There's been a few items in Science the last two weeks that are potentially philosophically interesting:
[This week]
1. Rats can learn rules and then generalize them to new, different situations to a degree that people previously thought was confined to humans or at least primates.
2. Two smells that are initially indiscriminable to a human can, with painful conditioning, be made discriminable. (The initial indiscriminability was not just in terms of verbal reports of conscious states; the scientists did fMRIs on the patients too.)
[Last week]
3. After your basic needs are met, having more money does not make you much happier (that's been known for a while); however, giving that money away instead of spending it on yourself does have a significant effect on your (self-reported) happiness.
4. One of my favorite biologists, Günter Wagner, argues that pleiotropy (one gene having several effects) is actually not as significant as once thought (philosophers of biology have used pleiotropy to argue for various points).
Of course, this is just the bumper-sticker version of each of these claims; the actual positions will be more sophisticated, and require various caveats. Nonetheless, it seems like each of these studies could merit philosophical attention.
3/28/2008
3/14/2008
Logical Pluralism, take 2
This post supersedes the previous one on logical pluralism; it's the post I would've written, had I bothered to do a bit of research before posting. I apologize in advance for how long it is...
Beall and Restall say we should be pluralists about logical consequence, because there are multiple acceptable ways of spelling out the notion of case in the standard criterion of validity:
(V) C is a logical consequence of P1 ... Pn iff in every case where all of P1...Pn are true, C is true also.
Different specifications of case, say B&R, yield different consequence relations.
My impulse is to address this issue 'from above'; that is, in general, when is any sort of pluralism an acceptable stance? Well, one case (though probably not the only one) in which it can be acceptable is when ambiguity is present. E.g., there are multiple, equally acceptable ways of spelling out 'Aaron is at the bank'. And Beall and Restall, on the 3rd page of "Defending Logical Pluralism," state that they think logical consequence is ambiguous; presumably the ambiguity is traced back to the word 'case' in (V) (what else in (V) could it be?). So if 'case' really is ambiguous, and (V) captures the core notion of consequence correctly, then we should be logical pluralists.
But I'm not sure 'case' is ambiguous -- prima facie, it doesn't feel like 'bank,' or 'duck'. It might just be 'general in sense' or 'lack specificity': for example, 'sibling' is general in sense between 'brother' and 'sister', the same goes for 'parent' and 'mother' and 'father.' And nobody wants to be a 'sibling-pluralist' or 'parent-pluralist.' (Note: 'thing', which seems to me closer to 'case', does not seem ambiguous either.)
Linguists, fortunately, have devised a test to distinguish ambiguous expressions from ones that are general in sense: the 'conjunction reduction' test. Suppose my friend Pat is making a monetary deposit, and my friend Tracy is sitting next to a river. Then the two sentences
'Pat is at the bank' and
'Tracy is at the bank'
are both true. However, these truths cannot be expressed in a 'conjunction reduced' sentence
'Pat and Tracy are at the bank,'
for this can only mean that both of Pat and Tracy are next to a body of water, or both are at a financial institution. No 'crossed reading' is possible. The impossibility of crossed readings in the reduced sentence suffices for the ambiguity of 'bank' (Jay D. Atlas, Philosophy without Ambiguity, OUP 1989, p.40). From the little I've seen, almost all linguists and linguistically-inclined philosophers accept this as an ambiguity test. And most also accept: If crossed readings are possible, then there is no ambiguity. E.g., 'Pat and Tracy are parents' can be read as saying that Pat and Tracy are both fathers, both mothers, or one of each -- and the possibility of that 'one of each' reading is what makes 'parent' non-ambiguous, but rather just general in sense.
With a test for ambiguity in hand, we can see if 'case' and 'consequence' are ambiguous (so pluralism is the right stance) or merely general in sense (in which case pluralism is not obviously the right stance). Let C0 be a construction (of the sort used in semantics for intuitionistic logic), and let S0 be a situation (of the sort used in semantics for relevance logic). (Cf. previous pluralism post if that doesn't make sense.) Then, I think, Beall & Restall would say
'C0 is a case'
is true, and so is
'S0 is a case'.
(If they don't, then 'case' is not ambiguous, but something else.)
Now the question is: Are 'crossed readings' possible for
'C0 and S0 are cases'?
That is: can that last sentence express that C0 is a construction and S0 a situation, or can it only be read as saying that C0 and S0 are both constructions or both situations? I lean towards the possibility of crossed readings, but I'm just not sure.
We might try the conjunction-reduction test with logical consequence as well:
not-not-A (relevantly) implies A [but not intuitionistically]
not-not-A (intuitionistically) implies 'If B, then B' [but not relevantly]
The conjunction reduced sentence is:
not-not-A implies A and 'If B, then B'
Here, a crossed reading DOES seem impossible, to me at least. So that makes it look like 'implies' is ambiguous. (Note: I'm not certain I've formed the correct conjunction reduction sentence.)
Now I'm stuck: it looks like 'implies' is ambiguous, while 'case' is not. If this is right, then we could deny (V) -- but what could we put in its place?
Final speculative thought: 'implies' is like 'before' in relativistic physics. If two events are spacelike related (= no signal can be passed between them), then 'e1 is before e2' is neither true nor false until a frame of reference is specified. In one frame of reference e1 will be before e2, and in another frame, e2 will be before e1. But once the frame (and a simultaneity convention) is chosen, then it becomes fully determinate which precedes the other. BUT no one frame is the 'right' one; each frame 'has equal rights'.
The analogy: picking a particular frame of reference is like picking situations over constructions or models etc. As there is no one right frame, so too there is no one right truth-maker. So 'A implies B' is then NOT like 'Aaron is at the bank', for I can use that second sentence meaningfully (= truth-valued-ly) without supplying some further information -- unlike 'e1 is before e2' for spacelike-related events. But once one picks a frame, all instances of 'e1 is before e2' become truth-valued; analogously, once one picks a specification of 'case', every instance of 'Does C follow from {P1, ... Pn}?' has a determinate answer.
In sum: ambiguity may not be the best way of thinking about the different consequence relations; rather, perhaps we should see how well we can make out this analogy with relativistic physics.
Beall and Restall say we should be pluralists about logical consequence, because there are multiple acceptable ways of spelling out the notion of case in the standard criterion of validity:
(V) C is a logical consequence of P1 ... Pn iff in every case where all of P1...Pn are true, C is true also.
Different specifications of case, say B&R, yield different consequence relations.
My impulse is to address this issue 'from above'; that is, in general, when is any sort of pluralism an acceptable stance? Well, one case (though probably not the only one) in which it can be acceptable is when ambiguity is present. E.g., there are multiple, equally acceptable ways of spelling out 'Aaron is at the bank'. And Beall and Restall, on the 3rd page of "Defending Logical Pluralism," state that they think logical consequence is ambiguous; presumably the ambiguity is traced back to the word 'case' in (V) (what else in (V) could it be?). So if 'case' really is ambiguous, and (V) captures the core notion of consequence correctly, then we should be logical pluralists.
But I'm not sure 'case' is ambiguous -- prima facie, it doesn't feel like 'bank,' or 'duck'. It might just be 'general in sense' or 'lack specificity': for example, 'sibling' is general in sense between 'brother' and 'sister', the same goes for 'parent' and 'mother' and 'father.' And nobody wants to be a 'sibling-pluralist' or 'parent-pluralist.' (Note: 'thing', which seems to me closer to 'case', does not seem ambiguous either.)
Linguists, fortunately, have devised a test to distinguish ambiguous expressions from ones that are general in sense: the 'conjunction reduction' test. Suppose my friend Pat is making a monetary deposit, and my friend Tracy is sitting next to a river. Then the two sentences
'Pat is at the bank' and
'Tracy is at the bank'
are both true. However, these truths cannot be expressed in a 'conjunction reduced' sentence
'Pat and Tracy are at the bank,'
for this can only mean that both of Pat and Tracy are next to a body of water, or both are at a financial institution. No 'crossed reading' is possible. The impossibility of crossed readings in the reduced sentence suffices for the ambiguity of 'bank' (Jay D. Atlas, Philosophy without Ambiguity, OUP 1989, p.40). From the little I've seen, almost all linguists and linguistically-inclined philosophers accept this as an ambiguity test. And most also accept: If crossed readings are possible, then there is no ambiguity. E.g., 'Pat and Tracy are parents' can be read as saying that Pat and Tracy are both fathers, both mothers, or one of each -- and the possibility of that 'one of each' reading is what makes 'parent' non-ambiguous, but rather just general in sense.
With a test for ambiguity in hand, we can see if 'case' and 'consequence' are ambiguous (so pluralism is the right stance) or merely general in sense (in which case pluralism is not obviously the right stance). Let C0 be a construction (of the sort used in semantics for intuitionistic logic), and let S0 be a situation (of the sort used in semantics for relevance logic). (Cf. previous pluralism post if that doesn't make sense.) Then, I think, Beall & Restall would say
'C0 is a case'
is true, and so is
'S0 is a case'.
(If they don't, then 'case' is not ambiguous, but something else.)
Now the question is: Are 'crossed readings' possible for
'C0 and S0 are cases'?
That is: can that last sentence express that C0 is a construction and S0 a situation, or can it only be read as saying that C0 and S0 are both constructions or both situations? I lean towards the possibility of crossed readings, but I'm just not sure.
We might try the conjunction-reduction test with logical consequence as well:
not-not-A (relevantly) implies A [but not intuitionistically]
not-not-A (intuitionistically) implies 'If B, then B' [but not relevantly]
The conjunction reduced sentence is:
not-not-A implies A and 'If B, then B'
Here, a crossed reading DOES seem impossible, to me at least. So that makes it look like 'implies' is ambiguous. (Note: I'm not certain I've formed the correct conjunction reduction sentence.)
Now I'm stuck: it looks like 'implies' is ambiguous, while 'case' is not. If this is right, then we could deny (V) -- but what could we put in its place?
Final speculative thought: 'implies' is like 'before' in relativistic physics. If two events are spacelike related (= no signal can be passed between them), then 'e1 is before e2' is neither true nor false until a frame of reference is specified. In one frame of reference e1 will be before e2, and in another frame, e2 will be before e1. But once the frame (and a simultaneity convention) is chosen, then it becomes fully determinate which precedes the other. BUT no one frame is the 'right' one; each frame 'has equal rights'.
The analogy: picking a particular frame of reference is like picking situations over constructions or models etc. As there is no one right frame, so too there is no one right truth-maker. So 'A implies B' is then NOT like 'Aaron is at the bank', for I can use that second sentence meaningfully (= truth-valued-ly) without supplying some further information -- unlike 'e1 is before e2' for spacelike-related events. But once one picks a frame, all instances of 'e1 is before e2' become truth-valued; analogously, once one picks a specification of 'case', every instance of 'Does C follow from {P1, ... Pn}?' has a determinate answer.
In sum: ambiguity may not be the best way of thinking about the different consequence relations; rather, perhaps we should see how well we can make out this analogy with relativistic physics.
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