Hi Jon, welcome,

On 27 Sep 2011, at 07:35, nihil0 wrote:

It's a little late for this post since I've already posted 2 or 3
things, but I figured I might as well introduce myself.

I'm majoring at philosophy at the University of Michigan, however I'm
studying abroad for a trimester at Oxford. I turn 21 on Oct. 4.

The main questions I've been researching are the following:

1. What kind of free will is worth wanting, and do we have it, despite
the deterministic evolution of the Schrodinger Equation?

Non determinism is useless to explain free will. You can illustrate this with iterated self-duplication, or with the use of random coin. It seems to me that adding randomness can only restrict free will. free will is more of the type of partial self-determination. It might be explained by the ability of some entities (machines) to be partially aware of some ignorance spectrum on the way to achieve some goal. For example your goal is "to be happy tonight", but you ignore if this will be realize through going to the movie or to the restaurant. Free-will might correspond to your conscious ability to make a choice despite you have not all information at your disposition. It generates a genuine feeling of responsibility, and dterminism does not eliminate it. A lawyer cannot defend a murderer by saying to the member of the jury that the murderer has only obey to to the deterministic equation of the universe. That defence will be nullified by the jury and judge who will condemn it to jail, arguing that they are also just obeying the same deterministic law.

2. Recent cosmological evidence indicates that our universe is
infinitely big, and everything that is physically possible happens an
infinite number of times.

Actually this is never justified. To have everything happening, you need the universe being infinitely big, but also homogenous, and robust enough for making possible gigantic connections and gigantic computations, etc.

Does this imply that I can't make a
difference to the total (or per capita) amount of well-being in the
world? I used to be a utilitarian until I read Nick Bostrom's paper
"The Infinitarian Challenge to Aggretive Ethics."

You can act on your own proportion of well-being, of you and the people you care about in some neighborhood, in your common future. I would say.

3. Can only mathematical truths be known for certain?

Is there any mathematical truth that we can known for certain? I really doubt so. A case can be made for arithmetical truth, but even here, I would say personally that I "believe them" only with a very high plausibility coefficient. We can do dream in which the feeling of certainty is associated with what we realize, after awakening, to be blatant non sensical idea. I thought, one feverish night, that the color of the curtains did refute the use of the modus ponens rule in classical propositional logic. What is clear is that arithmetic is the most lesser doubtful part of math, and with fever or drugs, seems to be shared by everyone, with the exception of the ultrafinitists, which are rare (and I think inconsistent). I have never meet someone doubting the excluded middle use in arithmetic. It makes sense for intuitionist people too, even if they interpret it differently. Above arithmetic and finitist thinking things are more doubtful, and all mathematicians are glad when analytical proofs are replaced by elementary first order reasoning, which certainty is amenable to finitist or arithmetical reasoning. The mathematical reality is globally not much more certain than physics, and is full of surprises and mysteries.

Can you know
something without knowing it for certain?

yes, and I can prove to you that if we are machine, and if you accept Theaetetus' theory of knowledge, it is even the general rule. In that theory knwoledge is true opinion, and with only once exception, true opinion is subjectively like an opinion and cannot be made certain. The only certainty exception is the fact that you are conscious <here and now>. All the rest can be doubted.

4. Do the laws of physics determine (i.e., enforce) events, or do they
merely describe patterns and regularities that we have observed?

The second one. I might argue from the mechanist hypothesis, but many things should be explained first. In fact I doubt very much about the existence of a primary physical universe. I am willing to think that this is epistemologically incoherent once we assume that the brain works like a machine. The laws of physics need, in that case, to be themselves complex pattern emerging statistically from infinitely many arithmetical relations. This cannot be explained shortly, but if you are patient, opportunities will appear to dig on this issue.




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