Here’s a quick (and probably pretty bad) argument that it is rational to believe contradictions (or at least why it's not irrational to believe contradictions) inspired by conversation with Dan.
1) One ought not believe contradictions (assume for reductio)
2) Ought implies can (ask Pete about this)
3) Possibly, one does not believe contradictions (from 1 and 2)
4) Necessarily, one believe contradictions.
A few things to note at the outset: First, by ‘believe contradictions’, I don’t necessarily mean believe that p and not-p. Believing that p and believing that not-p (in "separate compartments" if you’d like) would do fine. The ‘cans’ and ‘possibles’ of this argument should be read along the lines of nomic possibility. Also, this is a proof by reductio in favor of believing in contradictions – you might think the argument is self-defeating for this reason. You might also think that ought implies can is a bad principle (or at least shouldn’t be applied to this kind of case). I think premise 4 stands in the most need of justification.
I'm not entirely sure how to justify (4). Maybe we could say that, for some complex propositions P, we might fail to believe that P, fail to believe that not-P, but believe that P or not-P; this might not be a contradiction itself, but maybe we could draw one out. Or maybe we could say that believing the premises of an argument but not its conclusion commits us to contradiction (maybe by way of a possible-worlds analysis of content -- in all belief-worlds where I accept the premise, I accept the conclusion, but by hypothesis, I don't accept the conclusion)... I'm not entirely sure where to go, but I still think there's an argument in the neighborhood. Thoughts?
[Note: I've taken back my original justification for (4).]
Wednesday, May 23, 2007
Saturday, May 19, 2007
Friday, May 18, 2007
Just, wow.
I used to think I was an atheist, but the existence of the banana has convinced me of the error of my ways. Check it.
Sunday, May 13, 2007
Necessary Connections
Assume x and y are two non-overlapping (have no parts in common) contingent existents. It is then very plausible that there should be no necessary connections between them. That is, it should be possible for them to fail to co-exist as well as to co-exist. At least this is a fairly common assumption in the relevant literature.
It is further often assumed that two non-overlapping contingent existents should not be necessarily connected in virtue of some accidental intrinsic property they share.
I ask: how far should we push the spirit of such a denial of necessary connections? Is it plausible to hold that sometimes there should be no necessary connections between overlapping existents?
Take for example some plurality xx and its fusion ƒ(xx) (assuming it has one). Assume further that fusion is not a generalized form of identity (we all know what that means). Should we then hold that it is possible for xx to exist without ƒ(xx)? I think so. After all, they are not the same thing(s). Though it seems less plausible to hold that ƒ(xx) can exist without xx (though it is trickier than it might at first seem; cf. mereological essentialism). Do we here have a one-way necessary connection? Or, should we in general deny any necessary connection between any two things that are not identical (rather than non-overlapping)?
-Einar
PS: Personally, I think overlap is partial identity and that fusion is a form of identity, but most people don't for some reason. And that is why the above remarks are interesting.
It is further often assumed that two non-overlapping contingent existents should not be necessarily connected in virtue of some accidental intrinsic property they share.
I ask: how far should we push the spirit of such a denial of necessary connections? Is it plausible to hold that sometimes there should be no necessary connections between overlapping existents?
Take for example some plurality xx and its fusion ƒ(xx) (assuming it has one). Assume further that fusion is not a generalized form of identity (we all know what that means). Should we then hold that it is possible for xx to exist without ƒ(xx)? I think so. After all, they are not the same thing(s). Though it seems less plausible to hold that ƒ(xx) can exist without xx (though it is trickier than it might at first seem; cf. mereological essentialism). Do we here have a one-way necessary connection? Or, should we in general deny any necessary connection between any two things that are not identical (rather than non-overlapping)?
-Einar
PS: Personally, I think overlap is partial identity and that fusion is a form of identity, but most people don't for some reason. And that is why the above remarks are interesting.
Tuesday, May 8, 2007
Psycho-pluralism & QM
I'm interested in the Many Minds Interpretation of quantum mechanics (hereafter, MMI). A few other people are too. The people that go around defending it are usually committed to a thesis I'll call 'psycho-pluralism.' Psycho-pluralists believe that there are many subjective experiencers where there is usually believed to be only one such experiencer. Now, I know that I can't plausibly defend MMI--there's a lot of things about quantum probability I would need to know in order to do that properly. But I think I might be able to argue that MMI is better than the Many Worlds Interpretation (hereafter, MWI). The MWI involves commitment to what I'll call 'globo-pluralism': the view that there are many branches of the universe where we there is usually believed to be only one. Both psycho- and globo-pluralism are radically counterintuitive theses (i.e., the sort of theses that non-metaphysicians are moved to laughter by), so it is a prima facie strike against any theory to endorse them. (That said, the pluralisms I've formulated are pretty vague, since what is "usually believed" is far from clear.)
Here's one bad way to argue that MMI is better than MWI: MMI entails psycho-pluralism, but not globo-pluralism. MWI, on the other hand, entails commitment to both. Since one should avoid prima facie objectionable commitments whenever possible, one should endorse MMI rather than MWI. This argument fails miserably. For one thing, it seems that if one believed in globo-pluralism, one need not endorse psycho-pluralism, since it seems "usual" to believe there to be only one subjective experiencer for every individual located in some or other branch of the universe. So it seems to me that even if one endorsed globo-pluralism, one would not thereby be committed to psycho-pluralism. (Some philosophers have actually defended globo-pluralism and the view that holds there to be only one branch (viz., our branch) that is populated with conscious individuals. Interestingly, Peter Forrest likes a similar view of consciousness with respect to possible worlds.)
Here's a (slightly) better way to argue against MWI. There is independent reason to believe psycho-pluralism, but there is no such reason to believe globo-pluralism; therefore, MMI is preferable to MWI. This independent reason is courtesy of Peter Unger's "Mental Problem of the Many", which addresses the Problem of the Many that Lewis takes up in "Many, but Almost One." Suppose that consciousness is intrinsic. If x is an intrinsic property of F, then any object that is duplicate of F instantiates x. Assume your brain is conscious. Subtract a lone particle from your brain. Assume (reasonably, I think) that you remain conscious. Given such a possibility, there are two objects that are conscious that overlap parts of your brain: Your brain and your brain minus that lone particle. This is because 'you' would remain conscious even if you were to lose more than one particle of your brain. Plausibly, you could survive losing many particles and, less plausibly, you might survive the loss of an infinite number of increasingly small particles. It seems, then, that, independent of the considerations of quantum mechanics, psycho-pluralism might be true. (The premise doing the heavy-lifting here is the intrinsicality of consciousness. See Merricks and Sider's discussion of this issue in PPR (2001?))
I can think of no analogous argument for globo-pluralism (of the non-Goodmanian sort). I think this largely because being a world seems to be an extrinsic property unlike consciousness. So, absent an analogous argument for globo-pluralism, have I supplied you with some reason to think MMI is superior to MWI?
Here's one bad way to argue that MMI is better than MWI: MMI entails psycho-pluralism, but not globo-pluralism. MWI, on the other hand, entails commitment to both. Since one should avoid prima facie objectionable commitments whenever possible, one should endorse MMI rather than MWI. This argument fails miserably. For one thing, it seems that if one believed in globo-pluralism, one need not endorse psycho-pluralism, since it seems "usual" to believe there to be only one subjective experiencer for every individual located in some or other branch of the universe. So it seems to me that even if one endorsed globo-pluralism, one would not thereby be committed to psycho-pluralism. (Some philosophers have actually defended globo-pluralism and the view that holds there to be only one branch (viz., our branch) that is populated with conscious individuals. Interestingly, Peter Forrest likes a similar view of consciousness with respect to possible worlds.)
Here's a (slightly) better way to argue against MWI. There is independent reason to believe psycho-pluralism, but there is no such reason to believe globo-pluralism; therefore, MMI is preferable to MWI. This independent reason is courtesy of Peter Unger's "Mental Problem of the Many", which addresses the Problem of the Many that Lewis takes up in "Many, but Almost One." Suppose that consciousness is intrinsic. If x is an intrinsic property of F, then any object that is duplicate of F instantiates x. Assume your brain is conscious. Subtract a lone particle from your brain. Assume (reasonably, I think) that you remain conscious. Given such a possibility, there are two objects that are conscious that overlap parts of your brain: Your brain and your brain minus that lone particle. This is because 'you' would remain conscious even if you were to lose more than one particle of your brain. Plausibly, you could survive losing many particles and, less plausibly, you might survive the loss of an infinite number of increasingly small particles. It seems, then, that, independent of the considerations of quantum mechanics, psycho-pluralism might be true. (The premise doing the heavy-lifting here is the intrinsicality of consciousness. See Merricks and Sider's discussion of this issue in PPR (2001?))
I can think of no analogous argument for globo-pluralism (of the non-Goodmanian sort). I think this largely because being a world seems to be an extrinsic property unlike consciousness. So, absent an analogous argument for globo-pluralism, have I supplied you with some reason to think MMI is superior to MWI?
--Sam
Monday, May 7, 2007
acceptablity without truth
Consider the sentence:
(1) There are prime numbers
Arguably (1) is associated with two senses. Insofar as (1) is taken to be a claim about the numbers, namely, that some of them are prime, it is uncontroversially true. Insofar as (1) is taken to be a claim about the world, namely, that it contains (in a very loose sense) prime numbers, it is a substantive metaphysical claim. Very roughly, the first sense involves a presupposition of the existence of numbers whereas the second sense does not. I'm interested in your intuitions about two questions:
First, do you recognize these two readings of (1)?
Second, do you think that recognition of these two readings of (1) commits one to the Carnapian distinction between internal and external frameworks?
If you're in doubt as to how to respond, here's what you should do. Say "yes" in response to the first question, and say "no" in response to the second question. Then, if you're feeling ambitious, go on to present a detailed defense your answer to the second question. I will then be able to copy your comment and paste it into the blank document I have labeled "Draft for Metametaphysics paper". Thank you.
Edward
(1) There are prime numbers
Arguably (1) is associated with two senses. Insofar as (1) is taken to be a claim about the numbers, namely, that some of them are prime, it is uncontroversially true. Insofar as (1) is taken to be a claim about the world, namely, that it contains (in a very loose sense) prime numbers, it is a substantive metaphysical claim. Very roughly, the first sense involves a presupposition of the existence of numbers whereas the second sense does not. I'm interested in your intuitions about two questions:
First, do you recognize these two readings of (1)?
Second, do you think that recognition of these two readings of (1) commits one to the Carnapian distinction between internal and external frameworks?
If you're in doubt as to how to respond, here's what you should do. Say "yes" in response to the first question, and say "no" in response to the second question. Then, if you're feeling ambitious, go on to present a detailed defense your answer to the second question. I will then be able to copy your comment and paste it into the blank document I have labeled "Draft for Metametaphysics paper". Thank you.
Edward
Tuesday, May 1, 2007
Truth and Contradictions
This may be more of a request for something to read than anything else, but here goes:
Imagine this dialogue between a proponent of dialetheism and a proponent of classical logic:
A: You think that my logic is hopelessly strange, but I can give you a pretty good idea of what you have in mind. There are several paraconsistent logics out there -- consider FDE. Instead of a valuation function assigning 1 or 0 to propositions, imagine that it assigns either {1}, {0}, {1, 0} or {null}. A proposition is true, intuitively, if 1 is a member of its valuation. The logical connectives then work in the expected way (for instance, A&B is true ({1} or {1, 0}) when 1 is a member of the valuation of A and B). We can then see exactly which inferences are valid and which aren't, but we should both agree that things aren't totally crazy -- plenty of things will be false (and only false) in this system, and we can have meaningful discussions about contradictions.
B: I understand your system, but you've just changed the subject. For me, truth and falsity are exhaustive and exclusive. This is constitutive of my notion of truth and falsity. You've provided a model of something else entirely -- and maybe your model could do some interesting work, but to give your gloss on truth in this model is just plain disingenuous.
Does this sound right? What should A's response be? I'm sure people have talked about this before in phil logic, but I haven't seen anything particularly interesting said at this point in the dialectic (Stalnaker's Impossibilities paper being the only thing I can think of)...
Imagine this dialogue between a proponent of dialetheism and a proponent of classical logic:
A: You think that my logic is hopelessly strange, but I can give you a pretty good idea of what you have in mind. There are several paraconsistent logics out there -- consider FDE. Instead of a valuation function assigning 1 or 0 to propositions, imagine that it assigns either {1}, {0}, {1, 0} or {null}. A proposition is true, intuitively, if 1 is a member of its valuation. The logical connectives then work in the expected way (for instance, A&B is true ({1} or {1, 0}) when 1 is a member of the valuation of A and B). We can then see exactly which inferences are valid and which aren't, but we should both agree that things aren't totally crazy -- plenty of things will be false (and only false) in this system, and we can have meaningful discussions about contradictions.
B: I understand your system, but you've just changed the subject. For me, truth and falsity are exhaustive and exclusive. This is constitutive of my notion of truth and falsity. You've provided a model of something else entirely -- and maybe your model could do some interesting work, but to give your gloss on truth in this model is just plain disingenuous.
Does this sound right? What should A's response be? I'm sure people have talked about this before in phil logic, but I haven't seen anything particularly interesting said at this point in the dialectic (Stalnaker's Impossibilities paper being the only thing I can think of)...
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