Sunday, January 19, 2014

Truth-making and Reference-making: Revised and Expanded

A revised and much expanded version of my series of posts on truth-making and reference-making--including criticisms of previous theories, a reply to Greg Restall's arguments for the triviality of the truth-making relation, and answers to several objections--is now available here on Scholardarity, for only ten cents!

The problem of how best to explain the truth-making relation is a vexed one for truth-maker theory. As Raimi points out in his introductory survey, theories of this relation face four main difficulties:
An adequate definition of the truth-maker relation must satisfy at least four conditions. It should not fall victim to any of the following problems: (i) the problem of counterintuitive truth-makers; (ii) the problem of excluded truth-makers; (iii) the problem of missing truth-makers; and (iv) the problem of unnecessary truth-makers. A definition falls victim to the first problem if it classifies as truth-makers for a certain proposition entities that are intuitively not truth-makers for this proposition. It falls victim to the second problem if it fails to classify as a truth-maker for a certain proposition an entity that intuitively is a truth-maker for this proposition.  It falls victim to the third problem if it fails to account for any truth-maker for a certain proposition that intuitively has a truth-maker. Finally, it falls victim to the fourth problem if it classifies a truth-maker for a proposition that intuitively has no truth-maker. (Truth and Truth-Making, pp 13-4)
            In this paper I propose an account which I hope will not succumb to any of these problems. Section 2 sketches a couple of the major accounts that have been given of the truth-making relation, and explains what their problems are. In Section 3 I explain the basic ideas behind my own proposal, where I introduce the idea of reference-making, and use it to account for the idea of truth-making for subject-predicate sentences, taking a truth-maker to be a reference-maker for a sentence.  In Section 4, I give a quasi-formal account of how it can be applied to truth-functional compounds, quantified sentences, and modal sentences. Section 5 gives a reply to Greg Restall’s arguments that logical considerations lead quickly to the trivialization of the truth-making relation: that everything is a truth-maker for every true truth-bearer. I show that this does not hold for my approach, and in the process show how it avoids problem (i). Next, in Section 6 I discuss some of its philosophical implications. Then, in Section 7, I show how my account, contrary to first appearance, can be tweaked to avoid truth value gaps. Section 8 answers objections to my views. Finally, I conclude the paper in Section 9. 

Thursday, January 09, 2014

Philosophers' Carnival #159

Due to formatting Problems, the Carnival has been moved here.

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!