March is a Slow Month for Arguments

It looks like I have one reader, so I now feel guilty for not living up to my hopes and dreams of blogging arguments daily. Shoot. It turns out that's too much work. I think I'll set a new goal of posting an argument once a week. Hopefully I'll hear a whole bunch of new ones at the APA next week!

Richard/Salmon against Kaplan

David Kaplan has this view that a proposition can be true at one time and false at another. So the proposition expressed by "I am cold" when I say that was true this morning when I was waiting for the bus, but now it's false because I'm inside and warm. But others, like Nathan Salmon and Mark Richard, think that propositions contain the time of utterance, so the proposition I expressed this morning is different than the one I express now.

Here's their argument against Kaplan:

If Kaplan were right, the following argument would be valid:

P. In 1971, Mary believed that Nixon was president and today she still believes that.

C. Today, Mary believes that Nixon is president.

We can see why Kaplan would be committed to the validity of it by seeing the form of the sentences when made explicit with their temporal operators:

P'. [In 1971] Believes (Mary, {Nixon, being president}) and [Today] Believes (Mary, {Nixon, being president})

C'. [Today] Believes (Mary, {Nixon, being president})

So it's a simple 'and-elimination' from P to C (or P' to C'). But, the problem is that this argument is not intuitively valid, if we think about the English formulations of P and C. The way to read P is that back in 1971, Mary believed then that Nixon was president, and the belief that she has now is that in 1971 Nixon was president. It doesn't follow that she thinks Nixon is now president - just that she believes he used to be.

From this, Richard and Salmon think it follows that propositions must contain times in them. I can't say I'm completely convinced by this, but I think it's understandable enough.

Getting Around the Plus/Quus Problem

Roughly, the plus/quus problem is that it might be impossible for us to know if, when we use the word 'plus', we are actually referring to the addition function or some other function (call it 'quaddition') that behaves just like addition up to a point, and then does something different. Suppose nobody had ever added any numbers above 1,000,000. Nobody had in fact ever done a problem of the form x + y where either x or y was 1,000,000 or greater. Now suppose also that quaddition is the function that behaves just like addition up to the point that it takes 1,000,000 as one of its arguments, but if either of the arguments x or y is 1,000,000 or greater, the output (or the result of quaddition on those two numbers) is always 5. So 999,900 + 90 = 999,990, but 1,000,000 + 10 = 5, where '+' is interpreted as quus, or referring to quaddition.

So Kripkenstein (Kripke inspired by what Wittgenstein said on this) convinces us there's a problem here. We may actually be referring to quaddition instead of addition, and we may have always been doing so. No way to figure it out.

The Lewisian way (from David Lewis) of getting around this, if I understand it right, relies on the notion of naturalness:

1. Some properties are more natural than others (e.g. being a tiger is more natural than being a tiger-or-electron-or-shoe)
2. Natural properties are reference magnets (i.e., our general terms tend to refer to natural properties in cases where we're not completely specific).
3. Addition is a more natural function than quaddition.
4. So our regular uses of the word 'plus' or 'add' generally refer to addition rather than quaddition.

Lewis spells out this naturalness stuff in On the Plurality of Worlds and "New Work for a Theory of Universals", and Ted Sider discusses it, along with reference magnetism, in "Ontological Realism".

Descartes' Circularity Problem

Ever since Descartes published the 'Meditations', commentators have discussed whether or not he was guilty of some kind of circularity in the Third Meditation. When we mention 'circularity', that usually means that an argument's conclusion is also relied on in order to get to the conclusion. So when we think of arguments in the Third Meditation, we naturally think of the argument for the existence of God (posted below). But that argument doesn't have any circularity in it. The problems with that argument are the hierarchies and the causal principle connecting them. So where's this big circularity problem?

Well, it seems like the argument for the existence of God could be seen as just a part of the main argument of the Third Meditation, which is meant to establish the possibility of my knowing anything (like whether 2+3=5, etc.). He's worried about how we can know this stuff. Here's one way to look at the argument with the circularity problem:

1. If I know God exists and is not a deceiver, then it's possible for me to be certain of some things (because then I'll know that God is not tricking me into being sure of those things I feel very sure of).
2. [insert argument for the existence of God here]
3. God exists.
4. [insert argument for the non-deceiving of God here]
5. God is not a deceiver.
6. God exists and is not a deceiver. (by 3 and 4)
7. I know God exists and is not a deceiver. (by examining the above arguments)
8. It's possible for me to be certain of some things. (by 1 and 7)

This is the conclusion he wanted. The problem is that to get from step 6 to step 7, it would be required for us to already accept 8. That is, we might have arguments for the existence and non-deceiving of God, but for those arguments to create knowledge in us, it must be possible for me to be certain of some things. So in order to get to 8, 8 itself would really need to appear as a premise somewhere above 7, which would make this a circular argument. Notice that this makes it clear that the circularity has nothing to do with the argument for the existence of God, which appears up in step 2.

This whole thing could use some precisifying, but I think it's a good start.

Perry on Frege on Demonstratives

John Perry's argument about the irrelevancy of belief to the analysis of demonstratives (from "Frege on Demonstratives"):

1. Suppose that if a speaker S uses a demonstrative (e.g. today, here, this, etc.), then S has to have a descriptive belief that uniquely identifies the referent of the demonstrative.
   
2. Consider the following example: On 9/12/01 at 12:30 a.m., S looks at his wife and says, "Today the whole world changed". 
3. By (1), S must have a descriptive belief that uniquely identifies 9/12/01.
4. But S's beliefs in the vicinity identify only 9/11/01. 
5. So (1) is false. 

This was one of Perry's many arguments that, taken together, seem to show that Frege's philosophy of language can't handle demonstrative expressions.

Meditation 3

Descartes' argument for the existence of God:

1. I have an idea of God.
2. My idea of God has top-shelf objective reality.
3. There must be at least as much formal reality in the cause as there is objective reality in the effect (idea).
4. So the idea of God must have been caused by top-shelf formal reality.
5. So God exists.

Background Information:

Hierarchy of Formal Reality
1. Infinite Substance (God)
2. Finite Substance (rocks, chairs, people, etc.)
3. Mode (attribute/property - color, weight, shape, etc.)

Hierarchy of Objective Reality
1. Idea of Infinite Substance
2. Idea of Finite Substance
3. Idea of Mode

Note: Premise 3 of the argument (the most controversial bit) is a causal principle connecting the two hierarchies.