need not be empirical; they need only be capable of deciding the issue under examination, of resolving it one way or another. In light of this, I will henceforth talk of decidability instead of verifiability.        
In spite of the above qualifications, one might think that any verificationist-inspired project is doomed to failure for much the same reasons the Logical Positivists’ was. As hard as they tried to hammer out a workable verification criterion, everything they came up with proved to be either too strict or too liberal to suit their purposes. If one makes the criterion too strict, it will turn out, for example, that the notion of a natural law is meaningless, since one cannot verify that it holds in an infinite number of instances. Statements about the remote past, the far future, and theoretical entities would also go by the board. But if one liberalizes the criterion so that we count as meaningful statements about things that experience only renders probable, then one will have to admit things into one’s ontology that would make a positivist shudder, such as the “√©lan vitale” of the vitalists or the Absolute of the Absolute Idealists, if their existence would have any implications, however slight, for our experience. The verification criterion would then seem to impose no real constraints on the meaningfulness of statements. The simple fact is that no verification criterion could do what the positivists wanted it to do. One objection to my proposal, then, is this: Is not my “decidability criterion” dangerously close to a liberalized verification criterion? What, exactly, does the “decidability criterion” rule out?
My reply is that we should not try to deduce a priori that certain classes of statements are undecidable; for there is, I think, no single form or subject matter that unites all undecidable statements and makes them undecidable. In my opinion, the positivists’ failure to recognize this point is a major reason why their repeated attempts to formulate a workable verification criterion failed. And even if there were a single form or subject matter which all undecidable statements had in common, it seems unlikely that a priori reflection could discover it. (One reason to think this is that the sustained a priori reflection of the positivists failed to discover it.) Instead, we should look to the past to see what kinds of statement have proved easy to decide and which have not. My criterion, then, would counsel us to reject statements which are of the same kind as those which history has shown to systematically resist attempts at resolution. In future work, my task will thus be to show that this criterion imposes non-trivial constraints on philosophical practice.
            I intend to develop my own kinder, gentler verificationism by using the views of Rudolf Carnap as a foil. Though I sympathize with several facets of his position, and with the motivation behind them still more, I think there are a few important points about which he was mistaken. First, his conception of what philosophical practice should be is excessively formal; it focuses too much on language, and it seems to allow no room for the vagueness or open texture of words and concepts; and it also seems to rule out Wittgensteinian “family resemblances”.
            Second, his distinction between “internal” and “external” questions is too sharply drawn. If we consider “frameworks” that are actually in use, in both the sciences and in the humanities, I think we will find that it is not always so clear what counts as part of a framework and what doesn’t. Also, I doubt very much that pragmatic considerations are the only things relevant to the selection of a framework. Furthermore, there may be an objective truth—one transcends any particular framework—even if we can’t know what it is.
            Finally, Carnap’s views were bound up with the philosophy of language of his day, before the advent of externalism and causal theories of reference, and stand in need of substantial modification.
            As for my own account, I will try to accommodate the lessons we learned about language and categorization from Wittgenstein and the theories in cognitive science that his work helped to inspire, such as prototype and exemplar theories of concepts. Also, on my view, we might be able to attain knowledge of objective truth without having to “step outside” of our various frameworks—though we might also be able to know the objective truth by doing so, if doing so is possible—by comparing our frameworks themselves against each other and seeing what, if anything, they have in common. If all the viable, mutually comparable frameworks concerning a given subject matter agree about something, I think that is good evidence that it is probably true, provided that the different frameworks come close to exhausting the possibilities. (This is, in essence, a generalization of my approach for getting eithical guidance from ethical theories.) And I see no reason why our frameworks need to be (solely) linguistic. I will also try to give an account which is consistent with causal and externalist views on reference and mental content. And on my view, what counts as evidence for what is in part determined by what “context of inquiry” one belongs to, among other things, and so my view of evidence is in some sense externalist.
            In spite of the differences I have just spelled out, Carnap and I  have something important  in common: we both put great stress on engaging in disputes only if there is some way of resolving them.