Are there true contradictions? Via reddit, I saw the following, which seems like it might be a list of decent candidates for true contradictions -- and these candidates don't seem at first glance to fall into any of the existing categories of supposed true contradiction. (A relatively accessible list of proposed candidates can be found here.)
After thinking about it a little, I think these are probably not good candidates for true contradictions: rather, it looks like 'Sunday November 3rd, 2012 at 1:30AM' is ambiguous. And it is not a true contradiction when 'Maria was a philosophy major' is true and 'Maria was not a philosophy major' is also true, if there are two different people named 'Maria' (and the first majored in philosophy but the second didn't).
Or is there something special about time, that makes these daylight savings cases different from garden-variety ambiguity cases (like 'Maria')? Am I missing something?
(For any readers wondering 'Why does it matter whether there are true contradictions?': It is a theorem of classical logic that everything follows from a contradiction. Many people have found this counterintuitive and want to reject it. So many of these people look for true contradictions: if there are true contradictions, then there will be arguments that have contradictory premises, which are all true, but nonetheless a false conclusion.)
idiosyncratic perspectives on philosophy of science, its history, and related issues in logic
11/05/2012
9/11/2012
reporting from the Carnap archive
Did you know that Rudolf (née Rudi) Carnap was a teenage playwright?
6/18/2012
Need For Cognition and the Bias Blind Spot
This post isn't really about philosophy, but philosophers I know keep linking to this article on facebook. That's my excuse for talking about a psychology paper.
Jonah Lehrer posted, on the New Yorker website, this short piece entitled "Why Smart People are Stupid," with the more descriptive alternate title "Research Shows that the Smarter People Are, the More Susceptible They Are to Cognitive Bias." It's (supposed to be) a report of a recent article called "Cognitive Sophistication Does not Attenuate the Bias Blind Spot" in the Journal of Personality and Social Psychology, by Richard West, Russell Meserve, and Keith Stanovich. The bias blind spot, the authors of the latter paper tell us, is "reporting that thinking biases [e.g. the base-rate fallacy, the Alice the bank-teller conjunctive fallacy] are more prevalent in others than in themselves." What follows is about the original article, not the Lehrer post.
(The substantial gap between the Lehrer post and the actual article, which you could already figure out from the differing titles, is covered well here.)
The authors of the study used multiple instruments to judge cognitive sophistication, which includes not only cognitive ability (the authors use SAT scores to measure cognitive ability), but also 'thinking dispositions,' measured in part by a Need for Cognition test. (All the following quotations come from this site on the Need for Cognition Scale.) This test "quantitatively measures 'the tendency for an individual to engage in and enjoy thinking" (Cacioppo & Petty, 1982, p. 116)." I had heard of the Need for Cognition Scale before, but had never looked at the actual 18-question survey instrument (again, available here). Some of the questions are the sorts of questions I expected, given the name 'Need for Cognition':
"5. I try to anticipate and avoid situations where there is likely a chance I will have to think in depth about something.
6. I find satisfaction in deliberating hard and for long hours."
However, some of the questions seemed instead to measure something slightly different: the respondent's belief or faith in her rational faculties:
"2. I like to have the responsibility of handling a situation that requires a lot of thinking.
10. The idea of relying on thought to make my way to the top appeals to me.
15. I would prefer a task that is intellectual, difficult, and important to one that is somewhat important but does not require much thought."
Respondents who say that they 'agree very strongly' with 2, 10, and 15 seem like they would be much more likely to think of themselves as overcoming irrational biases. Speaking purely from my own case, I certainly agree very strongly with item #6 ('I find satisfaction in deliberating hard and for long hours'). However, I also believe humans (myself included) can exhibit irrational biases in (what what feels like) rational deliberations, so I would probably disagree or at least say I 'neither agree nor disagree' with 2 and 15. If there is an important task that I can get the right answer to that does not require much thought, then I would prefer that to a task where there a lot of rational speculation is required. To put the point more pithily: if a decision really is important, I'd rather be right than think -- since I think biases can creep into my thinking process.
My point is just that items 2, 10, and 15 seem to already be asking 'How much faith do you have that your rational faculties aren't clouded by bias?', which is pretty close to asking about the blind spot bias. Or at least, people who very strongly agree with 2, 10, and 15 would be people who think they can overcome bias when they are responsible for making important decisions. And that seems to be halfway to the bias blind spot (the belief that biases are more prevalent in others than ourselves) -- and it's the more substantive half, since just about everyone agrees that other people are suffer from biases.
And this fits the data: the correlation between 'Composite Bias Blind Spot' (the authors asked subjects about 7 different specific biases, not just 'Do you think you are less biased than other people?') and Need For Cognition score is .260, p<.001 (Table 2). (And interestingly, this correlation was by far the largest of the 4 four components of 'cognitive sophistication.')
So the interesting question for me would be: suppose we took each subject's Need For Cognition answers, dropped the answers to 2, 10, and 15 (or maybe just 2 and 15), and re-calculate each subject's NFC score. If I am right, the size of the correlation would drop significantly.
Jonah Lehrer posted, on the New Yorker website, this short piece entitled "Why Smart People are Stupid," with the more descriptive alternate title "Research Shows that the Smarter People Are, the More Susceptible They Are to Cognitive Bias." It's (supposed to be) a report of a recent article called "Cognitive Sophistication Does not Attenuate the Bias Blind Spot" in the Journal of Personality and Social Psychology, by Richard West, Russell Meserve, and Keith Stanovich. The bias blind spot, the authors of the latter paper tell us, is "reporting that thinking biases [e.g. the base-rate fallacy, the Alice the bank-teller conjunctive fallacy] are more prevalent in others than in themselves." What follows is about the original article, not the Lehrer post.
(The substantial gap between the Lehrer post and the actual article, which you could already figure out from the differing titles, is covered well here.)
The authors of the study used multiple instruments to judge cognitive sophistication, which includes not only cognitive ability (the authors use SAT scores to measure cognitive ability), but also 'thinking dispositions,' measured in part by a Need for Cognition test. (All the following quotations come from this site on the Need for Cognition Scale.) This test "quantitatively measures 'the tendency for an individual to engage in and enjoy thinking" (Cacioppo & Petty, 1982, p. 116)." I had heard of the Need for Cognition Scale before, but had never looked at the actual 18-question survey instrument (again, available here). Some of the questions are the sorts of questions I expected, given the name 'Need for Cognition':
"5. I try to anticipate and avoid situations where there is likely a chance I will have to think in depth about something.
6. I find satisfaction in deliberating hard and for long hours."
However, some of the questions seemed instead to measure something slightly different: the respondent's belief or faith in her rational faculties:
"2. I like to have the responsibility of handling a situation that requires a lot of thinking.
10. The idea of relying on thought to make my way to the top appeals to me.
15. I would prefer a task that is intellectual, difficult, and important to one that is somewhat important but does not require much thought."
Respondents who say that they 'agree very strongly' with 2, 10, and 15 seem like they would be much more likely to think of themselves as overcoming irrational biases. Speaking purely from my own case, I certainly agree very strongly with item #6 ('I find satisfaction in deliberating hard and for long hours'). However, I also believe humans (myself included) can exhibit irrational biases in (what what feels like) rational deliberations, so I would probably disagree or at least say I 'neither agree nor disagree' with 2 and 15. If there is an important task that I can get the right answer to that does not require much thought, then I would prefer that to a task where there a lot of rational speculation is required. To put the point more pithily: if a decision really is important, I'd rather be right than think -- since I think biases can creep into my thinking process.
My point is just that items 2, 10, and 15 seem to already be asking 'How much faith do you have that your rational faculties aren't clouded by bias?', which is pretty close to asking about the blind spot bias. Or at least, people who very strongly agree with 2, 10, and 15 would be people who think they can overcome bias when they are responsible for making important decisions. And that seems to be halfway to the bias blind spot (the belief that biases are more prevalent in others than ourselves) -- and it's the more substantive half, since just about everyone agrees that other people are suffer from biases.
And this fits the data: the correlation between 'Composite Bias Blind Spot' (the authors asked subjects about 7 different specific biases, not just 'Do you think you are less biased than other people?') and Need For Cognition score is .260, p<.001 (Table 2). (And interestingly, this correlation was by far the largest of the 4 four components of 'cognitive sophistication.')
So the interesting question for me would be: suppose we took each subject's Need For Cognition answers, dropped the answers to 2, 10, and 15 (or maybe just 2 and 15), and re-calculate each subject's NFC score. If I am right, the size of the correlation would drop significantly.
6/07/2012
In the current AJP: "Overcoming Metaphysics through the Logical Analysis of Language" for the 21st C
"[T]he isolation of non-naturalistic metaphysics from other disciplines as well as from empirical refutation has made it moribund. We claim that a defining feature of non-naturalistic metaphysics is that it can have no observable consequences."
James Maclaurin and Heather Dyke, "What is Analytic Metaphysics For?", Australasian Journal of Philosophy, Vol. 90(2), 2012. (freely available reprint here)
Of course, the paper does not reprise Carnap's "Overcoming Metaphysics through the Logical Analysis of Language" exactly; Maclaurin and Dyke's central claim is that the criteria for theory-choice in non-naturalistic metaphysics are not truth-conducive. The Carnap "Overcoming Metaphysics..." concludes instead that (non-naturalistic) metaphysics is cognitively meaningless.
So the precise problem with metaphysics is different for Carnap and for Maclaurin &, but a central premise used to reach their contra-metaphysics conclusions -- namely, (non-naturalistic) metaphysical claims make no difference to observation and are (inferentially) isolated from claims of the sciences -- is basically the same in both cases.
James Maclaurin and Heather Dyke, "What is Analytic Metaphysics For?", Australasian Journal of Philosophy, Vol. 90(2), 2012. (freely available reprint here)
Of course, the paper does not reprise Carnap's "Overcoming Metaphysics through the Logical Analysis of Language" exactly; Maclaurin and Dyke's central claim is that the criteria for theory-choice in non-naturalistic metaphysics are not truth-conducive. The Carnap "Overcoming Metaphysics..." concludes instead that (non-naturalistic) metaphysics is cognitively meaningless.
So the precise problem with metaphysics is different for Carnap and for Maclaurin &, but a central premise used to reach their contra-metaphysics conclusions -- namely, (non-naturalistic) metaphysical claims make no difference to observation and are (inferentially) isolated from claims of the sciences -- is basically the same in both cases.
6/05/2012
Submit a paper for the Creighton Club
4/26/2012
2/05/2012
Is 'human' ambiguous? (on M. A. Warren on abortion)
In class this week, we are reading Mary Anne Warren's classic "On the Moral and Legal Status of Abortion." For readers unfamiliar with the article, she argues against the following basic argument against abortion:
(1) It is prima facie wrong to kill human beings.
(2) Fetuses are human beings.
---------------------------------------
Therefore, it is prima facie wrong to kill fetuses.
Warren claims this argument commits the fallacy of equivocation:
The pedestrian question I want to ask is: is the word 'human' really ambiguous between 'person' and 'Homo Sapiens'? Linguists have developed tests to determine whether a word is ambiguous or not, and I'm not sure 'human' comes out ambiguous on these diagnostic tests. Here are three tests linguists consider useful.
1. The other languages test. Do other languages have distinct words for the various meanings of the supposedly ambiguous word?
2. The unrelated antonyms test. Does a word have two unrelated antonyms? E.g. the ambiguous word 'light' has both 'heavy' and 'dark' as antonyms.
3. The conjunction reduction test. Consider the sentence 'John and Jane each have a bat.' This could mean they both have baseball bats, or it could mean they both keep flying mammals as pets. However, it cannot (ordinarily/ without punning) mean that John keeps a pet bat and Jane has a baseball bat. That is, so-called 'crossed readings' are impossible, if the word is ambiguous. (This is called the 'conjunction reduction test' for the following reason: if John keeps a pet bat (but has no baseball bat), 'John has a bat' is true. If Jane has a baseball bat (but has no pet bat), then 'Jane has a bat' is true. But the reduced conjunction sentence 'John and Jane both have bats' is untrue, unless you are punning/ joking.)
The question now is how 'human' fares on each of these tests.
(Before proceeding to the official tests, it might be worth noting that, at least for me, 'human' does not intuitively/ pre-theoretically feel similar to 'bank' or 'light'.)
1. (other languages) Though I think 'human' apparently comes out unambiguous on this test for the languages I know, I don't know enough languages to be comfortable making a definitive pronouncement about this.
2. (unrelated antonyms) I think 'human' fails this ambiguity test too -- though I am open to evidence to the contrary. (hmmm... How unrelated do the antonyms have to be?)
3. (conjunction reduction) Suppose someone is 4 weeks pregnant, and she decides to name the fetus 'Pat'. Further suppose that we are at some point in the future where aliens are full-fledged members of our moral community. Call this alien 'Gordon Shumway.' (If you prefer robots to aliens, that would work too.)
For me, we can't even get the ambiguity test off the ground: 'Gordon Shumway is (a) human' (or 'Johnny Five is (a) human') are both false, according to my semantic intuitions. And if there is no true reading of 'Gordon Shumway is human,' then thinking about 'Pat and Gordon Shumway are human' won't reveal anything.
The (purported) fact that 'Gordon Shumway is human' is false suggests that belonging to the species Homo Sapiens is a necessary (but perhaps not sufficient) condition for being human. If that is correct, then we should not say that the traditional anti-abortion argument above trades on an ambiguity in 'human': there is no purely 'moral sense' of the word 'human' (i.e. full standing in the moral community is insufficient for humanity).
However, this is not a real problem for Warren's criticism of the traditional anti-abortion argument, as long as we think that "It is prima facie wrong to kill any member of Homo Sapiens" stands in need of some justification -- i.e. we think that we need some justification to think that the biological facts of species membership have anything to do with moral rights and obligations. And how to argue from biological premises to moral conclusions has been an extremely contentious philosophical issue.
(1) It is prima facie wrong to kill human beings.
(2) Fetuses are human beings.
---------------------------------------
Therefore, it is prima facie wrong to kill fetuses.
Warren claims this argument commits the fallacy of equivocation:
"the term `human' has two distinct, but not often distinguished, senses. This fact results in a slide of meaning, which serves to conceal the fallaciousness of the [above] argument ... For if `human' is used in the same sense in both (1) and (2) then, whichever of the two senses is meant, one of these premises is question-begging. And if it is used in two different senses then of course the conclusion doesn't follow.Warren does not explicitly call 'human' ambiguous between 'person' (= 'full-fledged member of the moral community') and 'Homo Sapiens' (what she thinks of as 'having a genotype within a certain range,' though that's not how biologists think about species), but I don't think it's too much of a stretch to attribute that view to her.
Thus, (1) is a self-evident moral truth,' and avoids begging the question about abortion, only if `human being' is used to mean something like `a full-fledged member of the moral community.' (It may or may not also be meant to refer exclusively to members of the species Homo sapiens.) We may call this the moral sense of `human.' It is not to be confused with what we call the genetic sense, i.e., the sense in which any member of the species is a human being, and no member of any other species could be. If (1) is acceptable only if the moral sense is intended, (2) is non-question-begging only if what is intended is the genetic sense."
The pedestrian question I want to ask is: is the word 'human' really ambiguous between 'person' and 'Homo Sapiens'? Linguists have developed tests to determine whether a word is ambiguous or not, and I'm not sure 'human' comes out ambiguous on these diagnostic tests. Here are three tests linguists consider useful.
1. The other languages test. Do other languages have distinct words for the various meanings of the supposedly ambiguous word?
2. The unrelated antonyms test. Does a word have two unrelated antonyms? E.g. the ambiguous word 'light' has both 'heavy' and 'dark' as antonyms.
3. The conjunction reduction test. Consider the sentence 'John and Jane each have a bat.' This could mean they both have baseball bats, or it could mean they both keep flying mammals as pets. However, it cannot (ordinarily/ without punning) mean that John keeps a pet bat and Jane has a baseball bat. That is, so-called 'crossed readings' are impossible, if the word is ambiguous. (This is called the 'conjunction reduction test' for the following reason: if John keeps a pet bat (but has no baseball bat), 'John has a bat' is true. If Jane has a baseball bat (but has no pet bat), then 'Jane has a bat' is true. But the reduced conjunction sentence 'John and Jane both have bats' is untrue, unless you are punning/ joking.)
The question now is how 'human' fares on each of these tests.
(Before proceeding to the official tests, it might be worth noting that, at least for me, 'human' does not intuitively/ pre-theoretically feel similar to 'bank' or 'light'.)
1. (other languages) Though I think 'human' apparently comes out unambiguous on this test for the languages I know, I don't know enough languages to be comfortable making a definitive pronouncement about this.
2. (unrelated antonyms) I think 'human' fails this ambiguity test too -- though I am open to evidence to the contrary. (hmmm... How unrelated do the antonyms have to be?)
3. (conjunction reduction) Suppose someone is 4 weeks pregnant, and she decides to name the fetus 'Pat'. Further suppose that we are at some point in the future where aliens are full-fledged members of our moral community. Call this alien 'Gordon Shumway.' (If you prefer robots to aliens, that would work too.)
For me, we can't even get the ambiguity test off the ground: 'Gordon Shumway is (a) human' (or 'Johnny Five is (a) human') are both false, according to my semantic intuitions. And if there is no true reading of 'Gordon Shumway is human,' then thinking about 'Pat and Gordon Shumway are human' won't reveal anything.
The (purported) fact that 'Gordon Shumway is human' is false suggests that belonging to the species Homo Sapiens is a necessary (but perhaps not sufficient) condition for being human. If that is correct, then we should not say that the traditional anti-abortion argument above trades on an ambiguity in 'human': there is no purely 'moral sense' of the word 'human' (i.e. full standing in the moral community is insufficient for humanity).
However, this is not a real problem for Warren's criticism of the traditional anti-abortion argument, as long as we think that "It is prima facie wrong to kill any member of Homo Sapiens" stands in need of some justification -- i.e. we think that we need some justification to think that the biological facts of species membership have anything to do with moral rights and obligations. And how to argue from biological premises to moral conclusions has been an extremely contentious philosophical issue.
2/02/2012
Spandrels of Truth (1?)
I am reading JC Beall's Spandrels of Truth this semester as part of an independent study. We've only made it through Chapter 1, but it's great so far: clear and interesting.
I, however, am having unclear (and probably uninteresting) thoughts about it. Specifically, I am wondering whether certain things Beall says are in tension with each other.
(1) "God could use only the T[ruth]-free fragment of English to uniquely specify our world. We are unlike God in that respect; we need a device that enables us to overcome finite constraints. That device is 'true'... [W]ere we God, or even just beings with infinite time or capacities, we wouldn't need to use 'true' in such generalizing contexts [e.g. 'Everything Pat says is true']." (p.1)
So (1a) God (or any other appropriately infinite being) can 'uniquely specify our world' without using the word 'true'. Furthermore, (1b) 'true' is only introduced to overcome a practical limitation.
(2) Our language, which contains 'truth,' gives rise to sentences like the Liar that are true falsehoods: these are sentences A such that both A and ~A are true. Beall calls such sentences 'spandrels of truth': they are unintended byproducts of introducing a truth-predicate.
(3) Beall uses the 'Routley star' semantics for negation. For those unfamiliar with this semantics, all that's needed for present purposes is that in a world where there are true falsehoods, that world's "star mate" cannot be the world itself, and must be an abnormal world (in an abnormal world, there is a sentence A such that neither A nor ~A is true, i.e. abnormal worlds exhibit truth-value gaps). (In brief: B is true in w* iff ~B is not true in w.)
(4) If a language contains no true contradictions, then abnormal worlds are completely superfluous. (We cannot show that the abnormal worlds do not exist, but they would do no semantic work not already done by the normal worlds.)
So now I will try to articulate my thought. If God can completely describe everything without using the predicate 'true,' then abnormal worlds are superfluous for a complete description. And if we subscribe to some sort of Ockhamian principle of parsimony, then such abnormal worlds don't exist. However, bringing 'truth' into our language requires (given Beall's other assumptions) that there must be abnormal worlds. That is unsettling enough: God needn't know about the abnormal worlds, even if God knows a complete description of everything.
Furthermore, the only thing that forces us to introduce abnormal worlds is a predicate that we introduced to overcome a practical limitation on our part. Devices for surmounting practical obstacles don't seem like the kind of thing that should be able to teach us about whether there are abnormal worlds or not.
I guess one response to this is to be a serious instrumentalist about the abnormal worlds: since they are unnecessary for the god's-eye view, we should (at least if we prune 'idle wheels' from our theories) say: they don't really exist, but we cannot give an acceptable semantics for a truth-predicate (satisfying certain conditions Beall finds natural) without them. But this response seems strange to me; though I cannot articulate precisely why, here's a try. If we ask: "Is our actual world's "star mate" a normal world or an abnormal world?", we would have to say 'From a God's-eye-view, no; but if we have a certain kind of truth-predicate in our language, then yes, the actual world's star-mate is an abnormal world.'
Hopefully, there will be further installments in my attempts to grapple with Spandrels... but I'm not making any promises.
I, however, am having unclear (and probably uninteresting) thoughts about it. Specifically, I am wondering whether certain things Beall says are in tension with each other.
(1) "God could use only the T[ruth]-free fragment of English to uniquely specify our world. We are unlike God in that respect; we need a device that enables us to overcome finite constraints. That device is 'true'... [W]ere we God, or even just beings with infinite time or capacities, we wouldn't need to use 'true' in such generalizing contexts [e.g. 'Everything Pat says is true']." (p.1)
So (1a) God (or any other appropriately infinite being) can 'uniquely specify our world' without using the word 'true'. Furthermore, (1b) 'true' is only introduced to overcome a practical limitation.
(2) Our language, which contains 'truth,' gives rise to sentences like the Liar that are true falsehoods: these are sentences A such that both A and ~A are true. Beall calls such sentences 'spandrels of truth': they are unintended byproducts of introducing a truth-predicate.
(3) Beall uses the 'Routley star' semantics for negation. For those unfamiliar with this semantics, all that's needed for present purposes is that in a world where there are true falsehoods, that world's "star mate" cannot be the world itself, and must be an abnormal world (in an abnormal world, there is a sentence A such that neither A nor ~A is true, i.e. abnormal worlds exhibit truth-value gaps). (In brief: B is true in w* iff ~B is not true in w.)
(4) If a language contains no true contradictions, then abnormal worlds are completely superfluous. (We cannot show that the abnormal worlds do not exist, but they would do no semantic work not already done by the normal worlds.)
So now I will try to articulate my thought. If God can completely describe everything without using the predicate 'true,' then abnormal worlds are superfluous for a complete description. And if we subscribe to some sort of Ockhamian principle of parsimony, then such abnormal worlds don't exist. However, bringing 'truth' into our language requires (given Beall's other assumptions) that there must be abnormal worlds. That is unsettling enough: God needn't know about the abnormal worlds, even if God knows a complete description of everything.
Furthermore, the only thing that forces us to introduce abnormal worlds is a predicate that we introduced to overcome a practical limitation on our part. Devices for surmounting practical obstacles don't seem like the kind of thing that should be able to teach us about whether there are abnormal worlds or not.
I guess one response to this is to be a serious instrumentalist about the abnormal worlds: since they are unnecessary for the god's-eye view, we should (at least if we prune 'idle wheels' from our theories) say: they don't really exist, but we cannot give an acceptable semantics for a truth-predicate (satisfying certain conditions Beall finds natural) without them. But this response seems strange to me; though I cannot articulate precisely why, here's a try. If we ask: "Is our actual world's "star mate" a normal world or an abnormal world?", we would have to say 'From a God's-eye-view, no; but if we have a certain kind of truth-predicate in our language, then yes, the actual world's star-mate is an abnormal world.'
Hopefully, there will be further installments in my attempts to grapple with Spandrels... but I'm not making any promises.
1/03/2012
History of Philosophy of Science at the Philosophy of Science Association meeting?
I'm currently trying to figure out what, if anything, I should submit for the 2012 PSA. I was thinking of sending in a paper on Carnap, but then I had a look at the Program Committee (here's the list), and 0 of the 20 people on the committee work primarily in history of philosophy of science. Furthermore, at the last PSA (see here), there were zero papers in HOPOS -- though there was one HOPOS person on the Program Committee then. I remember that there were HOPOS papers at PSA's in the recent past (I'm certain there was a HOPOS session at the 2004 meeting, because I presented).
Although I'm mildly curious about why HOPOS has apparently dropped off the PSA's radar, I guess the more immediate question for me is whether I should bother submitting the Carnap paper.
Although I'm mildly curious about why HOPOS has apparently dropped off the PSA's radar, I guess the more immediate question for me is whether I should bother submitting the Carnap paper.
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