A Short Argument that There is No God

I was thinking about Mackie and Plantinga on the problem of evil today and I thought of the following short argument that, I think, captures the spirit of Mackie’s point and avoids Plantinga appeal to transworld depravity. I would be interested to know what people thought of it.  

1.  If there is a God then He is metaphysically free and always freely chooses to do the right thing.

2. Thus, if there is a God it is possible that something be (metaphysically) free and always freely choose to do the right thing.

3. If it is possible to be free and always freely choose to do the right thing then, if God were to create a world He would create a world in which there were creatures that were metaphysically free and always freely choose to do the right thing.

4. But the world that we find ourselves in is not a world where we are free and always freely choose to do the right thing, and if we assume that God created it, then

5. It is not possible for something to be metaphysically free and always freely choose to do the right thing

6. So, there is no God

There Might Not Be Any Numbers

I was re-reading an old post where I expressed doubt that there are any necessary existents at all, not even numbers, and I saw Richard Chapell’s comment,

I’d expect the ontological status of numbers to be non-contingent — after all, what in the world could they be contingent on? Abstract objects seem to be the kind of things that exist necessarily, if they exist at all.

I guess I was being dense that month 🙂 because I didn’t see what the objection was supposed to be. But now I do. If numbers are the kinds of things that are not necessary then they must depend on something to exist. But what could numbers depend on? Since there is no plausable candidate we should conclude that if numbers exist they would do so necessarily. Here is what I should have said.

Whether a given possible world has non-physical elements is surely a contingent fact about that possible world. The worlds which do have non-physical elements will most likely have numbers and those that don’t won’t. If this were the case then the existence of numbers is contingent on which possible world best describes the actual world (or if one doesn’t like this way of characterizing the actual world as a possible world we can say it depends on what is actually the case). In some worlds, the existence of numbers may be contingent on whether they were created by some non-physical being. In short there are a couple of different ways in which the existence of numbers could turn out to be contingent.  

New Classes at LaGuardia

I am lucky enough to come to LaGuardia at a time when they are expanding the philosophy major and we are trying to introduce four new classes to the curriculum. I am responsible for designing two of them; Logic and Philosophy and Medical Ethics (the other two are Aesthetics and Environmental Ethics). I thought I would post the course descriptions and outlines in the hopes of getting some feedback from any LaGuardia students lurking around here on whether or not classes like these sound interesting and would be something you might consider taking if it were offered.

Logic and Philosophy

Course Description: An introduction to modern symbolic logic with a focus on its application to actual philosophical problems. Topics to be discussed include validty, entailment, truth-tables, proofs, translations from English into symbolic form, as well as more philosophical topics like the relation of modern logic to earlier syllogistic logic, the possibility of the use of logic to resolve philosophical problems (e.g. God’s existence or free will), the relation of English to logic, and the possibility of ‘alternative’ logics.

Course Outline

1. Validity & soundness
–Logic and the philosophical method.
–Entailment, inference, and validity.
–Aristotle’s identification of validity with the form of the argument.
–The seperation of validity (formal structure) and soundness (truth of premises).
–The counter-example method of testing validity

2. Syllogistic Logic
–The square of opposition and the cannonical A, E, I, and O sentence forms.
–Categories and Venn diagrams.
–The mood and forms of the valid syllogisms.

3. Philosophical issues in syllogistic logic
–Does ‘all’ imply ‘some’?
–Are some logical truths known by reason alone, independently of experience?
–some arguments cannot be expressed in syllogistic logic.

4. Basic Propositional logic I
–Beginning definitions of formal symbols for ‘and’, ‘or’, ‘not’ and ‘if…then’.
–Simple translations into symbols.
–The truth-table test for validity.

5. Basic propositional logic II
–More advanced translations.
–Introduction of rules for symbol manipulation.

6. Propositional proofs
–Introduction to natural deduction.
–Introduction to truth-trees.
7. Philosophical issues in propositional logic
–paradoxes of material implication.
–why accept valid inferences?

8. Basic quantificational logic
–Introduction of ‘all’ and ‘some’ into the formal language.
–Translations and proofs.

9. Identity and relations
–Introduction of identity into the formal language.
-Introduction of relational predicates (e.g. ‘taller than’).

10. Philosophical issues in quantificational logic.
–Is existence a predicate?
–Do mathematical truths reduce to logical truths?
–Treating names as descriptions.
–Informative identity statements.

11. Basic modal logic
–Introduction of ‘necessary’ and ‘possible’ into the formal language.
–Introduction to possible world semantics.
–translations and proofs.

12. Philosophical issues in modal logic
–The metaphysical status of possible worlds.
–one logic, or many?
–Names and rigid designators.
–different concepts of possibility: Epistemic, metaphysical, and logical.

13 Final Exam

Medical Ethics

Course Description:An introduction to some of the basic issues in medical ethics. The course emphasizes the application of moral theory to the issues that arise in the context of medical research and practice. Topics to be addressed include, among others, the role and responsibility of heathcare givers in death and dying, the use of stem cells and animals in medical research, the use of genetic information to influence the outcome of human pregnancy, cosmetic surgical addiction, and issues involving involuntary psychiatric care.

Course Outline

1. Review of basic ethical theories
–Virtue ethics.

2. Killing those who can’t speak for themselves
–Active vs. passive Euthanasia.
–patients that can’t make their own decisions.
–defective infants.

3. Physician-assisted suicide

4. Ethical issues in reproductive science
–surrogate motherhood.
–fertility treatments.
–Over population.

5. The use of human embryos in scientific research

6. Elective cosmetic surgery and surgical addiction
7. The use of animals in scientific research

8. Issues involving justice and the allocation of medical resources
–transplants and alchoholics.
–Transplants and the black market.
–Expensive treatments.

9. Involuntary psychiatric care

10. Issues in genomics (genetic counseling/genetic engeneering)

11. Universal heathcare

12. Issues involving HIV/AIDS

13 Final Exam

Where Am I?

I’m back!!

 The plane ride there was long and super bumpy (and I hate flying!!) and then I got strep throat and the plane ride back was a red eye that got into JFK at six a.m. (and I REALLY hate flying!!!!)…but other than that California was fantastic! 🙂

The APA was fun, though I got there on the last day of the conference and since I wasn’t feeling well (I was chaining Sucrets one after the other) I left after my talk. But I did see the session before mine, by Hanna Kim, on a proposed compositional semantics for metaphors which was interesting. She sketched an account that borrowed Jason Stanely’s idea of a hidden unarticulated variable that was context sensitive to metaphorical meaning. This would allow one to get the meaning of the metaphor in a way that was completely determined by the meaning of the parts (including the hidden, context sensitive variable). Marga Reimer responded with a couple of objections. One of which was the Gricean kind of objection one would expect. She invoked Grice’s modified Occam’s razor and asked why we need a semantic account of metaphor’s when we have a perfectly good account from Grice that appeals to speaker’s intentions and doesn’t posit all of these weird hidden variables? (Here! Here!) Kim’s answer, in part, was to point out that Grice’s account cannot take care of ‘impossible metaphors”.  The basic idea behind impossible metaphors is that there are semantic and syntactic constraints on what kinds of sentences we can make metaphors from. I don’t recall any of her examples and I can’t find the handout…but still, I wonder about this kind of strategy. Why is an objection to Gricean theories to point out that sentence construction is constrained by syntax? A speaker is constrained by what she can reasonably assume will alert a hearer to her communicative intention and thereby fulfil that very intention. The syntax of a language is definitely one thing that would suggest itself as something which would constrain which utterances a speaker can reasonably expect a hearer to successfully infer what one is communicating. No problem.

My talk went well, I think. We had some interesting discussion. The commentator (Imogen Dickie) posed a dilemma for me. If we can have rigid designation in thought then either the problem of necessary existence reoccurs at that level and we haven’t solved the problem or we can have rigid designation without the problem of necessary existence (in thought) and so we shouldn’t be worried about it in language. This is especially pressing when we think that S5 is attractive because it is supposed to be a logic for thought.     I responded that the problem of necessary existence is only a problem when we try to regiment our thoughts into a formal language. There is no problem with having a singular thought about Socrates, the problem is trying to formalize a sentence representing that thought. This is the evidence that we have that we need an separate account of the semantics of language. But S5 is still a logic of modal thought because we can formulate descriptions in it that ‘single out’ the object of thought without rigid designators. The absence of singular terms in our logic is nothing more than an inconvenience. She also mentioned, in passing, that Williamson thinks that necessary existence is not as terrible as one might think. One might argue that I exist in all possible worlds but in some worlds I exist without any properties. This was quite shocking to me, as I can’t really fathom what that would mean. Really, what does that mean? Anyone know?

From the audience I was asked several good questions. One was from Tim Lewis on how I felt about the fact that names on my account would fail the Church translation test. That is, we expect that ‘Richard’ and ‘Ricardo’ to be synonyms but if the really stand for ‘the bearer of “Richard”‘ and ‘The bearer of “Ricardo”‘ then pretty clearly they aren’t synonyms since they each have a separate quoted name in them. I thought that was a pretty nice objection. At the time I said that I would argue that names are not part of a language. So, in a complete dictionary of English there would be no ‘Richard’ or ‘Doug’ (forget about the dictionaries around now, they are half encyclopedia, I am talking about just a list of the words of a language and their conventional meanings, pronunciation guide, and syntactical/grammatical categories. That seems right to me, but then on the plane home, in a half trance, I started to think that maybe we could use Seller’s notion of ‘dot quotes’ to solve the problem if people don’t like the position on names. So instead of ‘the bearer of “Richard”‘ we could have ‘The bearer of *Richard*’ where ‘*P*’ is ‘dot-quote P’ and basically serves to single out all of the functional types that play the role that ‘Richard’ does in English. This would allow one to preserve the intuition that other language cognates of English names are synonyms. Or so it seemed on the plane…and besides I like the bit about names not being part of the language…

The other question that I remember was from Adam Sennet (there were a couple of others that I am forgetting). He echoed Williamson’s point that since we know quite well what a rigid designator is and how one would introduce them into a formal langauage it is then quite odd to say that there aren’t any. I responded that we know what it would be like for there to be all kinds of things that don’t exist. I know what it be like for there to be square circles (it would be for there to be one object that is both square anc circular at the same time), but that doesn’t mean that there are any. This is exactly what one would expect. We know what it would be like for there to be flogisten or tachyons or any other theoretical posit we come up with. It would be like finding the thing that we posited, but someimes we find out that they don’t exist. Interpreting that syntactical category proper noun as a rigid designator is a natural attempt at capturing what it is that we do when we think about some particular thing but when we do model that category that way we get the problems with necessary existence, which means that it is a mistake to model it in that way. I compared it to what happens when we try to mix quantuum theory with relativity theory. When we try to calculate the probabilities for things which we have well worked out answers for we get crazy results (like the probability of some event occuring being infinite). This let’s us know that there is a problem and then you get all of the different answers to solve the problem. Our finding the proofs for necessary existence in S5 are like the infinite probabilities in physics; it is an indicator that something needs to be done.

This is, by the way, why I disagree with Chappell’s charge that logic is over rated and that, in particular, my

employed logical apparatus merely serves to build in misunderstandings. The formal steps of the argument may be flawless, but that’s all for naught if the entire argument is based on a mistake — due to failing to understand precisely what all those formalisms really mean.

I understand what the formalisms mean and I am using them to apply pressure to a person who holds a certain kind of view. The proofs count as evidence that some assumptions don’t work. This is exactly what formal logic is good for…though I do agree that one needs to also make the argument in prose as well as symbols.

OK, well that’s enough for now, I gotta get to work on my Tucson presentation and grade some exams!!!!!!!

Language, Thought, Logic, and Existence

Well, I’m off to go present my paper at the APA! I’ll be back on Monday. I guess I have Philosophy Sucks! to thank, since I was noticing that the paper grew out of some interesting discussion I had here last year. Thanks to everyone who participated!!

You can enjoy the virtual version here (and on the sidebar with the other virtual presentations), which is a recording of a rehersal I did today (It may take a second to open since I recorded it in stereo, which I haven’t before).

More on the Ontological Argument

The traditional version of the ontological argument is usually criticized for treating existence as a predicate. If existence is a predicate, then it is a predicate that always applies, and as Russel quipped that is the sign of a mistake. A predicate must be fail to apply to some objects in order to count as expressing a genuine property.  But Kripke has shown that it is easy to introduce an existence predicate into our formal language that avoides this and related difficulties. We do so as (1),

(1) E(y) (y=x)

Where ‘E(y)’ is the standard existential quantifier and identity is understood normally.(1) is an existence predicate because it is an open sentence that can be satisfied by the values of the free variable x. Intuitively (1) says that x has the property of being identical to some thing (y) and this captures what we mean when we say that existence is a property.

(1) can fail to apply, the model is very easy to give. Imagine a universe of two distinct objects A and B. Now, say that there are two distinct worlds in this universe one containing only A and the other containing only B. E(y) (y=B) will be false at the world where only A  exists.

As Kripke points out the problem only arises when one mistakenly thinks that the claim that existence is a predicate is the claim that (2) makes

(2) (x) (E(y) (y=x))

(2) says that every thing exists and this cannot fail to apply and is a necessary truth, but it is also not a predicate (it is not an open sentence, it is closed by the universal quantifier ‘(x)’).

So if existence is a property then it makes sense to think it is the kind of property that God must have, since He is a being who would be without equal and if He lacked the property of existence then I or you would be His equal and better. So, He must exist. To concieve of God not existing is to concieve of an object that has everything and yet lacks something which is just as contradictory as concieving of an object that is triangular yet lacking three sides.

A Puzzle About Reductios

I finally got my internet connection back up at home now. Turns out I had a bad cable out on the side of the appartment building. Now all I have to do is get to the backlog of super interesting comments! I hope I’ll have some time to do that this weekend.

 In the meantime here is something I was puzzeling about today. Consider the following argument

If P then P
Not P
So, not P

Is this a valid argument? That would depend on whether it is an instance of modus tollens or denying the antecedent; but how can we tell which one it is an instance of? We have the same problem for modus ponens and asserting the consequent.

If P then P
Therefore, P

So what are we supposed to say about this? I suppose one could deny ‘p –> p’ since it is equivelent to the law of the excluded middle (~p v p) and there are those who would deny that it is true but that doesn’t seem to solve the problem. We still won’t be able to tell what argument form this is an instance of and so can’t know if it is valid or not. But if that is the case then we may be commiting a fallacy when we infer that a sentence must be true because its negation can’t be true and that would mean that reductio arguments have a deep problem.

So, any thgoughts on whether these are valid arguments or not?

Ontological Arguments

The ontological argument for the existence of God is often greeted with skepticism by atheists and theists alike. I don’t want to talk about particular versions of the argument, but about why people are suspicious of them. It seems to me that we are quite ready to accept ontological arguments in other areas.So, consider geometry. Why can’t there be any square circles? Because the very concept is contradictory. We infer from this that reality must be a certain way; it contains no square circles.  Isn’t the basic strategy behind the ontological argument for God the same? Why must there be a God? The concept of God’s non-existence is contradictory. Infer from that that reality must be a certain way. Now, I don’t mean to be saying that the ontological argument is a good argument or not. I only mean to point out that ontological arguments aren’t as strange as they seem.