Is the Possible Necessarily General?

I'm not going to try to settle this question right now, but merely to point out some of the consequences of answering it with either a 'yes' or a 'no'.

Charles Peirce once said "The possible is necessarily general; and no amount of general specification can reduce a general class of possibilities to an individual case." (Collected Papers 4.172). If this is right, then it seems to me that certain consequences follow:

(1) Merely possible worlds contain no individuals. Hence, no individual (not even God) exists in all possible worlds or in any world but the actual one.
(2) The coming into being of the actual world is not simply the instantiation of a possible world but its individuation.
(3) Divine providence of necessity must be general, not meticulous. That rules out Molinism and Augustinianism, but leaves room for either process theism or versions of open theism that limit omniscience.

In contrast to Peirce, I am inclined to hold that possible worlds are just as individuated as the actual world. If this is right, then,

(1') Merely possible worlds do contain individuals. Hence, it is possible that some individuals exist in multiple worlds.
(2') The coming into being of the actual world just is the instantiation of a possible world.
(3') Divine providence need not be general, but may (though I think need not) be meticulous. All of the competing providential options are still on the table (at least as far as this issue goes).

I should note that, in contrast to possibilists like David Lewis, I do not think that all possible worlds are ontologically on par with each other. There is one, the actual world, that uniquely obtains. All others "exist" in some abstract sense, perhaps in the mind of God.

Of Unicorns and Possible Worlds

A few posts back I suggested that there might be two senses of "exists": (1) a "there is" sense that functions linguistically as a second-order predicate (i.e., it says of a concept or predicate expression that its extension is non-empty), and (2) an "is actual" sense that functions linguistically as a first-order predicate of individuals.

I tried to support this distinction by appealing to what seem to be noncontroversial cases of possible but non-actual things (like dinosaurs, unicorns, the WTC, etc.). Consequently, it seems right to say that "There are possible things that do not exist." But for that to make sense, what is affirmed by "there are" cannot be what's denied by "do not exist". With two senses of "exists", however, this can be read without contradiction as saying "There are possible things that are not actual."

Commentator Ocham disputes my logic. He thinks I'm guilty of fallaciously reasoning from

(1) Possibly, there are unicorns.
to
(2) There are possible unicorns.

Perhaps I am guilty of some simple mistake like this, but I don't think so. In the interests of furthering discussion I'm going to try and restate my argument in more precise logical terms using possible worlds semantics.

Let A be the actual world, let U be a possible world accessible from A, and let U contain unicorns. Then, the following are true:

(3) It is not the case that unicorns are actual. (b/c A does not contain unicorns)
(4) It is possible that unicorns are actual. (b/c U does contain unicorns and is accessible from A)

I take (4) to say the same thing as (1).

Notice, we have here two distinct possible worlds, A and U. But if we can have two of a thing, then we can quantify over it. So let's quantify over possible worlds. The usefulness of this is that it allows us to restate (4) without using any modal qualifiers.

Let w be a variable that ranges over possible worlds, and let x be a variable that ranges over all individuals within a possible world. Also, let W_ stand for "... is a world", let U_ stand for "... is a unicorn", and let _E_ stand for "... exists (is actual) in ...". In these terms, (4) states:

(4') (∃w)(Ww & (∃x)(xEw & Ux))

which is just a generalization of the claim that U is a possible world that contains unicorns:

(5) (∃w)(Ww & w=U & (∃x)(xEU & Ux))

Ex hypothesi, the quantifiers (∃w) and (∃x) cannot mean "is actual" because we're quantifying over possible worlds and their contents without implying anything about whether they are actual or not. The predicate _E_, however, denotes world-relative actuality, which in the actual world A reduces to actuality simpliciter (i.e., xEA ↔ x is actual).

In light of the foregoing, my argument for two senses of "exists" can be restated as follows: We can quantify over non-actuals. Hence, if, in Fregean terms, existence is simply the denial of the number nought, there must be a sense of "exists" that does not imply actuality. On the other hand, we need to distinguish between actuals and non-actuals. Hence, we need a sense of "exists" that does imply actuality.

Actuality and Two Varieties of Possibility

In my previous post I contemplated the idea that actuality is the ontological delimiter of possibility (ODOP). That's a mouthful, but what it means basically is that the reason why one thing is possible rather than another is because something that already exists precludes some things from happening and not others. Here's a simple example: given the actual laws of nature, it is possible that a rock that is dropped will fall but (virtually) impossible that it will remain suspended in mid-air.

Matters are complicated, however, by the fact that there are different types of possibility. The example I just gave has to do with physical possibility. What is physically possible at a given time is delimited by the laws of nature and the physical state of the world at that time.

Another important type of possibility is logical possibility. Generally, something is logically possible if and only if there is a maximal, internally consistent state of affairs (a possible world) in which it exists. For example, is seems that there is a possible world that is just like our world except for the fact that the way colors appear is inverted--what appears red to us in this world appears blue to people in the other world, and vice-versa. Logical possibility is delimited by the laws of logic--most importantly, the law of non-contradiction--because that is what determines whether a maximal state of affairs is internally consistent or not.

There may be other types of possibility as well, but we can set them aside for now. It is important to note, however, that physical possibility is also constrained by logical possibility because physical possibilities are realized within the scope of a given possible world. It's natural, then, to focus first on logical possibility.

The issue now is this: If actuality is the ODOP, including logical possibility, then there must be some sort of reality that transcends all possible worlds. In other words, if W and V are different possible worlds then the actuality that delimits them both cannot be something that is merely actual in W or actual in V. Instead, it must be actual in both of them. And if there are other possible worlds, then it must be actual in them as well. In short, it must have universal transworld actuality. That, by the way, is what it means to be a logically necessary being.

So it seems that the thesis that actuality is the ODOP not only rules out the possibility of a null world (as I argued in the last post) but also requires sort of logically necessary being (or beings?). Moreover, since it is the laws of logic that delimit logical possibility, the laws of logic must either (a) be identical with this necessary being, (b) be part of this necessary being, or (c) be a production of this necessary being.

The examination of these options will have to wait for another post. One would I think be right to suspect at this point that the view that actuality is the ODOP looks rather favorable to theism. Conversely, Lewis's deflationary view of actuality is more amenable to atheism--as he points out in a follow-up to his "Actuality and Anselm" essay, his view of actuality gives him a fairly straightforward way of deflecting teleological (design) arguments for God's existence.

If this is right, then debates on the nature of existence and actuality are not neutral vis-a-vis theism and atheism. That recognition should, I think, give this issue greater importance than it generally receives in philosophical discussion.

Actuality is the Ontological Delimiter of Possibility

I'd like to take this idea out for a test drive. If actuality is the ontological delimiter of possibility (ODOP), what follows?

Offhand, it conflicts with the idea that possibility is ontologically prior to actuality, an idea that might seem attractive given that the actual world is generally thought to be one of a vast number of metaphysically possible worlds. On this picture, we start with a vast ensemble of possible worlds and either (a) one of these possible worlds is somehow "anointed" as the actual world, or (b) actuality is a reflexive relation between each possible world and itself.

The problem with (a) is that this "anointing" would have to come from outside the set of possible worlds, but that makes no more sense than something's coming from nothing (Some may beg to differ, but ex nihilo nihil fit seems to me nearly as secure as the cogito.). By definition nothing can be outside the set of possible worlds.

The problem with (b), as I see it, is its deflationary treatment of actuality. Actuality, according to (b), is nothing special, since every world has it in exactly the same sense. (As the character Dash from The Incredibles reminded us--yes, I liked the movie--"If everyone's 'special' then no one is.") But what's wrong with a deflationary treatment of actuality? If a philosophical all-star like David Lewis endorses it (see his "Anselm and Actuality" in Philosophical Papers, vol. 1), it's got to have something going for it, right? What, he asks, could possibly make the actual world so special? That's a good question and I'll answer it with a question.

What makes possible worlds possible? Why, for instance, is our world possible whereas a world containing square-circles is not? The laws of logic, you say. Fine, I agree. But how could the laws of logic do that if they weren't actual in the first place? How could non-actual laws of any sort constrain anything at all? I don't see how. My argument contra Lewis is therefore also an argument that actuality is the ODOP. If a deflationary account of actuality is accepted, then there is no way to account for the possibility of what is possible, including the alleged real possibility of actuality's being as the deflationist thinks. Hence, we must reject the deflationary account of actuality and recognize that actuality is ontologically prior to possibility. What makes the actual world so special? The very fact that it is the ontological delimiter of possibility.

I'll close with one more observation. If my thesis is correct, then a null world--one of absolute nothingness--is not an intelligible possibility. Its possibility would nullify its possibility. Consequently, there can be no null world. It is necessary that something exists.

It occurs to me just now that I've got to refine my view of the "actual world" to account for the difference between logical and physical possibility. I'll do that tomorrow.

Are There Non-Existent Objects?

The question may seem an odd one. If read as asking "Do there exist any objects that do not exist?" the answer is obviously No because the question presupposes a contradiction. But there is another way of reading the question that can be gotten at if we reflect on the relation between actuals, possibles that are not actual, and impossibles. Here are some uncontroversial examples of each:

Actuals: dogs, cats, grass, the Eiffel Tower, the Sun, etc.
Non-Actual Possibles: unicorns, the twin towers of the World Trade Center (they were actual, but are no longer), dinosaurs, etc.
Impossibles: Square circles, married bachelors, four-sided triangles, etc.

Now, in one sense of the word, to say something "exists" is to say that it is actual or real. But that can't be the sense implied when we say that something "is" possible but non-actual or that something "is" impossible because both of those categories exclude actuality. So we have to recognize at least one additional sense of "exists" besides "is actual". What could that sense be?

We can begin by noticing that the class of non-actual possibles and the class of impossibles are both non-empty. This fits nicely with Frege's claim that "affirmation of existence is ... denial of the number nought." Following Peter Geach, I'll call this the "there is" sense of "exists". This is the sense being used in a sentence like "There is a possible world in which JFK dies a natural death." Obviously, this is not saying that such a world is actual, but only that the class of possible worlds includes at least one in which JFK dies a natural death. In other words, the class of possible worlds in which JFK dies a natural death is non-empty.

With this distinction between the "actuality" and the "there is" senses of "exists" we can now read the opening question as follows: "Is the class of non-actual objects non-empty?" In light of the examples of impossibles and non-actual possibles above, the answer to this question would appear to be Yes.

This raises an interesting question: What is the ontological status of non-actual (or "mere") possibles and of impossibles? On the one hand, we don't want to reify them à la Meinong into quasi-actual entities that have a sort of independent existence [Addendum: Bill Vallicella informs me that this is not an accurate statement of Meinong's view.]. On the other hand, we don't want to dismiss them as irrelevant. Practically speaking, it makes a difference whether the things we attempt are really possible or not. My offhand thought is that to avoid both extremes we need to say that possibility and impossibility are parasitic on actuality--something is really possible iff what is actual does not preclude it and really impossible iff what is actual does preclude it.

Two Types of Methodological Naturalism

It is often claimed nowadays that "science", by definition, can only invoke "natural" causes as explanations, where "natural" causes are restricted to entities or laws that will presumably find inclusion in a completed form of physics or to things that are either ontologically reducible to or strongly supervenient on such entities and laws. In short, according to this view "science" has to approach the world as a causally closed physical system. Let's call this view strong metaphysical naturalism (SMN).

Now, I think this is the wrong way to define "science" for the reasons that I give here. But many people are apt to think that there is something right about SMN. After all, if we don't place any restrictions on what types of explanations are permissible, then don't we open the floodgates for all sorts of pseudo-scientific nonsense to masquerade as genuine science? How else could we exclude from science 'magical', paranormal, and miraculous explanations? Certainly a rational person ought to be very cautious if not downright skeptical about such explanations.

I'm very sympathetic to such concerns, but SMN is not the answer. So far as I can see, there's nothing intrinsically wrong with magical, paranormal, or miraculous explanations. I certainly don't want to rule out such things a priori on the off-chance that such explanations just might, on occasion, be correct. The problem with pseudo-scientists is not the types of explanations they propose but the fact that they invoke such explanations way too soon, before properly looking for and excluding the plausible alternatives. This leads to what I call weak methodological naturalism (WMN), which says that in science natural explanations are to be preferred over non-natural explanations unless there are no plausible natural explanations and there is good reason to think that no plausible natural explanation will be forthcoming.

The basic idea behind WMN has been captured by ID-theorist William Dembski in what he calls the 'explanatory filter': "Roughly speaking the filter asks three questions and in the following order: (1) Does a law explain it? (2) Does chance explain it? (3) Does design explain it?" Thus, explanations in terms of deterministic or stochastic natural laws need to be ruled out (i.e., shown to be implausible) before it is reasonable to appeal to chance or luck, and chance needs to be ruled out before it is reasonable to appeal to design. And, extending this further, it seems to me that appeals to little 'd' designers ought to be ruled out before we are justified in appealing to a transcendent Designer-God. In short, there's an appropriate epistemological order of explanation that good scientific methodology will respect. Miracle-type hypotheses are not ruled out a priori, but they do face a stiff burden of proof.

The Hitchhiker's Guide to Nihilism

I read Douglas Adams' Hitchhiker's Guide to the Galaxy series a few years ago. I found it hilariously funny overall, but by the time I got all the way to the end of the so-called "5-volume trilogy" it had become quite clear to me that Adams' worldview is fundamentally nihilistic. In other words, existence is utterly pointless and absurd. Perhaps the most well-known and obvious piece of evidence for this is the obviously silly claim repeated throughout that the answer to the question of the meaning of Life, the Universe, and Everything is '42'. Another strong piece of evidence (without revealing any spoilers) is how the final novel comes full-circle back to where the first one starts--we go through 5 books only to find that absolutely no meaningful progess is made.

I could go on, but what I'll say instead is that once I realized the nihilist undertones of the series, it actually detracted from the humor for me. What is the sense of laughter--that is to say, real hearty laughter, the kind that flows from what C. S. Lewis called "joy"--if life, the universe, and everything is meaningless? Why not weep instead? As T. S. Eliot put it: "This is the way the world ends; not with a bang, but a whimper."

But nihilism is a non-starter as a worldview--if it's true, there can be no good reason to believe it, and hence no good reason not to believe something else, because the very notion of a "good" reason is rendered vacuous given nihilism. So count me a metaphysical optimist. Life matters. Our choices matter. To quote the movie Gladiator, I believe that "what you do now will echo in eternity."

While I reject the worldview of the Hitchhiker novels, if I set the nihilism aside, they are funny. Here's one of my favorite passages (It's best read aloud in a projecting voice):

Far back in the mists of ancient time, in the great and glorious days of the former Galactic Empire, life was wild, rich and largely tax free. Mightly starships plied their way between exotic suns, seeking adventure and reward among the farthest reaches of Galactic space. In those days spirits were brave, the stakes were high, men were real men, women were real women and small furry creatures from Alpha Centauri were real small furry creatures from Alpha Centauri. And all dared to brave unknown terrors, to do mighty deeds, to boldly split infinitives that no man had split before--and thus was the Empire forged.

Is Religion Just for the Weak?

Sage thoughts from the Maverick Philosopher:

Jesse Ventura: “Religion is for the weak!” Religionist: “No it’s not!” Such knee-jerk opposition avails nothing. Ventura is in fact right. What Ventura doesn’t appreciate, however, is that we are all weak. The correct response to Jesse the Body is not one of diametrical opposition but one of ju-jitsu-like concession.

We are all weak relative to a standard of true strength. We are weak in body, in mind, in will. We vacillate in our affections. A body that can lose its strength in a split-second due to a brain aneurysm, say, is only relatively, contingently, and temporarily strong. Such strength is nothing to brag about. Or is Ventura’s strength so awesome that it is proof against every contingency? Can he maintain it indefinitely? Is he causa sui? If not, then why is he so proud of his prowess?

The great religions teach the simple truth about our weak and indigent condition. (Whether these religions provide a genuine solution to it is another question.) The proper counter to Ventura is to point out to him that the sense in which he thinks that religious people are weak is not the sense in which they know that we are all weak. Religion is not a projection of the merely contingent weakness of some of us, but a sober recognition of the necessary weakness of all of us. Religion doesn’t exist to make good the deficiencies that we can and must make good by our own efforts, but to ameliorate the deep-going deficiencies that none of us can ameliorate individually or collectively.

Philosophical Latin in Translation

Anyone who reads much philosophy will encounter a lot of Latin phrases. Leaving formal and informal fallacies out of it, the following are some of the most common. I have translated for the uninitiated.

a fortiori - all the more so; e.g., if you can refute a more general or more plausible version of a thesis, then it follows a fortiori that more specific and/or less plausible versions of that same thesis have been refuted.

a posteriori - known or believed on the basis of looking around and seeing that it is so; e.g., we know a posteriori that cats like milk--no one could have arrived at that conclusion apart from observation.

a priori - assumed or knowable at the outset, without looking around to see if it's so; e.g., we know a priori that, necessarily, a part cannot be greater than the whole of which it is a part--we see this with the "eye of the mind", so to speak; no set of empirical observations could show that this is a necessary truth.

ceteris paribus - all other things being equal.

ex hypothesi - according to the hypothesis currently under discussion.

mutatis mutandis - with the appropriate changes.

pace - contrary to, as in "pace Hume, the self is not just a 'bundle of impressions.'"

simpliciter - without qualification of any sort; e.g., one might say that a proposition is true-at-a-time if and only if what it posits is true at that time, but what then does it mean to say that a proposition is true simpliciter (i.e., independently of the "at a time" qualifier)?

sui generis - in its own unique category; not reducible to other categories.

Science and Methodological Naturalism

In yesterday's post I gave some background on the Intelligent Design (ID) debate and noted that an increasingly popular move by the mainstream scientific establishment has been to stipulate that "science" requires methodological naturalism. In other words, the claim is that properly "scientific" explanations can only make reference to 'natural' laws and entities, the kinds of laws and entities that would presumably find inclusion in a completed form of physics. Accordingly, any appeals to "designers" may only be to finite designers the existence of which can ultimately be explained by a naturalistic evolutionary-type process.

What I want to argue today is that invoking methodological naturalism as an essential characteristic of science is going to backfire on the mainstream scientific establishment.

First, this way of defining "science" is historically and philosophically arbitrary. Prior to the rise of Darwininsm and Comtean positivism in the 19th century, no one--not Galileo, not Newton, not Kepler, Boyle, you name it--would have thought to define "science" in terms of a commitment to methodological naturalism. Instead, beginning all the way back with Aristotle, the various sciences were defined in terms of the object of their study, not the types of explanatory entities they were allowed to invoke. Thus, physics was (roughly) the study of the mechanical properties of things, biology was the study of organic and living things, psychology the study of cognitive, emotional, and volitional phenomena, and so forth. Accordingly, Newton saw no problems with drawing God into his physics as the ground for his absolute space and time. He certainly didn't think he was stepping outside of science at that point. What may seem even more surprising is the fact that theology was regarded as a science (during the Middle Ages it reigned as the 'queen of the sciences'), and so was philosophy. In fact science and philosophy were practically coextensive. Galileo and Newton did not think of themselves as 'physicists' or 'astronomers' but as natural philosophers (i.e., philosophers who were trying to understand the natural world).

What history shows is that it's the methodological naturalists who have "re-defined" science, not the Intelligent Design theorists. And they have re-defined it in a way that undermines it's epistemic authority. Let me elaborate.

Noted 19th-century logician, philosopher, and scientist Charles Sanders Peirce argued that to "block the road of inquiry" was to commit a cardinal sin against rationality. To "block the road of inquiry" is to set up a priori restrictions on where inquiry can go and on what kinds of answers it can reach. The reason why Peirce saw this as a sin against rationality was because it takes our focus off of truth and insulates certain 'pet theories' from potential refutation. It's like saying "I've made up my mind about X, Y, and Z, and I refuse to countenance any evidence weighing against those opinions." Such dogmatism, Peirce held, is antithetical to the spirit of science. Ironically, in the name of promoting genuine "science", the mainstream scientific establishment wants to do the very thing that Peirce held to be fundamentally antithetical to science, i.e., block the road of inquiry. What they are saying, in effect, is that the only answers that will be tolerated are naturalistic answers.

But what if, in fact, some of the answers are not naturalistic? What if God really did have something to do with how things got to be the way they are? If that is so, then by embracing methodological naturalism the scientific community has guaranteed in advance that they will get the wrong answers to the questions in whatever areas God may have intervened. (And how can we know for sure in advance which areas those are?) Under this scenario, science could not be trusted to get the right answers, the true ones, because they scientific community isn't aimed at truth (whatever that may turn out to be), but rather at finding the best available naturalistic explanation. In other words, science will have been pressed into the service of insulating the 'pet theory' of naturalism from potential refutation.

The only way to have a globally truth-tropic science while restricting yourself to methodological naturalism is for metaphysical naturalism to be the case. If metaphysical naturalism is true then the natural world is all there was, is, and ever will be, in which case adopting methodological naturalism will tend to help science get to the truth rather than pull it away. But metaphysical naturalism is far from obviously true. Any suspicions we may have that metaphysical naturalism is not the case (and, as Intelligent Design theorists and other have repeatedly pointed out, there are plenty of grounds for suspicion) raise doubts about the extent to which a methodologically naturalistic "science" can be truth tropic, and consequently undermine the epistemic authority of such a "science". Such doubts won't bother those who are already convinced of metaphysical naturalism, but to define science in naturalistic terms completely begs the question against Intelligent Design theorists, who want to leave room for nonnaturalistic explanations should the evidence point that way.

Intelligent-Design and the Nature of Science

In the wake of a recent Pennsylvania court case there has been a lot of discussion about the scientific status (or lack thereof) of "Intelligent Design" (ID), an intellectual movement initially spearheaded by the works of Phillip Johnson and then picked up by Michael Behe, William Dembski, and a growing chorus of scientists, philosophers, and scholars. The basic tenets of ID are these:

(1) There are rigorous empirical tests (Behe's 'irreducible complexity'; Dembski's 'specified complexity') for detecting that something has been designed (i.e., is the product of mind).
(2) When applied to biological systems (esp. their biochemistry) and to the fine-tuning of the universe, these tests yield the result that, probably, many aspects of such systems have in fact been designed.

Now, while the major ID proponents (Behe, Dembski, Meyer, etc.) have been careful to draw only modest conclusions from these points that fall far short of claiming a proof for theism, many have been much more forthright in pointing out the theistic implications. And this has scared the mainstream scientific establishment, which has quite literally been thrown into a panic about this new "stealth creationism". Many scientists and some philosophers believe that ID is inherently "unscientific" or even "anti-scientific". Accordingly, they believe that any serious discussion of ID in a scientific setting constitutes a deleterious undermining of science itself. But is this so? Is ID inherently opposed to genuine science?

The first thing we must recognize is that the question of the nature of science is not a scientific question, but a philosophical one. And one thing that most philosophers of science have recognized for some time now is that it is very hard to define "science" in such a way that it is going to rule out ID without at the same time ruling out many other things that uncontroversially qualify as scientific, e.g., SETI, crytography, anthropology, etc.--all of which presuppose that design can be empirically detected.

There is one demarcation criterion that seems to do the trick, however. Accordingly, it has been repeated over and over, mantra-like, by the scientific establishment in their protests over ID. That criterion is ... (drum role) ... methodological naturalism, the claim that science can only appeal to natural causes as explanations. This criterion would rule out any theistic applications of the "design inference" without jeopardizing the status of SETI, etc.

But there are some big problems with this appeal to methodological naturalism as an essential characteristic of science. Indeed, I think it is likely to backfire on the scientific establishment, as I'll explain tomorrow in a follow-up post.

Tarksi's T-Schema, Truth-Conditions, and Senses

On a tip from hammsbear, I took a look at Peter Ludlow's article, "Do T-Theories Display Senses". Here are some of my thoughts on that article.

Tarksi's T-schema ("p" is true iff p) is often used to spell out the truth conditions for sentences. Thus, "snow is white" is true iff snow is white. ('iff' is short for 'if and only if')

By "senses" Ludlow means the ways in which something may be referred to. For example, "the Evening Star" and "the Morning Star" both have the same referent, namely, the planet Venus, but they pick out Venus in different ways, by appealing to different properties. Similarly, the names "Cicero" and "Tully" both refer to the same individual, Marcus Tullius Cicero. So they have the same referent. But they have a different sense because they pick out that individual in a different manner.

The question Ludlow raises is whether or not the expression on the right-hand side (RHS) of the T-schema can give information about the various "senses" of the expression on the LHS,. On the one hand, it seems that "Cicero is bald" and "Tully is bald" should have the same truth-conditions because they refer to the same individual. Thus,

(1) "Cicero is bald" iff Cicero is bald.
(2) "Tully is bald" iff Tully is bald.
(3) "Cicero is bald" iff Tully is bald.
(4) "Tully is bald" iff Cicero is bald.

On the other hand, suppose there is a person S who knows that Cicero is bald but does not know that Cicero=Tully. Such a person would affirm (1) and (2) but would not affirm either (3) or (4), in which case, (1)-(4) do not properly characterize S's semantic competence.

Here's how I understand this (and, mind you, I'm not a specialist in the philosophy of language):

Sentence tokens like "Cicero is bald" and "Tully is bald" have the same truth-conditions iff they express the same proposition. They express the same proposition iff they reflect the same belief on the part of the speaker. If, therefore, S believes that Cicero is bald and has no belief about whether Cicero=Tully or whether Tully is bald, then S's token "Cicero is bald" has the truth-conditions given in (1). If, however, S not only believes that "Cicero is bald" but also believes that Cicero=Tully, then the truth-conditions of S's token "Cicero is bald" may be given by either (1) or (3) or, more fully, by

(5) "Cicero is bald" iff Cicero/Tully is bald.

In (5) information about the senses is given in the RHS of the T-schema (by the '/' notation) and (5) does properly reflect S's semantic competence.

So I'm inclined to think, contra Ludlow, that information about senses can be supplied on the RHS of a T-schema expression when it does reflect the semantic competence of the speaker. The same state of affairs is being referred to in (1) and in (5), but (5) reflects a more extensive knowledge on the part of the speaker as to what that state of affairs is.

What To Do About Iran

Victor Davis Hanson provides an analysis of the options concerning Iran. In brief: It's a nasty situation that's only likely to get nastier unless decisive multilateral action is taken soon.

Sentence Tokens and Truth Conditions

I'm still reading Smith's book (Language and Time), and I've noticed that Smith, along with everyone he's critiqued thus far, makes an assumption about the truth conditions of sentence tokens that, frankly, seems false to me.

First, let me explain what a sentence token is. Consider the sentence "It is raining" uttered on two separate occasions. In the first instance, Bob utters "it is raining" at 2pm EST in Peoria, Illinois; in the second, Sally utters "it is raining" at 8am in Lihue on the island of Kauai. Each is an utterance of the same sentence type because it consist of the same string of words; nevertheless, each is an utterance of a distinct sentence token. So in these two instances we have two sentence tokens of one sentence type, namely, "it is raining."

Now, if you were able to follow that, then you should also be able to see that the two sentence tokens, uttered under the specified circumstances, would normally differ in meaning. The first would seem to say

(1) It is raining at 2pm EST in Peoria, Illinois.

whereas the second would seem to say

(2) It is raining at 8am EST in Lihue, Kauai.

Now, the assumption that Smith and nearly everyone else working in the philosophy of time make is this:

(3) A sentence token uttered at time T and place P is true if and only if what the sentence asserts is true at that time and place.

What (3) implies is that Bob's utterance of "it is raining" is true only if (1) is true and Sally's utterance of "it is raining" is true only if (2) is true. Thus (1) and (2) give the truth conditions for Bob's and Sally's utterances, respectively.

This seems mistaken to me. Here's why. When we consider what a particular sentence token means, we not only take into account the spatiotemporal context of the utterance, but we also factor in what we make of the doxastic (i.e., belief) state of the speaker. And if we don't think the speaker is accurately cognizant of the spatiotemporal context of the utterance, then we shouldn't pack information about that spatiotemporal context into our interpretation of the utterance.

For example, if a two-year old child utters "it is raining" at 2pm EST in Peoria, Illinois, it seems to me quite implausible to assume that the child means (1), for the child may have only the vaguest of ideas (or even wildly wrong ideas) of the time and place. But if the child doesn't mean (1), then (1) does not give the truth conditions of that sentence token.

Here's a starker example. Suppose that Bob, while uttering "it is raining" at 2pm EST in Peoria, Illinois, is under the spell of a powerful hallucination that has him utterly convinced that he is in Lihue, Kauai and that the time is 8am. On those assumptions, when Bob says "it is raining" what he means is (2), not (1). Hence (2), not (1) captures the truth conditions of Bob's utterance.

Summing up, (3) is false because it assumes that information about the speaker's doxastic state is irrelevant for fixing truth conditions. But such information is not irrelevant. What is meant by a given sentence token is controlled more by the speaker's beliefs than it is by the de facto context of utterance.

Some Philosophy Jokes

Some of these are fairly lame, I admit. And some are clever but opaque to the philosophically uninitiated. See if you can figure them out before I explain any of them. (I wouldn't want to spoil a good joke with premature commentary.)


Don't put Descartes before the horse.

One day Descartes walked into a pub and ordered a coffee. The server asked him, "Do you want that with cream and sugar?" Descartes answered, "I think not", and abruptly ceased to exist.

What did the pantheist say to the hot dog vendor? ... Make me one with everything.

Have you heard about the dyslexic insomniac agnostic? ... He lies awake at night wondering if there is a dog.

Who's the most egotistal type of person conceivable? ... A pantheistic solipsist.

Quentin Smith Contra Skepticism

I'm currently reading Quentin Smith's book Language and Time, in chapter 1 of which he has a nice argument against a certain kind of skepticism (pp. 14-18). His argument runs as follows.

Is it ever reasonable for you to believe something just because it seems true to you and, so far as you are aware, there are no good empirical, logical, or other relevant reasons to disbelieve it? Well, suppose there is a skeptic who says No, seeming is never sufficient grounds for believing. Such a skeptic proposes:

(1) Even if it seems to S that p and S has no reasons (empirical, logical, or other) to disbelieve p, S is not justified in believing p.

Now, asks Smith, what could possibly justify a belief in (1)? Suppose we grant the skeptic that there are no empirical, logical, or other reasons to disbelieve in (1). Obviously, the skeptic cannot justify (1) on the grounds that it seems right to him, since (1) disallows that move. So the skeptic needs to give positive empirical, logical, or other reasons to show that (1) is true. Call these reasons R.

Now, what justification could there be for thinking that R supports (1)? Again, given (1) it can't be that R seems to support (1). So we need further reasons, R', for believing that R supports (1). But now why should we think that R' supports the claim that R supports (1). Again, given (1) it can't be that R' seems to support that claim. So that claim has to be justified by appeal to still further reasons, R'', and so on. An infinite regress ensues. And the regress is vicious since, as a finite mind, the skeptic "cannot comprehend an infinite number of steps in a chain of alleged justifications" (p. 17). Even if he could, says Smith, the skeptic would still not be justified in believing (1) because he would have no justification for believing that the infinite chain justifies (1). A skeptic who appeals to a principle like (1) is, therefore, hoist on his own petard. If (1) is true, then no one (including the skeptic), could be justified in believing it to be true.

The moral of the story: (1) is false. It's seeming to S that p is, in the absence of S's possession of reasons for believing the contrary, sufficient to justify S's believing that p.

It's the Demography, Stupid!

This is a very sobering article. If Mr. Steyn's predictions bear out (and the demographics certainly support him), we'll be witnessing some major upheavals in Europe within the next few years.

Warning: The article is quite long, but well worth reading.

Peircean vs. Ockhamist Tense Logic

So far as I am aware, all philosophers agree that if it rains on a particular Tuesday then it will be the case every day thereafter that it rained on that particular Tuesday. If we let P stand for "it was the case that ...", F stand for "it will be the case that ...", N stand for "it is now the case that ...", and p stand for the proposition "It is raining on Tuesday" then we can express this symbolically as

(1) N(p) --> F(P(p)).

(1) claims that if it is now the case that it is raining on Tuesday then it will be the case hereafter that it was the case that it is raining on Tuesday. In other words, once something has happened and is past, it cannot change.

But not all philosophers agree that the following is true:

(2) N(p) --> P(F(p)).

(2) claims that if it is now the case that it is raining on Tuesday then it always was the case that it will be the case that it is raining on Tuesday. In other words, from the beginning of time it was already a settled truth that it would rain on that particular Tuesday. Indeed, (2) implies that there is already a settled truth about what will happen tomorrow and the next day and the next ... and so on, until the very end of time.

It is probably true that most philosophers would accept (2). Following Arthur Prior, we'll call them 'Ockhamists' after the medieval logician William of Ockham. Again following Prior, we'll call those who reject (2) 'Peirceans', after the nineteenth century logician Charles Sanders Peirce.

Those in the Ockhamist camp are apt to regard (2) as obviously correct, a truism, a platitude. Peirceans, however, regard (2) as a gross non sequitur, an invalid inference. Who is right? It all depends on the interpretation of "will" in

(3) "It will be the case that p" uttered at time T.

For the Ockhamist, to say that something "will" happen implies absolutely nothing about its chances of happening, except to say that its chances are not zero. So if someone tosses a coin and, while the coin is still in the air, another person predicts "the coin will land heads", an Ockhamist would not construe that to be implying that the coin was likely to land heads. Instead, he would construe the prediction as saying nothing more than "in fact the coin does land heads subsequent to T". Consequently, the mere fact that the coin does land heads is sufficient to make it true beforehand that it "will" land heads. In summary, then, the Ockhamist takes (3) to mean

(4) It is the case that p at some time T' subsequent to T.

If this is the right way to read statements like (3), then (2) is correct.

The Peircean, however, construes "will" differently. For the Peircean, to predict that something "will" happen is to say that the chances of its happening are 100% (or very close). In other words, they hold that to say that something "will" happen implies that the future is fixed, not by what does happen in the future (as the Ockhamist supposes) but by its being a causally necessary consequence of what is the case right now. If we follow the Peircean and construe "will" in this sense, then it should be pretty obvious that (2) is false. After all, says the Peircean, the mere fact that a tossed coin lands heads only proves that it was antecedently possible that it land heads, not that it was causally necessary that it land heads. In summary, then, the Peircean takes (3) to mean

(5) It is causally necessary that p occur at some time T' subsequent to T.

If this is the right way to read statements like (3), then (2) is false.

All Moral Relativisms Are Self-Refuting

Whenever someone says that something is relative--whether it be morality, truth, velocity, the color of emeralds, or what have you--you should always ask the question, "relative to what?" There are as many ways for something to be relative as there as ways to answer that question.

For example, some people think that morality (by which I mean a set of principles that determines what is right and wrong) is relative to cultures. Let's call this 'cultural moral relativism'. Others think morality is relative to individuals. Let's call this 'individual moral relativism'. In addition to these there are a host of other logically possible variants. For example, one might hold that morality is relative to the seasons of the year ('seasonal moral relativism') or to a particular geographical region ('geographical moral relativism') or to the square root of the current date on the Gregorian calendar ('calendrical root moral relativism') or to any criterion that yields different results in different contexts.

In general, whether S has property P is relative to criterion C if and only if (a) possibly, some S satisfy C and thus have property P, and (b) possibly, some S fail to satisfy C and thus fail to have property P. Conversely, whether S has P is not relative to C if and only if (c) necessarily, all S satisfy C and thus have P, or (d) necessarily, no S satisfy C and thus do not have P.

According to cultural moral relativism, some action is morally permissible in culture X if and only if that action is sanctioned by X's moral standards. S is the action in question. P is the property of being morally permissible in X. And C is the property of being sanctioned by X's moral standards.

Notice that we've expressed cultural moral relativism in terms of moral permissibility in X. But we can also express cultural moral relativism in terms of moral permissibility without reference to X. Thus, according to cultural moral relativism, some action is morally permissible simpliciter if and only if that action is performed in a culture the moral standards of which sanction the action. S is the action in question. P is the property of being morally permissible. And C is the property of being performed in a culture the moral standards of which sanction the action.

These two expressions of cultural moral relativism say the same thing. But the latter posits a criterion of moral permissibility, namely, the property of being performed in a culture the moral standards of which sanction the action, that is not culturally relative. In other words, cultural moral relativism affirms, as a non-relative truth, that all people morally ought to act in accordance with the moral standards of their culture. Since this is a culturally absolute moral principle, cultural moral relativism can be true if and only if some moral principles are not culturally relative.This means that cultural moral relativism is false as a global thesis about morality. If there are any moral principles at all, then at least one must not be culturally relative. The same holds mutatis mutandis for all other moral relativisms.

Neologism, Paleologisms, and Grelling's Paradox

Self-proclaimed "Maverick Philosopher" William Vallicella brought to my attention the following paradox:

'Neologism’ is not a new word, but an old word. Hence, ‘neologism’ is not a neologism. ‘Paleologism’ is not a word at all; or at least it is not listed in the Oxford English Dictionary. But it ought to be, so I hereby introduce it. Who is going to stop me? Having read it and understood it, you have willy-nilly validated its introduction and are complicit with me.

Now that we have ‘paleologism’ on the table, and an unvast conspiracy going, we are in a position to see that ‘neologism’ is a paleologism, while ‘paleologism’ is a neologism. Since the neologism/paleologism classification is both exclusive (every word is either one or the other)and exhaustive (no word is neither), it follows that ‘neologism’ is not a neologism, and ‘paleologism’ is not a paleologism. Such words are called heterological: they are not instances of the properties they express. ‘Useless’ and ‘monosyllabic’ are other examples of heterological expressions in that ‘useless’ is not useless and ‘monosyllabic’ is not monosyllabic. A term that is not heterological is called autological. Examples include ‘short’ and ‘polysyllabic.’ ‘Short’ is short and ‘polysyllabic’ is polysyllabic. Autological terms are instances of the properties they express.

Now ask yourself this question: Is ‘heterological’ heterological? Given that the heterological/autological classification is exhaustive, 'heterological' must be either heterological or else autological. Now if the former, then ‘heterological’ is not an instance of the property it expresses, namely, the property of not being an instance of the property it expresses. But this implies that ‘heterological’ is autological. On the other hand, if ‘heterological’ is autological, then it is an instance of the property it expresses, namely the property of not being an instance of the property it expresses. But this implies that ‘heterological’ is heterological.

Therefore, ‘heterological’ is heterological if and only if it is not. This contradiction is known in the trade as Grelling’s Paradox. It is named after Kurt Grelling, who presented it in 1908.

My thoughts on this are as follows:

(1) Heterological means not exemplifying the property it expresses. Autological means exemplifying the property it expresses. So defined, the two are mutually exclusive and jointly exhaustive. As such, every property expressing word must be one or the other.

(2) 'Heterological' and 'autological' are metaproperties--each is the second-order property of exemplifying some first-order property. Thus, 'short"s property of being autological supervenes upon its property of being short.

(3) Thus, "exemplifying the property it expresses" doesn't have any determinate meaning until the referent of "the property it expresses" is fixed. For example, is 'short" short or not? It depends on what 'short' means, that is, upon which property it expresses. If 'short' means less than a inch, then 'short' is indeed short and autological to boot. But if 'short' means less than a millimeter, then 'short' is neither short nor autological, but heterological.

(4) As metaproperties, heterologicality and autologicality are properties of exemplifying a certain property, namely, the property that 'heterological' and 'autological', respectively, express. But in each case that property is also a metaproperty, specifically, itself. This leads to an infinite regress. For just as 'short' is neither determinately short or not short until we fix the meaning of the term, so neither are 'heterological' and 'autological' determinately heterological or autological until we fix the meanings of those terms. But when we try to do so, we find that the meaning is continually deferred. Thus, heterologicality is the property of exemplifying heterologicality, which is the property of exemplifying the property of exemplifying heterologicality, which is the property of exemplifying the property of exemplifying the property of exemplifying heterologicality, and so on. Every time we try to spell out exactly what the metaproperty is we wind up invoking a metaproperty, which just pushes the analysis back a step.

(5) So it looks like there's something inherently problematic about ascribing metaproperties to metaproperties, for doing so generates an infinite regress. The only way that I can see to stop the regress is to restrict the application of metaproperties to lower-order properties. Thus, nth-order metaproperties cannot apply to nth-order metaproperties, but only to (n-1)th order properties, until eventually we come to some first-order, non-metaproperty.

Russell's theory of types is lurking in the shadows.