Let K be a class of sets such that whenever x is in K and x is a subset of y, then y is also in K. It follows that if the empty set is in K, then every set is in K. Let's rule this out by stipulating that some set is not in K. Thus every set that is in K is not empty. So instead of saying outright that some set is not empty we can instead say that it is in K, which sounds less controversial but really comes down to the same thing.
I think this is the trick in Gödel's ontological proof of god. His class K is the class of 'positive' properties, where properties are individuated intensionally. Gödel claims 1) that whenever some property Q is necessarily implied by a positive property P, then property Q is also positive (which is just the closure principle above), and 2) that not all properties are positive. On these assumptions saying that a property is positive means saying that it is not empty, that is, not necessarily uninstantiated. Hence when Gödel says that 3) necessary existence is a positive property he in effect says that a necessary being possibly exists, which in turn means that a necessary being actually exists.
The fallacy is to assume that there is any class of ('positive') properties satisfying (1)-(3).
Sometimes we wonder whether some thing A is identical with some thing B: Is the man in the brown hat (the same as) my neighbour? Is the table in the mirror over there (the same as) the one here in front of me? Is the square root of 841 (equal to) 29?
What determines whether A really is identical with B? According to a view I find very irritating it's the identity conditions of A and B. The idea is that all things fall under kinds, and every kind comes with an associated identity condition. Different kinds may be associated with the same identity condition, but there is never more than one identity condition for a kind. So to find out whether A = B, we first have to find the relevant identity conditions of A and B. A good way to find those is to find the relevant kinds and look for their associated identity conditions. If the identity conditions differ, A is not identical with B. If they are the same, they tell us under which conditions A and B is identical, and we only have to find out whether these conditions obtain.
Postbote now supports CC and BCC and sending attachments. (Attachments are still lost when forwarding mails though.) I've made a few other changes most of which should be obvious. Not so obvious is that sessions are now tied to IP addresses. So if you're on a dialup connection and reconnect to your ISP, you'll have to log in again. (The point of this restriction is that it makes it much harder for terrorists to break into your session when you click a link in an email.)
Here's a little question about David Chalmers' paper "Does Conceivability entail Possibility?". I'm interested in the relation between what Chalmers calls strong scrutability and what he just calls scrutability. In particular, I wonder if strong scrutability is really stronger than mere scrutability. This depends on a claim Chalmers makes in sections 10 and 11: that if there are inscrutable truths, it follows that some statements are epistemically possible (not ruled out a priori) but yet not really (primarily) possible. My question is: why does that follow?
There's something odd about Albert's reasoning:
If that stranger's predictions are true, he probably is a time
traveler. I want him to be a
time traveler. Therefore I should try to make his predictions
come true.
The problem is that by trying to make the predictions come true,
Albert decreases the evidential support their truth lends to the
claim that the stranger is a time traveler.
Albert is a time traveler. In 2015 he travels back to 1995. There he meets his younger self and tells him in great detail what he, the younger Albert, will do in the next 20 years: that he will quit smoking, be injured in a traffic accident at a certain date and location, that he will work very hard in a physics lab to build a time machine, and so on. All these predications come true.
Isn't that puzzling? For example, on the day of the predicted traffic accident, why did Albert, who knew about the prediction, not avoid getting to that particular location? Why does he always behave exactly as he was predicted to do? This is certainly not what ordinary people would do. If you claimed to know that I will raise my left hand in a minute and told me so, I would try not to raise my left hand. Does Albert never try to make the predictions false? Or does he, but always fails? That seems unbelievable. How can you try not to work hard in a physics lab but fail? In fact, we may assume that Albert is told by his older self that he will never even try to make the predictions false. Then he never tries and fails because he just never tries. How strange. And how stupid: Albert knows since 1995 that he will eventually travel back in time with a time machine. For he has already met his older self. So why does he work hard at the lab? Why not lie in bed and watch TV instead? No matter what you do, you can't change the past. So no matter what Albert does in 2003, he can't change the fact that in 1995, he arrived as a time traveler from the future. So he's a fool when he's working hard to make it happen (or rather, to make it have happened).
I've often read that thermodynamic entropy is some measure of disorder, so that tyding up our rooms means working against the second law of thermodynamics. For example, in section 9.3 of his book Space, Time and Quanta, Robert Mills demonstrates that if we put 10^20 toys back on the shelf, that decreases the total cosmic entropy by 0.02 J/K. He then suggests that this doesn't actually violate the second law because in the process of putting back the toys we use up energy and thereby increase total entropy by much more than 0.02 J/K.
So I don't see any means to escape the conclusion that given mereological universalism, some things trivially move faster than light. Lots of things, in fact. Perhaps that's less troublesome than I thought because these things don't actually violate any physical laws.
For instance, I guess the principle that physics looks the same for all things that move with constant speed relative to each other has to be restricted to things with speed < c anyway. (At least Lorentz transformation doesn't make much sense if v = c.) If so, the exclusion of faster-than-light fusions from the principle is already built in and we don't need to worry about e.g. what such a fusion's proper time might be.
The Brock/Rosen objection against modal fictionalism goes as follows. The modal fictionalist holds that
1) Necessarily p iff according to the modal fiction, at all worlds, P*,
where P* is the modal realist's paraphrase of P, and the modal fiction is the modal realists' theory. But the modal realist holds that it is true at every world that there are many worlds. That is,
2) According to the modal fiction, at all worlds, there are many worlds.
It follows from (1) and (2) that
Let A and C be two distinct objects such that C exists at a later time and a
different place than A.
Let F be the mereological fusion of A and C. Question: Does F move from
the location of A to the location of C? I don't think so. If a thing moves
from one location to another, there should be a continuous path from the one location
to the other along which the thing moves.
So let B1, B2, ... be (continuum many) further objects (perhaps spacetime points, if nothing else is around)
that lie on a continuous spacetime path
between A and C, and let F be the fusion of A, B1, B2, ..., C. Does F now move? I'm not sure.
Maybe when a thing moves the later stages should depend causally on the earlier
stages. Or maybe the concept of movement is not applicable to gerrymandered fusions like F.