Worship

The following argument is sound (given Christian doctrine), where possibility and necessity are metaphysical throughout:

1. It is possible to worship properly.
2. Necessarily, worship is not proper when it is not of a maximally great being.
3. Necessarily, worship is not proper when it is of a non-existent being.
4. Therefore, possibly, someone worships an existent maximally great being. (1-3)
5. Therefore, possibly, there is a maximally great being. (4)
6. Therefore, there is a maximally great being. (S5 and concept of a maximally great being, as in ontological argument)

Here is a subsidiary argument for (1):

7. All basic human forms of activity have proper functions.
8. Worship is a basic human form of activity.
9. Necessarily, when an activity fulfills its proper function it is being done properly.
10. Any basic human form of activity that has a proper function can have that proper function fulfilled.
11. Therefore, worship can have its proper function fulfilled.

A final comment. Dan Johnson has found a nice way to generate arguments like this one. You look for arguments whose premises are each either obvious or entailed by theism. This way, the arguments are guaranteed to be sound (if you think theism is true). However, nonetheless, there might be people who appropriately accept the arguments. Why? For one, maybe they have a left-over of a theistic conviction which they have irrationally rejected. For another, their sensus divinitatis might be telling them to accept premises like some of the ones about worship. Arguments like this will not appeal to a wide audience perhaps. They may appeal to a very narrow audience. But that is OK.

Some sound theistic arguments

Argument 1:

1. Possibly, the Principle of Sufficient Reason (PSR) is true.
2. Necessarily, if the PSR is true, then there is a causally efficacious necessary being.
3. Therefore, possibly, there is a necessary causally efficacious being.
4. Therefore, actually, there is a necessary possibly causally efficacious being.

Argument 2:
Let @ be the actual world. Say that a being is omnipotent* provided it is omnipotent at at least some explanatory point in the history of the world (so omnipotence* is prima facie compatible with giving up omnipotence).

1. Possibly, there is an omnipotent being.
2. Necessarily, if x is omnipotent, then x exists at @.
3. Necessarily, any omnipotent being is essentially omnipotent*.
4. Therefore, there is an essentially omnipotent* being.

Premises (2) and (3) need support. First, necessarily, a being is only omnipotent if it could create me (directly or mediately). But by essentiality of origins I could be created by a being only if I am created by the being. Therefore, if there is a being that could create me, that being creates me at @, and hence exists at @. Thus, (2). Also, plausibly, an omnipotent being could be the First Cause in any possible world. Hence, an omnipotent being must be a necessary being, and hence exist at @. Thus, (2).
What about (3)? Well, an omnipotent being could exercise its omnipotence to put itself in any state possible to it. Suppose it's possible for an omnipotent being to fail to be omnipotent*. Then the omnipotent being could make itself be non-omnipotent* by exercising its omnipotence. But then the being would be omnipotent at some explanatory point in that world where it makes itself non-omnipotent*, and hence it would be omnipotent* there. So absurdity arises. So it's not possible for an omnipotent being to fail to be omnipotent*.

Argument 3:
Say that x knows* p iff x knows p or knows some proposition of which p is a conjunct.

1. Possibly, there is a being x such that for any proposition p that could be true, x could know p.
2. Therefore let w be a world and x a being such that x exists at w and for any proposition p, if p could be true, x could know p.
3. Therefore, if w* is any possible world and p be any proposition true at w*, then x could know that w* is actual and p.
4. x could know that w* is actual and p only at w*.
5. Therefore, if w* is a possible world and p is true at w*, then x exists at w* and knows* that p at w*.
6. Therefore, there is a being that exists at every world and knows* every truth at every world.

God's attributes and the naturalness of hypotheses

For any perfection P, there are two fairly natural hypothesis:

1. God has P to an infinite, maximal degree (e.g., knows everything, is perfectly just, etc.).
2. God has P to zero degree.

So it may seem to be reasonable to suppose, for instance when solving the gap problem in the cosmological argument, that God has each perfection to a maximal degree, or to assign a higher prior probability to that.

But there is an objection to this line of thought. In the case of some perfections, like knowledge, there may be a fairly natural in-between hypothesis, such as:

3. God knows all and only necessary truths.
4. God knows all and only the truths about the present and anything entailed by them.

(Actually, I think (4) is not natural, but a presentist may think it is.)

Fortunately, there is a response to the objection. While for any particular perfection there may, in addition to zero and infinity, be other natural hypotheses, the only two global hypotheses that are really natural (simple, elegant, etc.) are:

5. God has all perfections to infinite degree
6. God has all perfections to zero degree.

If we use "God" to stipulatively designate the necessary being whose existence the cosmological argument demonstrates, hypothesis (5) is clearly preferable to (6), since in order to be the first cause, God cannot have power to zero degree.

Another problem for this line of reasoning is that one might think there are conflicts between perfections. I don't think there in the end are such. But if there were, one might have to modify (5) by saying that God has the best combination of the perfections or something like that.

Self-identification

To identify myself in the relevant sense with some quality is to see that quality as embodying a particularly important feature of myself, as making others who have that feature be potential particularly salient role models for me, etc. This isn't any sort of attempt at an analysis of identification, but simply to hint at which sense of "identify with" I am using. In particular, to identify myself with Q involves existentially more than just identifying myself as having Q, and does not imply a weird claim that I believe I am identical with the Platonic entity Q.

I think I should identify myself with being a child of God, a Christian, a father, a husband, a son or daughter, and maybe a philosopher. I should not identify myself with being big-nosed or lazy or a Frenchman. The last sentence may seem a mix: Maybe I shouldn't identify myself with being a Frenchman, because I am not one. Maybe I shouldn't identify myself with being lazy, because although I am lazy, that is something to fight against rather than identify with. Perhaps I shouldn't identify myself with being big-nosed, because although I have a big nose, and that's nothing to fight against, it's still superficial.

Is there some general story we can tell about what qualities of myself I should identify myself with, a story that will help with the question: Should I identify myself with my ethnicity, sex, gender, sexual orientation, etc.? 

Clearly, the virtuous person identifies with having certain values, and there are certain things that no virtuous person would identify with.

Identifying oneself with a quality, even a quite innocent quality, can carry serious dangers. There is a danger of being guided by stereotypes rather than healthy role models. There is a danger of self-reduction--of not sufficiently seeing oneself in one's individuality (and, correlatively, not sufficiently seeing others in their individuality). There may be a self-curtailing of one's autonomy.

Here is a rough hypothesis. You should only identify with having Q when having Q places you under serious role-obligations whose fulfillment either requires this identification or at least is very difficult without such identification.

Since something that constricts one to fulfill one's serious duties does not objectionably curtail one's autonomy, the autonomy worry about qualities does not apply. Moreover, when the role involves serious role-obligations, the need for role models may outweigh the danger of stereotyping. When the physician identifies herself with being a physician, there is the danger she will rely on stereotypes of her profession, but more likely it will help her fulfill her serious obligations by looking to good role-models. Moreover, one's individuality is particularly importantly expressed in one's serious role-obligations.

The hypothesis fits with what I think about the cases. I think that being a child of God, a Christian, a father, a husband, a son or daughter, and maybe a philosopher each implies serious role-obligations, and the need to fulfill these calls for a self-identification. (My choice to put "father" and "husband" rather than "parent" and "spouse", and "son or daughter" rather than "son", is deliberate and obviously controversial. I am inclined to think the parental and spousal roles are gendered in a way in which filial roles are not, though I am not able to provide a full account. But my bigger points do not depend on this controversial claim.) But being big-nosed, lazy or a Frenchman does not provide me with role-obligations. Being a Frenchman doesn't provide me with role-obligations because I'm not a Frenchman. Being big-nosed is too superficial. Being lazy provides me with an obligation to cease to be lazy, but that is just a special case of a general obligation to be industrious.

Presentism and induction

Start with this rough principle:

1. If a hypothesis that is both simpler and weaker can cover the same data, we should prefer it to an alternate hypothesis that is both more complex and stronger.

For instance, if our data is that all observed emeralds are green, we should prefer the hypothesis that all emeralds are green to the stronger and more complex hypothesis that all emeralds-or-diamonds are green (where x is an emerald-or-diamond iff x is an emerald or diamond). On the other hand, often we should prefer a stronger but simpler hypothesis to a weaker but more complex one.

Now suppose we acquire this data:

2. Every time a star was observed to be formed, that was in a nebula.

And now consider two hypotheses:

3. Every time a star was formed, that was in a nebula.
4. Every time a star was, is or will be formed, that was, is or will be (respectively) in a nebula.

Hypothesis (3) is simpler and weaker than hypothesis (4). So (3) should be preferred to (4). That's a problem, since we want to do induction to the future! Now consider another hypothesis:

5. Every time a star is (tenseless) formed, that is (tenseless) in a nebula.

If eternalism is true, the temporally unrestricted quantifier in (5) is simpler than the temporally restricted quantifier in (3), and so (at least if B-theory holds, but maybe even if not) (5) is simpler than (3). On the other hand, if presentism is true, the quantifier in (5) requires a complex presentist analysis (e.g., using quantification over haecceities or a conjunction of past, present and future quantifiers), and (3) will be simpler than (5). So if presentism holds, then by (1), we should prefer (3) to (5). But if eternalism holds, there is a case to be made for preferring (5) to (3) due to its simplicity, despite the greater strength.

Numinous beings and naturalism

I think the following argument is sound, at least if the conditionals are material.

1. (Premise for reductio) Naturalism is true.
2. (Premise) If naturalism is true, nothing is numinous.
3. (Premise) If naturalism is true, and F is a simple concept that someone has, then at least one individual's having the concept F is caused by something that falls under F.
4. (Premise) The concept of the numinous is simple.
5. (Premise) Someone has a concept of the numinous.
6. If naturalism is true, there is something numinous. (3, 4)
7. Naturalism is not true. (2, 5)

Perhaps, though, the naturalist will say that the numinous is something subjective and merely intramental, and thus deny 2. But:

8. (Premise) There could be a numinous deity.
9. (Premise) Necessarily, if a deity exists, it's not subjective.
10. (Premise) If the numinous is subjective, it is always necessarily subjective.
11. Therefore, the numinous can never be subjective.

Or:

12. (Premise) If something is numinous, it is in some respect greater than us.
13. (Premise) Nothing merely intramental is greater than us.
14. Therefore, the numinous is not merely intramental.

"Causes" and tense

Suppose A is earlier than B and A causes B. Some possibilities. Suppose A is present and B is future. We say:

1. A will cause B.

Suppose A is past and B is present. We say:

2. A caused B.

Suppose we're some time in between the time of A and the time of B. We say:

3. A will cause B.

So, we transition from "A will cause B" to "A caused B" without there ever being a time when we say "A is causing B". This is different from many other relational locutions. First, we might say "A will love B". In the end we might say "A loved B". But in between there is a time when we would say "A is loving B".

The verb "to cause" seems to fit not too well into the tense structure of English. I think that this is because it is a relation best expressed in a tenseless language. And if it is a natural relation, it is a relation that is apt to be problematic for presentists.

The PSR, contrastive explanation and "rather than"

The Principle of Sufficient Reason (PSR) says that every contingently true proposition has an explanation. Suppose you are impressed by the following thought:

1. In cases of libertarian free choice, while we can explain why x chose A by citing the non-necessitating reasons R for A, we cannot explain why x chose A rather than B by citing such reasons, since x would have had R even had x chosen B. In other words, there is no contrastive explanation for x's choosing A.

I think this is mistaken: there is a contrastive explanation, and it is given by the reasons. However, suppose that I can't convince you of this, and so I concede that one can't explain why x chose A rather than choosing B. Does it follow that the PSR is false?

On its face, it seems to. Let p be the "contrastive proposition" that x chose A rather than choosing B. If one can't explain why x chose A rather than choosing B, then one can't explain p. However, I have the following objection (developed with the help of various folks at the philosophy of religion summer seminar at the University of St Thomas). To demand an explanation of why x chose A rather than choosing B is not the same as simply to demand an explanation of any proposition. Instead, the "rather than" in "explain why x chose A rather than B" signals what sorts of explanations will be accepted for the conjunctive proposition that x chose A and x did not choose B—for instance, only those explanations that are contrastive in the sense that they would not hold if x chose B instead. So, on this response, in the contrastive demand for explanation, the proposition whose explanation is demanded has a perfectly good explanation, say in terms of the reasons for choosing A and the incompatibility between A and B, but the "rather than" phrasing contextually says that this sort of explanation is not going to be accepted (or, perhaps, modifies the meaning of "explanation" to "explanation of such-and-such sort"). And it is no counterexample to the PSR to observe that some contingently true proposition might not have an explanation of the sort one is demanding (it is no objection to the PSR that not every contingent truth has a biological explanation). For the PSR does not say that every contingently true proposition has an explanation of every sort one could demand, but only that it has an explanation.

So, if the above is right, there really are no contrastive propositions that demand special kinds of explanations. Compare the following two demands for explanation:

3. Why did George eat the banana?
4. Why did George eat the banana?

I do not think many will want to multiply propositions to the point that we have the following multiplicity of propositions:

• that George ate the banana
• that George ate the banana
• that George ate the banana
• that George ate the banana

A plausible thing to say is that there is only one proposition that (3) and (4) both demand an explanation of, the proposition that George ate the banana (are there italics in the Platonic heaven?), but that the italics specify contextually what explanations would be accepted. It seems very plausible that the phenomenon of emphasis in the demand for explanation is essentially the same phenomenon as the use of "rather than". Indeed, we might even be able to paraphrase (3) as:

5. Why did George eat the banana rather than doing something else with it?

There is one more point to be made (which I basically got from Josh Rasmussen). Sometimes in a report of a choice, the "rather than" occurs in the content of the choice. Thus, someone may choose to eat the banana rather than the orange or, perhaps equivalently, choose to eat the banana over eating the orange. In this case, the content of the choice is contrastive. But a choice with a contrastive content does not demand a contrastive explanation in any sense problematic for the PSR. For there may well be a reason for someone making a contrastive choice—for instance, they may normally eat oranges, but be making a political statement by eating the banana rather than the orange (maybe orange is the color of one political party and yellow that of another). In this sense, there is a difference between:

6. George chose to (eat the banana rather than the orange)

and

7. George chose to eat the banana rather than choosing to eat the orange.

In (7), it is implicated or presupposed or maybe even stated (though I don't think so) that George could have chosen to eat the orange. But no claim is made in (7) that George deliberated between the banana and the orange, nor that he mentally compared them, nor that his chose of the banana was made under a description that said anything about oranges. (Maybe (7) holds because George didn't realize the orange was even an option.) On the other hand, (6) is only true when both the banana and the orange entered into George's deliberation, and he chose the banana under a description that included something like "alternative to an orange". And then we can give a reason, perhaps a non-contrastive one.

I cannot be the greatest being

And here is yet another argument that is sound (given that theism is true):

1. Alexander Pruss couldn't be the greatest being.
2. If theism is not true, Alexander Pruss could be the greatest being.
3. Therefore, theism is true.

The better you know me, the more plausible (1) should be. What about (2)? Well, the intuition is that if theism is not true, then there need not be any infinite beings (I am dismissing as implausible alternatives to theism like Leslie's with multiple necessarily infinite beings, or like weird hypotheses on which there has to be an infinite being in any world where I exist, but it's not God, etc.). But one could imagine a world where I grow smarter, better, stronger and more knowledgeable in every respect, in such a way as to exceed every finite being at that world. Unless there has to be an infinite being in that world, which isn't going to be the case if theism is not true, in that world I will be the greatest being.

If you don't know me well enough to accept (1), replace "Alexander Pruss" with your own name.

A heuristic about contraceptive policy

Here is a quick heuristic about social policy. Suppose it is in the social interest to decrease pregnancy rates in some population of teenagers. Then my quick heuristic is this:

• One cannot expect the promotion of a contraceptive to lower the pregnancy rate very much below the typical-use failure rate of that contraceptive for that population.

For instance, one set of estimates pegs the typical failure rate of condoms for the first year of use at 15% and the pill's failure rate for the first year of use at 9%. In the case of condoms, failure rates decrease with use, and I've seen 5% cited elsewhere for the pill.

What is the reason for the heuristic? It is obviously difficult to simultaneously provide contraception, and instruction on their use, while promoting abstinence. Intuitively (and I'm just giving a heuristic) we do not expect mixed messages to work well. But the only way we're going to get a pregnancy rate below the typical-use failure rate of the contraceptive is by having some people abstain totally or to decrease their sexual frequency significantly below the number used in the typical-use failure rate calculations. But we would expect, for rational choice reasons, the availability of contraception to decrease the rate of total abstinence by reducing the costs of intercourse, and we would also expect it to increase sexual frequency. Here is a rough estimate. Suppose Sally disvalues pregnancy in her circumstances at somewhere between 1.2 and 20 times the value of a year of sex (very roughly: she'd be willing to abstain about 1.2 years to avoid a pregnancy in her circumstances but she wouldn't be willing to abstain 20 years to avoid it). It seems intuitively right to me that many teens will fall in this range. Then if pregnancy is the only consideration, it is decision theoretically rational for Sally to max out her sexual activity if she is on the pill but to abstain totally if she is not using any contraceptive (this is a pretty easy calculation using an 85% no-contraceptive annual conception rate).

The U.S. teen pregnancy rate in 2006 was 7%. Promotion of the pill could imaginably lower that somewhat, if the 5% figure is correct, but not if the 9% figure is. However, unless these teenagers use both the pill and condoms, there will be significant health risks for sexually transmitted infections. Because of these, any contraceptive-based policy would likely involve condoms as well. But intuitively one does not expect all that many teens to double up and use both the pill and condoms. If condoms are promoted, we'd expect a significant percentage of the sexually active population to use only condoms. If we have a half-and-half mix between condoms and the pill, and no overlap, there'll be a failure rate around 10-12%. Which is significantly higher than the pregnancy rate, at least with 2006 data.

The value of the pleasure in sex

When loving parents make decisions concerning their teenage children, they put very small, if any, weight on the physical pleasure of sex as isolated from other things. For instance, that some course of action is likely to increase the number of times that the child experiences the physical pleasure of sex counts very little in favor of the course of action—it may even count against it. Parents are either mistaken in this weighting or not.

We would expect parents to be more reliable in weighing the values of pleasures of activities that they themselves find pleasurable. But typical adults do find sex pleasurable, and presumably that includes the parents (and may even help explain why they are parents). Indeed, typical adults find sex physically as pleasant as teenagers do, or more so due to greater experience. Moreover, I think we would expect parents if anything to be better judges of the values of outcomes in the case of their children than in their own case, at least when the outcomes are ones that the parents are familiar with and find pleasant or unpleasant in much the way that the children do. One is likely to be more clearheaded when one is making decisions for someone else.

But if this is right, then parents are probably right when they put very low weight on the physical pleasure of sex in the case of their children. Thus, probably, the physical pleasure of sex has very low value in the case of children, at least in itself. But since this physical pleasure is basically the same in adults (perhaps somewhat greater due to experience, but likely not an order of magnitude greater, at least in males), it follows that the physical pleasure of sex in and of itself, isolated from other considerations, has very low value in general. (Of course, the pleasure as combined with other goods may have significant value.)

Can it be instrumentally rational for a parent to object to a child's receiving contraception?

Let's bracket all moral concerns, and simply suppose that the parent does not count sexual activity by her minor children as having positive utility (or at least counts it as of such low utility as to be negligible), but does count a pregnancy (in the child or caused by the child) as a significantly negative outcome. Rhetoric from those advocating greater availability of contraception to children suggests that such a parent would be instrumentally irrational to object to the child's receiving contraception.

However, this is mistaken. Typically, children also consider a pregnancy a significantly negative outcome. Therefore, in a large enough population, there will be children who would be very unlikely to engage in sexual activity if there is a significant danger of pregnancy, but if that danger were significantly reduced, would engage in sexual activity. In the case of such children, it may very well be the case that the availability of contraception increases the risk of pregnancy. For instance, suppose that without contraception, over the period of a year the child would have a probability of 0.98 of not engaging in sexual relations at all. But if the pill is made available, the child has a probability of 0.50 of using it and having an average sexual frequency for sexually active persons.

Now, if contraception is not made available, the likelihood of a pregnancy is (0.02)(0.85)=0.017, where I shall suppose 0.85 is the probability of conception without contraceptives at an average sexual frequency for a sexually active person. This is actually an overestimate of the likelihood of a pregnancy, since if the child is afraid of a pregnancy outcome, the frequency is likely to be significantly lower. If the pill is made available, the likelihood of a pregnancy then will be (0.50)(0.05)=0.025, where the 0.05 is permthe typical-use failure rate for oral contraceptives.

Therefore, a parent who knows with a sufficiently high probability that her child satisfies the above assumptions and seeks to prevent the child's pregnancy will be instrumentally rational in refusing contraception for that child.

Moreover, since there surely are such children in the population (there is, obviously, a broad distribution in the attribute of caution in teenagers, and there are teenagers who are very cautious), it follows that even if making contraception available to all teenagers were to reduce the overall pregnancy rate (and I am not aware of any data that it would), there would be some individuals the risks for whom would be increased by the availability of contraception. And, of course, there will be individuals the risks for whom would be decreased by the availability of contraception—namely, those who would have a sufficiently large sexual frequency even without contraception. Therefore, making contraception available to all teenagers results in a redistribution of risks—some come to be better off pregnancy-wise and some come to be worse off.

Now, while it can be licit to have a public health initiative that redistributes risks, increasing those of some and decreasing those of others, significant gathering of empirical data is needed before any such policy is put into place, to ensure not only that the overall risk is decreased, but also that no subgroup's risk is increased in a way that is morally unacceptable. For instance, if a chemical added to the water were to improve the dental health of a majority ethnic group but decrease the dental health of a minority ethnic group, the introduction of that chemical would be morally problematic—significant amount of information-gathering would need to be done, and attempts to limit the application of the initiative to the minority might well need to be made (e.g., not adding the chemical in the areas where members of the minority group are more likely to be found).

In particular, the following empirical outcome is imaginable. It could be that the availability of contraceptives significantly increases the likelihood of pregnancy among religiously conservative teenagers, because without the availability of contraceptives they have two reasons to avoid sex: (a) religion and (b) pregnancy (and disease, but what I say about pregnancy applies to STIs mutatis mutandis), which two reasons may result in a high probability of abstinence and hence a close to zero pregnancy rate (rape can happen despite abstinence, so it's not exactly zero), while with the availability of contraceptives the second reason largely drops out, and the abstinence rate may significantly decrease. If that were so, then there would be an identifiable group for whom the risk of pregnancy would be increased by the availability of contraception. I do not know if it is so or not—that is an empirical question, and either answer is possible depending on how the probabilities work out. But it is not irrational for parents of religiously conservative children to worry that the availability of contraception might increase the risks of pregnancy for these children, and it might well be irrational to be confident that it does not increase these risks unless one has significant empirical data (of which I am not aware).

Getting to S4

This is an outline with proofs omitted. Start with a notion of necessity L that satisfies the constraints of System T and take as an axiom the Natural Numbers Barcan Formula (NNBF):

1. L(n)(Fn) iff (n)LFn,

where the quantification is over natural numbers only. I think NNBF is pretty plausible. It certainly avoids all of the implausibilities of the standard Barcan Formula. Basically, it just says that every world has the same natural numbers.

Now, we can bootstrap our way up to a logic satisfying S4 from the logic that uses L. Let Lⁿp be L...Lp with n Ls. Let L*p be (n)Lⁿp. I think the following is true, though it may take some work to prove it and will need for every p a predicate F such that Fn iff Lⁿp: if L satisfies System T and NNBF is an axiom, then L* satisfies S4. Moreover, intuitively, L* has every bit as much, and maybe more, right to be called "metaphysical necessity" as L does. So, given a modal logic that satisfies T and NNBF, both of which are pretty plausible, we can define a metaphysical necessity operator that satisfies S4. I think this makes it plausible that ordinary metaphsyical necessity satisfies S4.

Radical Essentiality of Origins and a crazy theory of names

Radical Essentiality of Origins (REO) is the thesis that the complete origins of an entity x are necessary and sufficient to the identity of x. In other words, for any x, if D is a complete description of the origins of x (all the history prior to x, as well as x's initial state), then necessarily something is an x if and only if it has D. In other words, according to REO, origins function like haecceities.

REO has a number of benefits. It reduces the number of brute facts (one doesn't have to explain why I exist instead of someone just like me), it reduces transworld identity facts to REO and diachronic identity, it explains how God knows whom he will create, and so on. It has one cost: it reduces the number of possibilities, eliminating apparent possibilities that people might think are real (like the possibility that I might have lived your life, or had a slightly different causal origin, or that there be two indiscernibles). Moreover, Kripke's quantified modal logic has the deficiency that it has no room for names; but if REO is true, names aren't needed, as we can just use definite descriptions, pace Kripke.

Here's something really crazy you can do with REO. You can rescue something like the definite description theory of names. You say: a name functions as an abbreviation (in a broad sense—I will say a bit more) for a definite description in terms of origins. Thus, "Socrates" abbreviates: "The son of Phaenarete and Sophroniscus, grandson of ..., conceived at ..."

An apparent problem is that it seems that to grasp an abbreviation, you must grasp what it is an abbreviation for. But that may well be false. One can have the concept of the U.N. or of a someone's being a POW without knowing what the abbreviations stand for. (We could explain this datum by saying that there are in fact two words "POW"—one is an abbreviation and the other is a word in the idiolect of those who don't know it's an abbreviation. But the proposal that one can understand an abbreviation without knowing what it stands for is simpler.)

Maybe, though, some user of the abbreviation has to know what it's an abbreviation for. But suppose that Sally wrote down on a piece of paper some definite description, and sealed the piece in an envelope. Then she told me some facts about what satisfies the description, without telling me the description. Maybe it's a riddle and I'm supposed to guess what the description is. So I say: "Let 'D' abbreviate that definite description." I can then use "D" grammatically as a definite description. For instance, if Sally's hints imply that the description isn't (even de facto) rigid, then I can say: "D might not have been D." So I can use "D" in my language. Now, there is a question whether such use is sufficient for counting as grasp. It either does or does not. If it does, then there is no objection to the REO account of names—we just suppose that names function as abbreviations for definite descriptions of the origins, but we don't know what these definite descriptions are. But if it is not sufficient for counting as grasp, we can still say the same thing about how names function. We just have to say that we don't grasp names, though we are able to use them. Maybe only God grasps my name. Or, perhaps, the better thing to do is to distinguish different kinds of grasp. We have a sufficient grasp of a name to use it.

I don't know how this can be extended to fictional names. But Kripke's account of names has that problem, too.

A problem with this theory of names is that there isn't a unique definite description of origins. Conjuncts can be re-ordered, etc. I think to some people this isn't going to be a great cost—maybe a name is an ambiguous definite description (i.e., it's ambiguous which definite description it is), but the ambiguity does not affect extension in any possible world. (Then, maybe a fictional name is an ambiguous definite description where the ambiguity does affect extension?) I don't like that. Another problem this is that I actually think "Tully" and "Cicero" mean different things. To me, this is a very strong, maybe fatal, objection to the crazy REO-based theory of names. But it is a standard view that "Tully" and "Cicero" have the same sense, so to others this won't be much of an objection.

Enough fun for now.

Another argument against gear-minds

Here's another argument against gear-minds. Start with the intuition that one cannot make a mind cease to exist without causally interacting with the individual whose mind it is or a part of the individual. Now imagine that the gears that the mind is made of are like those in this diagram . They have radiating spokes, and between the spokes is a hollow area. This reduces the weight of the gear while maintaining a significant portion of the strength.

Now, imagine that an inflexible spike is simultaneously inserted into the middle of every gap between spokes, without the spike touching any gear. Because the gears are no longer able to turn more than, say, a sixth of a rotation, and because any mental operation would surely require a larger turn of at least one wheel (we can stipulate this about our gear-person), a result of the introduction of the spikes is that the individual is no longer capable of any mental functioning. The gears can turn a little, but not enough to result in a mental operation. Moreover, no counterfactuals of the form "If input A were given, the individual would believe Q" are true any more. This means that if the functionalism requires such counterfactuals or the capability of mental functioning, as non-Aristotelian functionalisms are apt to require, there is no longer a mind. But because the spikes went between the spokes in such a way that no contact was made with any part of the individual, this violates the principle that one cannot make a mind cease to exist without causally interacting with the individual or a part thereof.

Could something made of gears be a person?

Leibniz offers as a reductio of materialism the idea that if materialism is true, one could have a mind whose functional parts are like the parts of a giant mill, and you could walk right through that giant mill, seeing big wheels of all sorts. But, he thinks, you'd never meet with consciousness.

Leibniz's argument has two parts:

1. If materialism is true, a mind could be made of large gears (together with some source of kinetic energy, like a large water wheel).
2. A mind could not be made of large gears (plus energy source).

I think step (1) can be backed up as follows:

3. If materialism is true, functionalism is true.
4. If functionalism is true, then any physical system that can do sufficiently complex computations can be a mind.
5. A system of large gears (with an energy source) can do arbitrarily complex computations.
6. Therefore, (1) holds.

Leibniz doesn't do much to back up (2). The purpose of this post, and perhaps some succeeding ones, is to try to do this.

Here's one approach. If a mind could be made of gears, so could a person. Imagine a person made of hard plastic gears. Moreover, every so often the gears are given a rest (maybe so they can cool off—we don't want them to melt)—a small clockwork contraption disconnects the energy source, and everything, except that clock, becomes motionless. Now, a person exists while asleep, and it's plausible that in the rest state, the person would still exist.

Scenario 1: The whole set of gears, but not the wake-up clock, is in a big closed box, and while the gear-person is in a rest state, a thin slow-set two-part epoxy is poured into the box. It turns out that the person could still function with the epoxy, because the source of energy is powerful enough to move the gears through the liquid. However, slowly, the epoxy sets. Within 24 hours, what we have in the box is basically a single solid chunk (if we like, we can imagine the gears were themselves made of the same kind of epoxy, and then maybe one can't even tell where the gears were—but Scenario 2 won't work in that case). A single solid chunk like that isn't a person. So, during the 24 hour epoxy curing process, the person gradually ceases to exist. If we believe there cannot be vague existence, then that's enough to yield absurdity: persons can't cease to exist gradually. But it would be absurd if some slight change in the set of the epoxy were to make the difference between existence and non-existence. But even if vague existence is possible, here there is something weird. We have a continuum between something with the kinds of non-occurrent mental states that a person has—states like knowing how to speak German and believing that naturalism is true—and something without them. Moreover, if the epoxy cures uniformly, all of these states fizzle out uniformly. Now, maybe, we could imagine a person ceasing to exist gradually by having mental abilities go away one by one, losing memories one by one, and so on. But here at any time at which we have a person, we have a person with the same full set of the non-occurrent mental states of a person, adn then eventually we have something with no mental states at all. That seems weird.

If one thinks that the person continues to exist when the epoxy cures, but simply is encased in epoxy, then one is going to have to say that a plain block of marble with an energy source can also be a person, but one encased in marble (one can make gears out of marble): there really is a Hermes in the stone. And that's absurd.

Scenario 2: The epoxy has a slightly different chemical composition from the gears. After the person has ceased to exist due to the epoxy having set, a chemical removes the epoxy, leaving the gears intact. And so we have a person again. If temporal gaps in existence are possible, this case doesn't add anything to the story. But suppose temporal gaps are impossible. Then we have something weird. For we can make an argument that the person after the removal of the epoxy is the same as the person before. Here's the argument. We can imagine a variant story. In order to clean out and cool the system, during the rest state, water is poured into the gearbox and frozen. Then it's melted and removed. Intuitively, the person should count as surviving that. But how is that different from the epoxy case when the epoxy is going to be removed? It's not—so after the removal of the epoxy, we have the same person, which contradicts the assumption that temporal gaps are impossible.

Best guess at objective probability

I think I may have once thought that epistemic probabilities are something like one's best guess at the objective probability. But that's obviously mistaken. Suppose Sally tells me that the objective probability of some future event is 0.8. Sam tells me the probability is 0.2. God tells me that either Sally or Sam is right. Moreover, I know that that Sally tends to be right 60% of the time. What should my epistemic probability of the event be? Well, my "best guess at the objective probability" is 0.8—what Sally says, since she's right 60% of the time. But obviously my epistemic probability should be (0.6)(0.8)+(0.4)(0.2)=0.56. Which I know is at least 0.24 away from the actual objectively probability.

Mumford's "Ungrounded Argument"

Mumford's argument for dispositions not grounded in non-dispositional properties is:

1. Some subatomic particles are simple.
2. Simples have "no lower-level components or properties".
3. All properties of subatomic particles are dispositional.
4. If x has a grounded dispositional property, the ground of that property is "among the lower-level components or properties" of x.

Here is one problem. A proton is supposed to be composed of two up quarks and one down quark, and this is a compositional, and not a dispositional, property of the proton. Maybe it is charitable, however, to restrict 3 to simple particles.

However, even after this modification, it seems that 3 is dubious. For instance, suppose an up quark is simple. But then, isn't simplicity a property, and a non-dispositional one at that, so that the up quark has a non-dispositional property?

Perhaps, then, we need to have a sparse view of properties. But simplicity seems sufficiently natural to qualify as a property even on sparse views. A different way to save 3 would be to restrict to intrinsic properties, and have a very narrow view of intrinsic properties: having an intrinsic property does not depend on an entity's relations to other entities or the lack of such relations. But being simple depends on not standing in a whole-to-part relation to anything else. In fact, the same restriction lets us not worry about the proton counterexample to 3, since being composed of quarks is not an intrinsic property, then. Note, however, that such a notion of intrinsic properties is narrow enough—for instance, squareness might not be an intrinsic property, since maybe an object is a square only because its parts are arranged a certain way.

But let us continue with such a narrow sense of intrinsicness. Is 3 true? Maybe not. Bill the Up Quark seems to have all sorts of non-dispositional properties: being identical with Bill, being u seconds old, having a worldline that is shaped in such-and-such a way, etc. Maybe some of these don't count as properties on a sufficiently austere sparse account of properties. But all that needs significant argument.

Actually, I am not completely sure about 4, or more precisely the conjunction of 3 and 4. Suppose Occasionalism is true. Then properties like "charge" are grounded in God's dispositions to move particles around. In such a case, we might keep 4 but deny that anything other than God has dispositional properties, or else we might keep 3, but allow that the particles' dispositions are grounded in God's dispositions. Now, Occasionalism is false. But the same issue comes up if one thinks that laws of nature are grounded in global entities—say, fields—that push particles around. Now, in such a case, we can try to ask about the entities that push particles around—don't they have dispositional properties, and aren't they simple? And quite possibly the answer is positive. But a lot more work is needed here.

Content externalist solutions to sceptical problems

A standard solution to general sceptical problems is to move to an externalist account of content. Grossly oversimplifying, if what makes a thought be about horses is that it has a causal connection with horses, then thoughts about horses can't be completely mistaken. This sort of move might be thought to be anti-realist, though I think that's a poor characterization. If this sort of move works, then we couldn't have thoughts and yet have our whole system of thoughts be completely mistaken. And hence, it seems, scepticism is dead.
But it just occurred to me that there is a hole in this argument. Why couldn't the sceptic who accepts the externalist story about content still say: "So, if I am thinking at all, then global scepticism is false. But am I thinking at all?" This may seem to be a completely absurd position—how could one doubt whether one is thinking? Wouldn't the doubt be a thought? Yes, the doubt would be a thought. Hence, the person who doubts whether she thinks would not be able to believe that she doubts. And, of course, the person who thinks she's not thinking has a contradiction between the content of her thought and the fact of her thought, but it's not so obvious that that's a contradiction in her thought (just as a contradiction between the content of an astronomical belief and an astronomical fact need not be a contradiction in the thinker's thought). Besides, the Churchlands think that they have no thoughts, and have given arguments for this.
If I am right in the above, then the content externalist move does not solve the problem of scepticism—it simply radicalizes it. But it raises the cost of scepticism—it forces the sceptic to stop thinking of herself as thinking. And as such it may be practically useful for curing scepticism if the sceptic isn't a full Pyrrhonian, in the way a rose or some other creature that has no thoughts is. However, if the motivation for the content externalism is to solve the problem of scepticism, rather than cure the sceptic, then the motivation seems to fail. (One difference between solving and curing is this. If a theory T solves a problem, then we have some reason to think T is true by inference to best explanation. But if believing a theory T would cure someone of a problem, inference to best explanation to the truth of T is not available. Though, still, I think the fact that believing T is beneficial would be some evidence for the truth of T in a world created by the good God.)

Theft

Common sense says that if you leave a more valuable item out, it is ceteris paribus more likely to be stolen. If we're asked why, I think we'd say: "The temptation is bigger." But this can't be the whole story. For while the reason for stealing is proportional to the item's value v_t to the potential thief, the moral reason not to steal seems proportional to the value v_o to the owner (after all, surely it's about equally bad to steal two items that are worth 50 thalers each than to steal one that's worth a hundred). Moreover, roughly, v_t is proportional to v_o (with a convex tapering off at the high end of v_o as very valuable things are hard to fence). So we might expect that as we double v_o, we roughly double the strength of the potential thief's reason to steal and roughly double the strength of the moral reason not to steal, and we might expect the two effects to cancel out, leaving the chance of theft unchanged. Compare theft to bribery. One has no greater a moral reason to refuse a large bribe than to refuse a small one, at least if the briber can afford it. In the bribery case, there is nothing surprising about people being more likely to take greater bribes.

The above analysis, however, neglects the fact that one also has a non-moral reason not to steal from the chance of getting caught and punished. And the punishment is not directly proportional in intensity to v_o: one doesn't go to jail for ten thousand times as long for stealing ten million dollars as for stealing a thousand dollars, I assume. Moreover, there is an initial non-proportional disvalue just in getting caught, dealing with the legal system, etc.

However, I do not think the lack of exact proportionality in punishment fully accounts for our intuition here. For, I think, we may also have the intuition that more valuable items are more likely to be stolen in the case of thefts where the thief thinks he can't get caught. We just see the more valuable items as "more corrupting". (Actually, maybe, the function is somewhat more complex. Items of very low value may get stolen more easily "because it doesn't do any harm", and items of very high value may get stolen more easily "because they corrupt", while items of middle value might be less likely to be stolen. I will ignore the extreme low end of value.)

The "more corrupting" intuition can, I think, be accounted for in this way. We recognize an intrinsic disvalue in acting viciously or becoming a vicious person. But the disvalue is more binary: being a thief versus being a non-thief; committing this theft versus not committing this theft; being a criminal versus being innocent. Catholics might make a ternary distinction: acting rightly versus sinning venially versus sinning mortally. But still there is a lack of proportionality.

It may be quite beneficial to have such a lack of proportionality—it keeps us from first stepping over the threshold of a new kind of moral evil, such as theft. If we were willing to commit small thefts on the grounds that they are not really morally all that wicked, we would be likely to slide towards greater ones. So it makes sense for there to be a bar against embarking on a new kind of wickedness. And then the greater temptation helps overcome that initial bar. If so, then the felt disvalue of committing a theft when one has not done so as yet is: B+cv_o, where B is the initial bar against "becoming a thief" and c is some proportionality constant. If that is the right story, then we might predict that people who see themselves as thieves are as likely to steal small amounts as great when they do not expect to get caught, while people who do not see themselves as thieves are more likely to fall for a greater amount.

Proxies for actualists and presentists

Suppose that, necessarily, propositions exist necessarily and that things that exist necessarily exist always. Also suppose that, necessarily, for any actual object x, there is a proposition that x=x. Then there are proxies for all non-actual objects. Say that a proposition p is a "self-identity proposition" if possibly there exists an x such that p is the proposition that x=x. Say that a self-identity proposition p is "about a" if there actually is an x such that x=a and p is the proposition that x=x. Say that the "proxies" are the self-identity propositions.

Then if w is a world (respectively, a time), P is a property, and p is a self-identity proposition, we can say that P*(p,w) iff it is true at w that: (a) there is an x such that p is about x and (b) x has P. So we have a proxy of world- (respectively, time-) relative predication for our proxies. We can similarly extend this to relations, as long as they are not inter-world (respectively, cross-time) relations.

What this seems to mean is that as long as all propositions exist necessarily, we don't specifically need haecceities to have proxies for actualists and presentists. But the gain is illusory. For if we want haecceities, we can define them using self-identity propositions: Necessarily, for all x, x's "haecceity" is the property of being such as to have the proposition that x=x be about one.

That all propositions exist necessarily follows from two plausible claims: (a) all necessary propositions exist necessarily; and (b) if a disjunctive proposition exists, so its disjunct propositions. For if p is any proposition, and q is any necessary proposition (say, that 1=1), then their disjunct is a necessary proposition, hence exists necessarily (by (a)) and hence its disjunct p exists necessarily.

I think it follows that the enemy of haecceities needs to deny, with Adams, that necessary propositions exist necessarily. And someone who wishes to deny the presentist the use of proxies needs to deny that necessary propositions exist always.

Can presentists say enough? Part I: Counting

There are eternalist sentences which seem to make perfect sense, but which it is hard for a presentist to make sense of. For instance, consider this sentence:

1. There were, are and will be a total of n horses,

where n is a finite or infinite cardinality. David Lewis showed that there is a way for presentists to make sense of (1) for finite n, but last time I checked, it wasn't known if this can be done for infinite cardinalities. Of course, if there are haecceities it's easy: (1) is equivalent to saying that the set of haecceities that have been, are or will be exemplified by a horse has cardinality n. But haecceities seem to me to be a cheat, whether for presentists or for modal actualists. Besides, (1) doesn't seem to be about haecceities—it seems to be about horses. So it's an interesting question whether (1) can be made sense of for infinite cardinalities without haecceities.

It turns out it can. For the solution, the presentist needs an "ExistAgo(x,t)" operator, where t is a real number (in some fixed unit system), so that "ExistsAgo(x,7)" means that x existed 7 units ago, "ExistsAgo(x,0)", which we can abbreviate "Exists(x)", means that x presently exists, and "ExistsAgo(x,−3)" means that x will exist in 3 units, and a "t ago:" sentential operator (where t is a real number in the same unit system), with the embedding rules being such that "t ago: u ago: p" is roughly equivalent to "t+u ago: p"[note 1] while "t ago: ExistsAgo(x,u)" is roughly equivalent to "t+u ago: Exists(x)".

For with such operators, we can define counting as follows. Let S be the set of all non-empty subsets of the reals. If K is a kind-term and s is a member of S, there is a unique cardinality n(K,s) such that for any member t of s we have:

2. t ago: n(K,s)=Card { x : Kx & ExistsExactlyAgo(x,s−t) },

where s−t = { u : u=v−t for some v in s }, and ExistsExactlyAgo(x,s) iff for all real t, ExistsAt(x,t) iff t is a member of s. In other words, n(K,s) is the number of Ks that exist exactly at the times indicated by s. Then we say:

3. There have been, are and will be exactly n Ks iff the sum of n(K,s), as s ranges over the members of S, equals n.

So the non-haecceitist presentist can solve the problem of counting items at different times, even up to arbitrary cardinality. Moreover, it seems like here horses really are being counted, not just horse haecceities, though they're being counted in a funny sort of aggregation.

There are, of course, other expressibility challenges for presentists, especially non-haecceitist ones. More on that on a later occasion.

Fun semantic paradoxes

If you're told "Don't do anything Jones tells you to do today", and the speaker is Jones, have you done what you were told to?

If you promise to do today whatever I ask for, and I ask you to do nothing today that a fool asks you for, but unbeknownst to me I am a fool, have you done what you promised?

If I say: "I'll have whatever the chef recommends" and the chef recommends that I have what I ordered, and I get fried bananas, have I got my order?

Property entailment as the ground of modality

Consider a view on which all modality is grounded in property entailment: the relation between properties F and G expressed by "having F entails having G". Jubien has defended a view that might sound like this (though see comments at the end). One way to make this precise is to say that the theory of necessity is generated by the axiom schema

1. (x₁)...(x_n)(A(x₁,...,x_n)→B(x₁,...,x_n)),

where A expresses a relation that entails the relation expressed by B (I take relations and properties to be the same thing here, just that we use different words depending on the adicity), and where → is material implication, together with the rule of inference that

2. from a subproof of p that reiterates no assumptions other than instances of (1), we can derive Necessarily(p).

Here is one quick problem. This fits best with a Platonic metaphysics of properties (Jubien certainly does that). On a Platonic metaphysics of properties:

3. Necessarily(a is a circle → circularity exists).

Actually, standard Platonists will say that the consequent holds necessarily, independently of the antecedent, but we don't need this for the argument. But (3) cannot be proved via (1) and (2), unless the system is inconsistent. Why? Here is a simple way to see this. The axioms make no reference to circularity. There are instances of (1) that use the predicate "is a circle", but that's not good enough.[note 1] But then take any proof of (3) and replace "circularity" with a non-referring singular term. We will then get a proof that the referrent of the non-referring singular term exists, and given that the axioms are all true (this is uncontroversial), the only way we can get a proof of a falsehood is if the system is incoherent.

One might think that something could be done if existence is a property and there are entailment relations like that being a property entails existence. But that won't help unless we add to the axioms that circularity is a property. But the axioms are automatically necessary by (2), so now we are no longer just giving a property entailment account. We are adding axioms that directly force cerain essentialist claims, like that any property is essentially a property.

Alright, maybe that's unfair. Maybe any Platonist who has a property entailment view of modality will also have among the axioms the schema:

4. exists(P)

for every property P. But what about other very plausible necessities, like:

5. Necessarily(circle(a) → circularity is a property).

We had better not make existence entail propertyhood, as then Obama becomes a property.

Of course, we can add things like (5) to our axiom scheme. But the theory is now really swelling, and it is no longer true that it grounds modality in property entailment. It grounds modality in provability from a whole bunch of axiom schemata, one of which is the property entailment one.

My fairly quick glance at Jubien doesn't show him discussing this. But it does show him discussing a related issue, Kripkean arguments that a certain particular table must be made of wood. Jubien says that the table has a "table-essence" being this table and being this table entails being made of wood. So he could handle (5) by saying that circularity has an "object-essence" (I think it had better be an obejct essence, in his terminology), being circularity, and that being circularity entails being a property. Fine so far, but what about the following necessities:

6. Necessarily(exists(circularity) → circularity has being circularity).

So what this shows is that on the proposed account we need additional necessity-generating axioms governing object essences. When Jubien introduces object essences, he explicitly says that they have modal properties, such as that an object necessarily has its object essence. So perhaps Jubien is not someone we should describe as giving an entailment view. For maybe he has an axiom schema that generates (6), as well as the Platonist schema that generates (5). Now as long as the theory of necessity was generated by (1) and (2), it was a pretty cool partial reduction. But once we had to add the schemata (4) and something generating (6), we start to wonder: what guarantees that no further schemata need to be added? All the axioms are automatically necessary, after all, and once we have a plurality of schemata, we have failed to explain what they all have in common—what makes them all be necessary. The account becomes in effect disjunctive.

Here is a different kind of problem. Consider this claim:

7. Necessarily(wrongs(x,y) → agent(x)).

Only agents can wrong. But (7) isn't an instance of (1). Now, maybe, "wrongs(x,y)" is an abbreviation for something one of whose conjuncts ascribes to x a monadic property that entails being an agent. But what if it's not like that? And is it really plausible that all relations that entail a monadic property in one of the relata are abbreviations for stuff that includes a monadic property attribution? (Here is an example every Platonist should accept: Instantiates(a,circularity) entails circle(a).)

So, it seems, the system needs to be extended to include entailments between relations of different adicities. Moreover, it needs to be extended to include entailments between relations of the same adicity but with the relata reorganized:

8. Necessarily(wrongs(x,y) → iswrongedby(y,x)).

We no longer have just entailment between relations, then, at the base of the system. We have what one might call "twisted entailment". Specifically, if f is a function from {1,...,m} to {1,...,n}, we can say that the n-adic property P f-twistedly-entails the m-adic property Q provided that:

9. Necessarily(A(x₁,...,x_n) → B(x_f(1),...,x_f(m))),

where A and B express P and Q respectively.

The view is still non-trivial. But it is messy, and it is difficult to see what motive one has for believing it rather than just giving up on the grounding project altogether—or going for my view. :-) After all, f-twisted-entailment is not such a natural property as entailment.

[Fixed definition of twisted entailment.]

Feeling at home in the universe

When I was a kid, and early in my amateur astronomy hobby, I found the night sky spooky. But now I feel relaxed and at home in the starry dark, with a telescope and (electronic) charts. There is a pleasant familiarity (though I still don't know the constellations by name very well; I often just see the shape on the chart and think of them as "the one that has such-and-such a squiggle"). I wonder if the feeling of at-homeness in the universe isn't some evidence that the universe is created for humans. On the other hand, we are made for heavenly life and exiles here. So maybe the feeling is pernicious. But the "here" where we are exiles, maybe that is not a spatial here. Perhaps the new earth and the new heavens will include--as in the last Narnia book--all the best features of the present earth and the present heavens. (For the report of the observing session that led to this reflection, see here.)

Presentism and the contingency of time

1. (Premise) If presentism is correct, it is impossible that something has a timeless existence.
2. (Premise) Possibly, there is no time.
3. (Premise) Necessarily, something exists.
4. (Premise) Necessarily, if there is no time, everything has a timeless existence.
5. There is a world w where there is no time and yet something exists. (2 and 3)
6. In w, something has a timeless existence. (4 and 5)
7. Presentism is not correct.

Premise 3 is pretty plausible. It's accepted by theists (who think God necessarily exists), Platonists (who think abstracta do) and by Bergsonians who think it is a necessary truth that there is at least one contingent being. Presentists thus have to deny 1 or 2 or both.

Here is an intuition in favor of 1. A timeless mode of being is an intrinsic characteristic of a being. Now it should be possible to combine beings with all sorts of possible intrinsic characteristics. Thus, if a timeless mode of being is possible, then it should be possible to have a world much like ours but where there is also a timeless being. But that would be a world where presentism is false, since then existence of timeless beings is incompatible with presentism, as presentness would no longer be coextensive with existence. Now, we make this move: as soon as it is admitted that such a world is possible, what reason do we have to think it's not actual? We are in no position to know there aren't any such timeless beings, given that they could coexist with beings like us. And now, while presentism could be true, we have little reason to think it is. So presentists should accept 1.

Maybe, though, presentists should make this move: Timelessness is just presentness in the absence of anything past or future. In that case, 1 may be false. Timelessness is no longer an intrinsic characteristic of a being, and there could be worlds where all there is is a present. However, it seems to me that it is essential to a present to be evanescent. But timelessness is opposed to evanescence. On this analysis of timelessness, some instantaneous event would be timeless if nothing came before it and after it. But surely that would make it no less evanescent.

So, perhaps, presentists should deny 2. But, the following seems quite possible: there is a time than which there is no earlier. It is also imaginable that there is a time than which there is no later. And there is no reason why you shouldn't be able to combine the two, and have a time than which there is no earlier or later. In such a world, there would still be a time—a single present—but there would be no past or future, no flow of time. Everything in such a world would be maximally evanescent, if there were no timeless beings. But, plausibly, neither God nor Platonic abstracta could be maximally evanescent.

Talking of God brings us to another argument, or, actually, a pair of arguments (it's up to you which version you find more plausible):

8. (Premise) Possibly, time has a beginning (respectively, an ending).
9. (Premise) God can have no beginning (an ending).
10. (Premise) God exists necessarily.
11. (Premise) If presentism is true in a world, everything in that world is a temporal being.
12. (Premise) If there is a world where time has a beginning (ending) and if presentism is actually true, there is a world where time has a beginning (ending) and presentism is true.
13. (Premise) In a world where time has a beginning (an ending), every temporal being has a beginning (an ending).
14. If presentism is true, possibly God has a beginning (an ending). (8, 10, 11, 12)
15. Presentism is not true. (9, 14)