Tigers, snakes, morals and evolution

Case 1: Your ancestors evolved (genetically or mimetically) a belief that a local forest was full of tigers. This belief has kept your ancestors out of the forest where they would have been eaten by tigers, and that is why the belief evolved.

Case 2: Your ancestors evolved a belief that a local forest was full of tigers. This belief has kept your anceestors out of the forest where they would have been killed by snakes and that is why the belief evolved—a belief in tigers, let us suppose, is better at keeping people away thant a belief in snakes. Coincidentally, the forest is full of tigers, but these tigers are shy—they silently run away when people approach, and no one has ever had an encounter with one.

If Case 1 is a case of knowledge, Case 2 is a Gettier case, and hence not a case of knowledge that the forest is full of tigers. And if Case 1 is not a case of knowledge, Case 2 isn't either. So, either way, Case 2 is not a case of knowledge.

Case 3: Your ancestors evolved moral beliefs. These beliefs kept social cooperation going and that's why they evolved. The beliefs are by and large true.

In Cases 2 and 3, unlike in Case 1, there is no relevant connection betweeen why your ancestors evolved the belief and the belief's truth. Case 3 is relevantly like Case 2: it is not a case of knowledge but at most of Gettiered justified true belief.

A story like Case 3 is the only plausible account of the genesis of moral belief available to the non-Aristotelian naturalist. Since we do know moral truths, mon-Aristotelian naturalism is false. Can the Aristotelian do better? Maybe. Moral truth is grounded in natural human inclinations, she can say, and the same inclinations often give rise, noncoincidentally, to correct moral beliefs. I wonder if the only way for a naturalist to be a realist about morality is for her to be an Aristotelian.

A gratitude/resentment argument

This argument is inspired by an argument of Kenneth Pearce.

1. (Premise) It is sometimes appropriate to be grateful for or to the universe or to be resentful for or at the universe.
2. (Premise) It is only appropriate to be grateful for or to A if A is an agent or an effect of an agent.
3. (Premise) It is only appropriate to be resentful for or at A if A is an agent or an effect of an agent.
4. Therefore, the universe is an agent or an effect of an agent.
5. (Premise) If the universe is an agent or an effect of an agent, naturalism is false.
6. Therefore, naturalism is false.

Philosophy and literature

Different genres of literature are apt to give insights in different areas of philosophy:

• science fiction: metaphysics and mind
• mystery: epistemology
• fantasy: philosophy of religion
• non-genre fiction: ethics

Of course there are many exceptions.

Reflections on Horwich's minimalism

Horwich's minimalism is a theory of truth generated by the axiom:

1. If p is true, then p is a proposition

and the axiom schema obtained by taking all sentences s of extensions of English and substituting them into:

2. <s> is true if and only if s

(with this understood in the same extension of English as s was), with the exception of those sentences that lead to paradox (e.g., "This sentence is false"). Here, <s> denotes the proposition that s.

Here are some issues. None of them are fatal. But they all mean that minimalism isn't quite as simple as it initially seems.

Issue 1: What is an extension of English? We need to include sentences of extensions of English because no doubt there are propositions that no sentence of English can express. Now, an extension of English had better not change the meanings of "is true" or "if and only if"—for if that is allowed to change, then some instances of (2) will become false. Presumably, then, what makes L an extension of English is that for any linguistic element e of English, e is also a linguistic element of L, and it has the same meaning (semantic value, etc.) in L as it does in English. Thus, Horwich's minimalism in its description of the axiom schema presupposes the concept of meaning (semantic value, etc.). To avoid circularity, the concept of meaning had better not depend on that of truth.

Issue 2: Nitpicky stuff. Strictly speaking, (2) generates bad orthography. Suppose s is "Snow is white." Then we are told that <Snow is white.> is true if and only if Snow is white. But the last "Snow" should not be capitalized. This can be easily handled—we specify that when substituting s in, we adjust the first letter's case as needed. There is also that odd looking period after the first "white"; again, we can specify that it is to be omitted. A slightly less easy case is where s is "This sentence is short." Suppose s is true. But now consider:

3. <This sentence is short> is true if and only if this sentence is short.

But the second occurrence of "this sentence" refers not to s but to (3), and that sentence is not short, so (3) is false. Presumably, we handle this by not allowing sentences with indexicals or demonstratives. This requires the substantive assumption that any proposition that can be expressed with indexicals/demonstratives can be expressed without them. Next, let s be "u if and only if v" (for some u and v). Then (2) yields:

4. <u if and only if v> if and only if u if and only if v.

But this is wrong or badly ambiguous. Maybe then we're supposed to use an extension of English that has grouping parentheses, and then replace (2) with:

5. <s> is true if and only if (s).

Issue 3: Contingent liar. Axioms normally are supposed to not vary between worlds. But there are contingent liar sentences, like "The sentence on Alex's board is false", which is paradoxical when it is the unique sentence on Alex's board but need not be paradoxical when written on Jon's board (unless we have something like "The sentence on Jon's board is false" as the only sentence on Alex's board). This means that dropping those instances of (2) (or of (5)) that generates the paradox requires dropping different instances in different worlds, thereby making the axioms of truth differ from world to world.

There are two ways for axioms to differ between worlds. In the weak sense, whether p is an axiom varies between worlds, but p is true at all worlds. In the strong sense, the truth value varies between worlds, too. This is the kind of variation that we'd need to get out of the contingent liar. And this just doesn't fit with what we understand by "axiom", I think.

Hunting for micrometeorites

Inspired by stuff on the web (e.g., here), I went hunting for micrometeorites. I wrapped a magnet with plastic wrap, and ran it through the dirt under one of our house's downspouts. Apparently meteorites have high iron content so magnets capture them. There was some magnetic dust. I then transfered a couple of pieces of it to a microscope slide and had a look. I saw black chunks of stuff with transmitted light, unsurprisingly, but they became pretty and shiny when I shone a flashlight on them. The two largest ones had rough edges. Micrometeorites are supposed to be smoother due to their hot passage through the atmosphere. But moving the slide around, I cam on a smaller piece with smoother edges and interesting texture that matched what one would expect a meteorite to look like. There was some shiny bumpiness, some small pit-like spots and some interesting rod/wave like areas.

I tried to save the tiny piece for future observations. I tried to stick it to some sticky tape, but the goo made it very hard to observe under the microscope. So I ended up dissolving the goo with acetone to recover the piece. As a side-effect, the piece became cleaner and was brightly metallic under the microscope. Unfortunately, I eventually lost it. It was very small, about four or five times longer than wide, and the width was about that of a hair or maybe a touch more. I lost it when I tried to transfer it with the tip of a needle from a dirtier cover glass to a cleaner one, but somehow it just disappeared--I used a powerful loupe to try to find it, but couldn't. Oh well.

At least the kids got to see it. I don't know it was a meteorite, of course. Too bad I lost it before taking a picture.

Pluralist theories of predication

According to anti-pluralist theories of predication, there is only a small handful of fundamental predicates and they are all of a highly general and abstract nature.  Sometimes there is only one.  For instance, strong Platonism has as fundamental only the multigrade predicate Instantiates.  All other predications should be analyzed in terms of it.  Resemblance nominalism has the fundamental predicate ResemblesInRespect and then needs some story about respects (which story may involve one or two more fundamental predicate).  Bundle theory will have the fundamental predicate CobundledWith, plus perhaps the predicates of set theory (∈ and IsASet) or of some other highly general theory for constructing objects out of bundles.

According to pluralist theories of predication, there are many fundamental predicates and many of them are of a very concrete nature.  For instance, the pluralist is likely to have predicates like Horse, Daphnia and NegativelyCharged.  She may also have highly abstract predicates like ∈ as well.

Ostrich nominalists are pluralists.  But one can also be a weak Platonist and a pluralist.  I am inclined to think that the solution to the problem of the unity of form and matter given in Metaphysics H.6 commits Aristotle to pluralism.

The big insight of the pluralist is that the puzzle of predication is no less of a puzzle when that puzzle concerns a small handful of fundamental predicates.  There may be theoretical simplicity grounds to prefer particular anti-pluralist theories of predication over particular pluralist theories, but I suspect these will result in a stalemate.  And then the pluralist will win, as her fundamental predicates fit better with our intuitions, I think.

Two kinds of Platonism about properties

According to strong Platonism about properties, if F is a fundamental predicate, then F expresses the property Fness and the sentence "x is F" should be analyzed as saying that x instantiates Fness.

Weak Platonism makes no such analysis claim. It merely claims that to each fundamental predicate F there corresponds a property Fness such that, necessarily, x is F if and only if x instantiates Fness. Weak Platonism thus drops two claims that strong Platonism makes: (a) that the predicate expresses the property; and (b) that we should analyze predications in terms of instantiation.

Here is a problem with strong Platonism.

1. If strong Platonism is true, then in an ideal logic—one that follows the metaphysics as closely as possible—there is one and only one (multigrade) predicate: Instantiates.

Thus, instead of saying that Romeo loves Juliet, we would say something like: Instantiates(Romeo, Juliet, love). But:

2. In an ideal logic there would be more than one predicate.
3. So, strong Platonism is false.

I don't think this is a very powerful argument against strong Platonism, but it does highlight something a little troubling—Platonism objectifies all predicates but one, and in effect has only one predicate.

If strong Platonism were true, then in some sense there would only be one thing one would ever be doing—instantiating (of course sometimes one would be instantiating together with others, and what property one would be instantiating would vary).

I think weak Platonism is much more attractive. An example of weak Platonism is Lewis's account of properties as cross-world sets of objects. This is merely weak Platonism. We don't want to say that "is a circle" expresses the set of all of circles. Nor do we want to say that "Socrates is a circle" holds because of Socrates' membership in the set of all circles. But Lewis does not intend it as more than a weak Platonism.

I think that on some readings, divine conceptualist views on which properties are divine ideas are a weak Platonism.

Names, quantifiers, Aristotelian logic and one-sided relations

This is going to be a pretty technically involved post and it will be written very badly, as it's really just notes for self. Start with this objection to Aristotelian logic. A good logical system reveals the deep logical structure of sentences. But Aristotelian logic takes as fundamental sentences like:

1. Everyone is mortal.
2. Socrates is mortal.

In so doing, Aristotelian logic creates the impression that (1) and (2) have similar logical form, and it is normally taken to be that modern quantified logic has shown that (1) and (2) have different logical forms, namely:

3. ∀x(Mortal(x))
4. Mortal(Socrates).

I shall show, however, that there is a way of thinking about (1) and (2), as well as about (3) and (4), that makes them have the same deep logical form, as Aristotelian logician makes it seem. (This is a very surprising result for me. Until I discovered these ideas this year, I had a strong antipathy to Aristotelian logic.) Moreover, this will give us some hope of understanding the medieval idea of one-sided relations. The medievals thought, very mysteriously, that creation is a one-sided relation: we are related to God by the created by relation, but God is not related to us by the creates relation.

Now to the technical stuff. Recall Tarski's definition of truth in terms of satisfaction. I think the best way to formulate the definition is by means of a substitution sequence. A substitution sequence s is a finite sequence of variable-object pairs, which I will write using a slash. E.g., "x₁"/Socrates,"x₂"/Francis,"x₃"/Bucephalus is a substitution sequence. The first pair in my example consists of the variable letter "x₁", a linguistic entity (actually in the best logic we might have slot identifiers instead of variable letters) and Socrates—not the name "Socrates" (which is why the quotation marks are as they are). We then inductively define the notion of a substitution sequence satisfying a well-formed formula (wff) under an interpretation I. An interpretation I is a function from names and predicates to objects and properties respectively. And then we have satisfaction simpliciter which is satisfaction under the intended interpretation, and that's what will interest me. So henceforth, I will be the intended interpretation. (I've left out models, because I am interested in truth simpliciter.) We proceed inductively. Thus, s satisfies a disjunction of wffs if and only if it satisfies at least one of the wffs, and so on, the negation of a wff if and only if it does not satisfy the wff, and so on.

Quantifiers are a little more tricky. The sequence s satisfies the wff ∀xF iff for every object u, the sequence "x"/u,s (i.e., the sequence obtained by prepending the pair "x"/u" at its head) satisfies F. The sequence s satisfies ∃xF iff for some object u, the sequence "x"/u,s satisfies F.

What remains is to define s's satisfaction of an atomic wff, i.e., one of the form P(a₁,...,a_n) where a₁,...,a_n are a sequence of names or variables. The standard way of doing this is as follows. Let u₁,...,u_n be a sequence of objects defined as follows. If a_i is a variable "x", then we let u_i be the first object u occuring in s paired with the variable "x". If for some i there is none such pair in s, then we say s doesn't satisfies the formula. If a_i is a name "n", then we let u_i=I("n"). We then say that s satisfies P(a₁,...,a_n) if and only if u₁,...,u_n stand in I(P).

Now notice that while the definition of satisfaction for quantified sentences is pretty neat, the definition of satisfaction for atomics is really messy, because it needs to take into account the question of which slot of the predicate has a variable in it and which one has a name.

There is a different way of doing this. This starts with the Montague grammar way of thinking about things, on which words are taken to be functors from linguistic entities to linguistic entities. Let us ask, then, what kind of functors are represented by names. Here is the answer that I think is appealing. A name, say "Socrates", is a functor from wffs with an indicated blank to wffs. In English, the name takes a wff like "____ likes virtue" and returns the wff (in this case sentence) "Socrates likes virtue". (The competing way of thinking of names is as zero-ary functors. But if one does it this way, one also needs variables as another kind of zero-ary functor, which I think is unappealing since variables are really just a kind of slot, or else one has a mess in treating atomics differently depending on which slots are filled with names and which with variables.) We can re-formulate First Order Logic so that a name like "Socrates" is (or at least corresponds to) a functor from wff-variable pairs to new wffs. Thus, when we apply the functor "Socrates" to the wff "Mortal(x)" and the variable "x", we get the wff (sentence, actually) "Mortal(Socrates)". And the resulting wff no longer has the variable "x" freely occurring in it. But this is exactly what quantifiers do. For instance, the universal quantifier is a functor that takes a wff and a variable, and returns a new wff in which the variable does not freely occur.

If we wanted the grammar to indicate this with particular clarity, instead of writing "Rides(Alexander, Bucephalus)", we would write: "Alexanderx Bucephalusy Rides(x,y)". And this is syntactically very much like "∀x∀y Rides(x,y)".

And if we adopted this notation, the Tarski definition of satisfaction would change. We would add a new clause for the satisfaction of a name-quantified formula: s satisfies nxF, where "n" is a name, if and only if "x"/I("n"),s satisfies F. Now once we got to the satisfaction of an atomic, the predicate would only be applied to variables, never to names. And so we could more neatly say that s satisfies P(x₁,...,x_n) if and only if every variable occurs in the substitution sequence and u₁,...,u_n stand in I(P) where u_i is the first entity u occurring in s in a pair of the form "x_i"/u.  Neater and simpler, I think.

Names, thus, can be seen as quantifiers. It might be thought that there is a crucial disanalogy between names and the universal/existential quantifiers, in that there are many names, and only one universal and only one existential quantifier. But the latter point is not clear. In a typed logic, there may be as many universal quantifiers as types, and as many existential ones as types, once again. And the number of types may be world-dependent, just as the number of objects.

If I am right, then if we wanted to display the logical structure of (1) and (2), or of (3) and (4) for that matter, we would respectively say:

5. ∀x Mortal(x)
6. Socratesx Mortal(x).

And there is a deep similarity of logical structure—we simply have different quantifiers. And so the Aristotelian was right to see these two as similar.

Now, the final little bit of stuff. Obviously, if "m" and "n" are two names, then:

7. "mx ny F(x,y)" is true iff "ny mx F(x,y)" is true,

just as:

8. "∀x∀yF(x,y)" is true iff "∀y∀xF(x,y)" is true.

But the two sentences in (8), although they are logically equivalent, arguably express different propositions. And I submit that so do the two sentence in (7). And we even have a way of marking the difference in English, I think. Ordinarily, what the left hand side in (7) says is that u has the property P_xnyF(x,y) while the right hand side in (8) says that v has the property P_ymxF(x,y), where u and v are what "m" and "n" respectively denote, and P_xH(x) is the (abundant) property corresponding to the predicate H (the P-thingy is like the lambda functor, except it returns a property, not a predicate). These are distinct claims.

The medievals then claim that in the case of God we have this. They say that "Godx ny F(x,y)" is true in virtue of "ny Godx F(x,y)" being true. It is to the referent of "n" that the property P_y Godx F(x,y) is attributed, and the sentence that seems to attribute a property to God is to be analyzed in terms of the one that attributes a property to the referent of "n".

The combination view of hell

There are four possible views on suffering in hell:

1. Traditional View (TV): Some people have everlasting suffering in hell.
2. Weak Universalism (WU): Everyone lives forever and nobody has everlasting suffering in hell.
3. Annihilationism: Nobody has any suffering in hell but some are annihilated.
4. Combination View (CV): Some suffer in hell and then are annihilated.

I called (2) Weak Universalism, since it's compatible with the idea that some people go to hell for a finite amount of time and with the idea that some people stay forever in hell but only suffer for a finite amount of time. In this post I want to examine and reject the Combination View.

In principle, CV could be motivated over and against TV by claiming that TV is too lenient—hell is too good for some people. Such a view is rare, I think, and I won't argue against it. Instead, I want to argue against those versions of CV on which TV is too harsh.

Those who accept CV presumably think that punishment is primarily retributive in nature—otherwise it's hard to see why CV is more appealing than straight Annihilationism. For if punishment is there to protect the innocent, Annihilationism seems to work even better than CV. And if punishment is there to reform the wicked, then either all the wicked are reformed by the punishment, and hence should not be annihilated at the completion of it, or else some of the wicked are not reformed. If some of the wicked are not reformed by the punishment, why shouldn't God prolong it, hoping for results? (And if there must be a cut-off, then why shouldn't that cut-off be at death instead?)

So suppose that punishment is primarily retributive. But now I worry that WU is a better view than CV. The CVer thinks that everlasting suffering in hell is too harsh, but that nonetheless some people deserve some post-death suffering in hell. Well, wouldn't it be better for God to keep those people in hell until their total punishment is sufficient to pay the penalty, and then once their penalty has been paid, give them a life that is neither heavenly nor hellish? I suppose one could insist on this odd view: no finite amount of post-death suffering in hell is sufficient penalty but an infinite amount of post-death suffering in hell is too harsh a penalty, and CV manages to produce a punishment that is in between, but this just does not seem very plausible.

I expect that the motivation for CV is often a hybrid of theological and philosophical reasoning. For reasons of Scripture and Christian tradion, WU and Annihilationism are rejected, and I think rightly so. For philosophical reasons, however, TV is rejected. CV is not philosophically superior to WU and Annihilationism but maybe in terms of Scripture and tradition it is superior. Still, I think CV is not a stable position. And if one really thinks a finite amount of suffering in hell is better, why not just hold to the traditional Christian view that hell is forever, but tweak it so that the total amount of suffering is finite? I am not defending that modified view, but it seems superior to CV in terms of conformity to Scripture and tradition, and philosophically no worse.

Pain and machines

Some of Descartes' followers are accused of treating the noises animals make when to all appearances in pain  like the grating of a machine and hence as unconscious.  But someone could have the reverse attitude:

"The pump," said Mma Potokwane.  "It is making a very strange noise.  The water comes all right, but the pump makes a noise as if it is in pain."
"Engines do feel pain," said Mr J.L.B. Matekoni. "They tell us of their pain by making a noise." (Alexander McCall Smith, Tears of the Giraffe)

Without endorsing Matekoni's conclusion, doesn't it feel like one is causing pain to a tool if one uses it in such a way that it complains by creaking, grating or binding?

Filing taxes

Here's a curious thing: everybody who prepares their own tax forms (or prepares records for someone else to prepare the tax forms) has a conflict of interest.  On the one hand, the person filing is supposed to be trying to figure out the truth as to who owes whom and how much.  On the other hand, the person filing has a financial stake in the answer.

HB 2454

I rarely comment on current politics.  Still, I want to say something here.  A bill has been proposed in the Texas Legislature to ban discrimination on the basis of Intelligent Design (ID) research at colleges.  To lay my cards on the table, I think it is still an open question whether the amount of time available for evolutionary processes was sufficient for the sort of complexities we observe to be at all likely to observe, and I suspect we are still quite some distance from having mathematical models of the development of anything with sufficient complexity to close the question.  So research on ID should, I think, continue.  And no doubt unjustified discrimination connected with research on ID exists.  But the bill is really embarrassing:

Sec. 51.979.  PROHIBITION OF DISCRIMINATION BASED ON RESEARCH RELATED TO INTELLIGENT DESIGN. An institution of higher education may not discriminate against or penalize in any manner, especially with regard to employment or academic support, a faculty member or student based on the faculty member's or student's conduct of research relating to the theory of intelligent design or other alternate theories of the origination and development of organisms.

Here are three reasons for embarrassment:

1. Theories of "the origination and development of organisms" concern not evolutionary theory as such but reproductive and developmental biology.  As a commenter here noted, an alternate theory in this realm is "storkism" (presumably the theory that human children come from storks rather than from human mating).  ID concerns something else, something more like the origination and development of types of organisms.
2. A French Department should be able to discriminate against a prospective faculty member whose primary research is on ID rather than French language, culture and/or literature.  Likewise, it is perfectly reasonable for a Biology Department that required students in a class to do laboratory research on the present functioning of red blood cells to discriminate against a student who, instead, did a research on ID.  Maybe an implicit exception for the bona fide requirements of a task can be assumed, but it would also take some of the teeth out of the bill.
3. Everyone, whatever they think of ID, should agree that it is reasonable for a college to deny tenure/promotion, refrain from hiring or giving a low grade on the basis of intellectually shoddy ID research.  Now, the bill either does or does not allow discrimination on the basis of shoddy ID research.  If it does not, then it is clearly unacceptable--it provides a delightful formula for tenure and promotion: do research on ID, and they have to promote you no matter how bad the research is, or else you sue.  Suppose, charitably, discrimination on the basis of shoddy ID research would stil be permissible.  But now the bill is close to useless.  For those scientists who are likely to discriminate on the basis of ID research also say that it is their professional judgment all ID research (or at least all ID-supportive research) is intellectually shoddy.  So if they can still discriminate on the basis of shoddiness of research, the bill does nothing to protect ID researchers.

A common mistake about hell

A common mistake about hell, often made by both contemporary advocates of the doctrine and their opponents, is the Horrific Thesis:

(HT) It is better not to exist at all, or even not to have existed at all, than to spend eternity in hell.

Given HT, it is easy to argue against hell.  All things that exist, exist by the continual creation of God.  Everything that God creates, or continually creates, is on balance good.  Therefore, nobody is better off not existing.  Hence if HT is true, nobody spends eternity in hell.  

But HT is false.  First, consider its Scriptural warrant.  There is one New Testament text directly related to HT, given in Matthew and Mark:

As for that man [the betrayer], it would have been better [kalon] for him had he not been born [ei ouk eggenêthê] (Matthew 26:24, Mark 14:21).  

But that text simply does not sufficiently support HT.  First, it does not say that it was better for Judas not to have existed, but at most that it would have been better for him not to have been born.  Since Judas had already existed by the time of his birth--I say he existed about nine months before his birth, but in any case surely he existed some time before his birth--the counterfactual taken literally compares two scenarios: Judas being born and Judas dying in utero.  Now had he died prior to birth, his eternal destination would be wherever Jewish babies ended up after death--either heaven or limbo.  On this reading, then, we are told that Judas would have been better off dying in utero and ending up in heaven or limbo than wherever he ended up.  (If he would have ended up in heaven had he died prior to birth, then the text does not even entail that Judas went to hell.  Maybe he would have been better off had he died in utero because then he would have ended up in a better state in heaven or because then he would have avoided purgatory.)  Second, the word kalon might also have been translated as "noble" or "honorable"--in classical Greek that is the primary meaning and the word seems to have that meaning in some New Testament uses as well.  Thus, even if we take the "had he not been born" non-literally as meaning "had he not existed", the text could simply be telling us that it would have been more noble or more honorable for him had he not existed, rather than altogether better.

The other part of HT's Scriptural warrant are the scary descriptions--lake of fire, worm that dieth not--of what existence in hell is like.  But we should read Scripture consistently with Scripture.  And Scripture also tells us of a God who loves all, whose sun shines on sinner and righteous alike, who created everything and it was all good.  Thus we should temper our interpretations of the harrowing descriptions with the conviction that God does not create or sustain in existence that for which it would be better not to exist.

(Objection: Maybe it is agent-centeredly worse for the person in hell to exist than not to, but it is better that she exist than not.  Response: But better for whom or what?  God's activity is primarily guided by love.  When he acts for a good cause, he does so for someone or something.  Is it better for God that the person suffer?  The Christian tradition will not be happy with this reading.  Is it better for others?  But how?  Tertullian suggested that the saved will get joy from watching the punishment of the damned.  But even if he is right, this can only be true if the punishment of the damned has a value independent of the saved watching it, since the saved get joy only out of watching good things.  No, if it is better simpliciter that the person be in hell than not exist, it is better for the person in hell.)

One might ask, of course, if it is possible to have eternal suffering and yet to have a life worth living.  But surely the answer is positive.  One way for the answer to be positive is for Augustine and Aquinas to be right about the value of existence, or at least human existence: this value is such that it is worth existing no matter how much one suffers.  Another way would be if the overall suffering is combined with other valuable features that make the life overall worth living, whether or not the agent feels it to be worth living.  These could perhaps include:

• the intrinsic value of receiving one's just deserts
• the value of knowing various truths (such as that God exists and that one is a sinner)
• moral improvement (though one never actually reaches moral purity)
• the value of useful work
• playing a part in God's plan, especially the justice aspect of it
• etc.

It should also be remembered that an externally infinite length of suffering is logically compatible with the total amount of suffering being finite (though I am not endorsing the view that the total amount of suffering in hell is finite), e.g., due to asymptotic decrease or changes in the subjective flow of time.

We should, in fact, take the rejection of HT to be a part of the doctrine of hell.  For the rejection of HT follows from central theological commitments of the Christian tradition, and doctrines must be understood not in isolation but in the context of the implications for them of other doctrines.  And a fortiori we should not take HT to be an essential part of the doctrine of hell.  If we did that, we would have to absurdly say that neither Augustine nor Aquinas believed in hell, since they rejected HT.

Suppose we reject HT.  Then we can imagine the following.  God is considering creating ten billion people and then making sure, or all but making sure, that they are all saved, whether by means of offering them opportunity after opportunity for salvation, over a potentially infinite amount of time, until they agree, wiping their memories as needed, or by means of eventually canceling people's freedom and making them be saved whether they so choose or not, or by giving them such strong inclinations towards virtue that they are practically certain to do right.  But God might consider the following attractive alternative.  Create twenty billion people instead, where each has probability 3/4 of being saved.  So, about 15 billion people will be saved on this scenario (and so in terms of the number of people saved, it is better than the first scenario).  Moreover, each of these 15 billion people now has a much more serious chance of being damned, and hence her free choice has a greater significance and value than the choices that the ten billion people in the first scenario does.  Now, this scenario is tough on the approximately five billion people who will end up damned.  But these people are at least as well off existing as not, and so as long as God didn't intend them to be damned, and as long as God offered them serious opportunities for salvation, it does not seem that anything problematic has been done by God.  So there seems to be a serious case for God to actualize the second scenario instead--God could have a good reason to do so.  (This argument works poorly if Molinism is true.  Too bad for Molinism.)

Hence, if we reject HT, hell seems justifiable.  And we should reject HT.

Infinite culpability

It's time to defend something like Anselm's idea of infinite culpability.  I once expressed a hope that I'd eventually do so, but couldn't think of good things to say.  Anselm's idea was that there was an infinity in our sins, because they were sins against an  infinite God.  Here, I just want to defend the real possibility that a human being is infinitely culpable.

Case 1. Mason justifiedly believes (correctly or not) that the universe contains infinitely many inhabited planets, each of them with rational beings as deserving of respect as humans are.  Mason works as a janitor at the Large Hadron Collider, and also justifiedly (but incorrectly) believes that if he loosens some bolts, the Collider will malfunction in such a way that it will destroy the universe with all its rational beings.  Mason wants destructive power--he wants to outdo Hitler and Stalin in their destructiveness--and so he loosens these bolts so as to kill infinitely many rational beings.  In so doing, he commits attempted murder of an infinite number of people.

Now, in most nearby possible worlds where Mason does this, he is likely so insane as not to be fully culpable for his action.  But it is within the bounds of real possibility (causal possibility consistent with the basic structure of the world and humanity as we know it) that Mason is not so insane as to fail to be culpable.

Case 2. Lara justifiedly believes (correctly or not--I think correctly) that there is a heaven and a hell, and that hell involves eternal suffering and heaven involves infinite eternal bliss.  She hates Samantha and tempts her into a serious sin, in order that Samantha would suffer forever in hell and lose the infinite joy of heaven.

For evaluation of Lara's culpability, it doesn't much matter whether her belief about hell is correct or whether she succeeds in destroying Samantha's soul.  Lara has acted so as to make Samantha lose an infinite good, and that is an infinite culpability.

Case 3. Alex justifiedly believes (correctly or not--I think correctly) that memories of moral goods had in this life contribute to the joy of heaven on infinite numbers of occasions, adding an infinite amount of joy.  He acts in a way that makes someone lose a moral good in this life.  According to his beliefs, he has acted in such a way as to have made someone lose an infinite number of goods.  Assuming he was sufficiently aware of this when acting, he is apt to have an infinite culpability.

What is helpful about Cases 2 and 3 is that the beliefs in them have some chance of being correct.

Question: Are there flip-sides of these cases that show that we can gain infinite merit?

Answer: This is not as obvious as it may seem.  For while it is twice as morally wicked to commit an act that kills two innocents, it is not twice as morally good to commit an act that saves two innocents.  If by giving a dollar I can save one life, and I do so, I have shown a small amount of virtue.  But if by giving a dollar I can save two lives, and I do so, I have not shown any more virtue, since I did something that was more strongly required and at no greater cost.  On the other hand, had I refrained from giving the dollar, in the two-life case I would have done something about twice as bad.  So one does not generate cases of infinite merit simply by supposing beliefs about infinite goods.

Nonetheless, one can manufacture cases of infinite merit by supposing beliefs about infinite sacrifice:

Case 4. Chuck justifiedly believes that (a) if he helps a slave escape, he will suffer infinite pain in hell; but (b) it is his moral duty to help the slave escape.   In that case, there is a kind of infinity to the merit of Chuck's helping the slave escape.  (There will, of course, be questions about ulterior motives.  If he does it to have a self-righteous feeling, there may not be such merit.  So this suggestion does not do away with the idea that one needs grace for infinite merit.)

(I don't know how close the case of Chuck is to the much-discussed case of Huck.)

"I am obliged to A at t"

Under the influence of my previous post, no doubt, I found myself wondering about ought and tense. Specifically, whether "I am obliged to A at t" (e.g., "I am obliged to teach at 9:30 am today") is a statement about two times—the present and t—or just a statement about t. On the one-time reading, "I am obliged to A at t" has the logical grammar of "At t, I will be obliged to A." On the two-time reading, the logical grammar is "Now, I am obliged to A at t.

The conclusion was that the two-time reading is correct. Here's an easy argument. The following is intelligible. You are not currently obliged to A tomorrow. But five minutes later you validly promise me to A tomorrow, and after you've made the promise, you are obliged to A tomorrow. Five minutes later, I release you from your promise. You are no longer obliged to A tomorrow. So you can change in respect of what you are obliged to do tomorrow. On the two-time reading, this makes perfect sense. At t₀, it is not yet the case that you're obliged to A at t₃; at t₁ you are obliged to A at t₃; then at t₂ you cease to have this obligation to A at t₃. But if the statement were solely about what happens at t₃, then there could not be any change in respect of it, since what happens at t₃ does not change in this back-and-forth way.[note 1] Moreover, that I am currently obliged to A tomorrow places constraints on what I may permissibly do today.

Time travel and interlibrary loan

The following argument is valid. I don't vouch for soundness!

1. (Premise) If I ought to A, then I can A.
2. (Premise) If I have received an interlibrary loan item, I ought to return it on or before its due date.
3. (Premise) If I can return an item on a date before today's date, then time travel is possible.
4. (Premise) Today I have received an interlibrary loan item due on March 8, 2011.
5. So, I ought to return an item on or before March 8, 2011.
6. So, I can return an item on or before March 8, 2011.
7. (Premise) Any date on or before March 8, 2011 is before today's date.
8. So, time travel is possible.

Premises (3), (4) and (7) appear to be true.

Why ontology matters

For all x, x should be loved if x exists (eternally or at some time or other) and x should not be loved if x does not exist. Thus fundamental ontology matters for life.

Adding and multiplying

Two oranges plus three oranges equals five oranges. Two oranges times three oranges equals...? That just sounds malformed. One can add objects but one can't multiply them, it seems.

I suppose one could do a Cartesian product of sets, though, and say that two oranges times three oranges equals six pairs of oranges. If you're a mereological universalist, the "pairs of oranges" might be genuine though unnatural objects; otherwise, you might take them to be abstracta. So addition is either more concrete or more natural than multiplication.

Is there a point to these observations? Not really. They just struck me.

Lies and nonsense

To lie is to assert falsely, though what exactly it is to assert falsely is unclear. It probably doesn't mean to assert a falsehood. Some say it is to assert what one doesn't believe. Some say it is to assert what one what one disbelieves. Some say that it is to assert without believing that what one is asserting is true. Some add the condition that it is to deceive. But a common denominator in all of these is that a lie is a special kind of assertion.

But suppose I deliberately and deceptively start spouting pseudoscientific nonsense to my students, in aid of some argument I am pushing—nonsense in the literal sense of the word, namely stuff that has no meaning at all. I tell my students: "The paramorphogenophilic field surrounds us all and photons are submorphizations of that field." I am not lying, since I am not asserting anything. If it were the case that I was asserting something, one could ask: What am I asserting? And the only potentially possible answer would be: "He is asserting that the paramorphogenophilic field, etc." But this answer is itself nonsense—nonsense in indirect quotation renders the whole sentence (if one can even call it a sentence) nonsense.

So I am not asserting. But what I am doing is surely just as wrong as lying and for the same reasons.

What then are these reasons? It is not the production of false belief. For the students would not form a belief, at least not directly. There is no belief that the words which they then could parrot on a test express. The best account here seems to be that of Jorge Garcia's account of lying. I am inviting their trust and simultaneously breaking it.

Healing and harming

Plato was impressed with the idea that he who can best heal is he who can best kill. I doubt it. The big brawny person with the nail-studded club can kill as well as a physician. But a weaker claim seems plausible: those who are competent to make one well are competent to make one unwell. The reverse is false. Competence with clubs and poisons does not imply competence in surgery and healing drugs. Similarly, it is easy to completely destroy a car and hard to be a mechanic. The asymmetry is interesting. It suggests an important asymmetry between good and evil.

Divine Command Metaethics

The following simple and valid argument came out of discussions with Mark Murphy (who has a forthcoming book that contains related arguments, though perhaps not this one).

According to the identity version of Divine Command Metaethics (IDCM), to be obligated to A is to be commanded to A by God (or to be willed to A by God or to be commanded to A by a loving God--details of this sort won't matter). But:

1. If p explains x's being F, and to be F is the same as to be G, then p explains x's being G.
2. My being commanded by God to follow Christ explains my being obligated to follow Christ.
3. It is not the case that my being commanded by God to follow Christ explains my being commanded by God to follow Christ.
4. Therefore, it is false that to be obligated to A is the same as to be commanded by God to A. (By 1-3)

And so IDCM is false.

The argument more generally shows that no normative-level answer to a "Why am I obligated to A?" question can provide a property identical with being obligated. Thus, sometimes at least the answer to "Why am I obligated to A?" is that Aing maximizes utility. Hence, by an exactly parallel argument, being obligated to A is not the same as having A as one's utility maximizing option.

The argument is compatible with constitution versions of DCM on which the property of being obligated to A is constituted by the property of being commanded to A. But such theorists then have the added complication of explaining what the constitution relation means here, over and beyond bidirectional entailment (after all, many non-divine-command theorists will agree that necessarily x is obligated to A iff God wills x to A).

Infinity

As I walking to class this morning, I was struck by this thought. Historically, the most popular answer to the cosmological argument has been an infinite regress of causes. (That's why the Kalaam argument has such crowd appeal.) And currently the most popular answer to the fine-tuning argument is a multiverse, and probably an infinite one. This shows a kind of inevitability of infinity. Either you believe in an infinite being (assuming one can argue that the First Cause or Designer is God) or you believe in an infinite number of finite beings. In any case, it is an impressive fact about our dim and finite intellectual faculties that they can show us the reality of infinitude. There is a kind of paradoxicality here: learning that there is infinitude (whether an infinite being or an infinite number of finite beings) shows us how limited we are in comparison to that which is not us, and yet it is an impressive feat that we can know of infinitude.

Maybe there is a design argument here, too.

Epistemicism, vagueness and theism

Epistemicists say that our vague natural language is, in fact, fully sharp. If I place grains of sand onto a sheet of paper, there will eventually be a grain of sand such that prior to placing it, there was no heap, and after placing it, there was a heap. We don't know which grain it is, but we know there is one on the basis of the following argument. Let G_n be the sand after the nth grain has been placed. Then, G_1000000 is a heap, and G₁ is not a heap. It is a logical consequence of this that there is a number n, between 1 and 1000000, such that G_n is not a heap and G_n+1 is. And it's obvious that there is no number n which we know to be as above. So, epistemicism is true--there is a boundary, and plainly we don't know where it lies.

The above is a very plausible argument. But it runs into two kinds of problems. First, the incredulous stare: it just doesn't seem like there should be such an n. This has some force, but only if the alternative to epistemicism is something other than revising logic. Plus the epistemicist can give a good explanation of why we are mistaken here. We have a tendency, often exploited by anti-realists, especially in ethics and aesthetics, of confusing what we cannot know with what there is no fact about. Still, the incredulous stare does indeed have a pull on me here.

Second, there is this argument: Language is defined by our practices. Our practices underdetermine which number n is such that G_n fails to fall under the predicate "is a heap" but G_n+1 does fall under it. But something falls under the predicate "is a heap" if and only if it is a heap. Hence, there is no fact about which number n is such that G_n is not a heap but G_n+1 is. One might try to deny that language is defined by our practices or that our practices underdetermine the number n, but unless there is a theory of how language is defined in such a way as to determine the nmber n, this is intellectually unsatisfying.

Theism seems to make it possible to be an intellectually fulfilled epistemicist. For the theist can accept the following theory. God thinks perfectly precise thoughts with no vagueness of any sort. Our language comes to us from God. Just as my use of the words "Beijing" and "quark" get their meanings from other people's earlier use of it, so too our language ultimately gets its meaning from God's decision as to what should mean what. God thinks perfectly sharply, and then set perfectly sharp boundaries for human language's predicates. He didn't, in general, inform us as to the perfectly precise independent specifications of the boundaries. But our language is, nonetheless, perfectly precise.

There are two paths to further development. One path has it that each time our practices have seemingly created a new predicate, God was behind the creation. Jones hears an idea and says it is "cool". No one has used the word earlier in this sense, and the usage takes off. But, in fact, Jones didn't introduce the word by herself in to the language. God cooperated with Jones and filled out the vagueness in Jones' concept of the "cool".

The second path is that God defined precise rules by which bits of language gain meaning. These rules are every bit as precise and deterministic as the laws of Newtonian physics. These rules specify what exactly falls under the predicate "is cool" when the predicate is introduced by Jones in such-and-such a way under such-and-such circumstances.

Both paths further divide into two variants: a constitutive and a causal variant. On the constitutive variant, God's intentions as to what should mean what (specifically in each case, on the first path, and under more general descriptions, on the second) at least partly constitute what meaning-facts there are—that would be akin to divine command theory (in its divine-will variant). On the causal versions, God causes meaning-facts. These meaning-facts may be embedded in the natures of speakers—that would be a Natural Law version—or they may be "out there" (wherever "there" is). (I like the Natural Law version most.)

This gives us a cool argument:

1. (Premise) G₁ does not fall under "is a heap".
2. (Premise) G_1000000 does fall under "is a heap".
3. There is a number n such that G_n+1 falls under the predicate "is a heap" and G_n does not. (Follows by classical logic from 1 and 2)
4. (Premise) The best explanation of (3) is that human language was created by an agent whose thoughts suffer from no sort of vagueness.
5. (Premise) Every non-supernatural agent's thoughts suffer from some sort of vagueness.
6. Probably, there is a supernatural agent whose thoughts suffer from no sort of vagueness and who created human language. (Inductively from 3-5)

I am not endorsing epistemicism. I am still pulled to thinking the sentence-proposition relation is many-many and that classical logic governs propositions rather than sentences. But the above line of thought, and the comparison with Natural Law, makes epistemicism very attractive to me. If God, in creating human beings, can create them with a nature that grounds normative facts about them, he can create them with a nature that defines meanings as well. (Moreover, there may be a reduction of meaning to normativity. One might say that a type A of action is an asserting that p if and only if A ought not be done if not p. There are difficulties in this—it makes the notion of assertion very expansive—but it has its attractions.)

And I can't, off-hand, think of a credible Euthyphro problem here.

[Some minor refinements made from the initial post. -ARP]