Yesterday I was in Toronto’s downtown core and saw several same-sex couples. Each of the same-sex couples I saw had a commonality between them: For every same-sex couple, there was a person of the male gender and the other was of the female gender. That is, for every same-sex couple I saw, biological sex aside, there was one member who took on the traditional male gender: He or she was sort of burly, walked authoritatively, confident, dressed like a man, and so on. You know the type. The other took on the more traditional feminine gender. You know this type too, and so I don’t need to explain.
From this, I began to wonder. Do these couples frustrate our common understanding of sexual preference? After all, here we have (presumably) each member of the couple attracted to the other member, and (presumably) each member is also attracted to the other member’s sex and gender. Yet, for every couple, the identity of one member’s sex does not correspond to his or her gender. Thus, for every couple, we have a member who has an attraction to the female sex as well as the male gender or the male sex and the female gender. Are these members gay, bisexual or straight?
If we call these members ‘gay’ on virtue of being attracted to the same sex, then we seem to have too much of a parochial understanding of sexual preference. Biological sex and body is only a part of sexual preference, after all. If we call these members ‘bisexual’ even though they have no preference to the opposite sex, then we seem to have abandoned our understanding of bisexuality. And a similar abandonment would be had if we called these members ‘straight’. So…what the fuck do we say?
Let’s consider something else. Some male-sexed transsexuals are hot. Don’t deny this, fellas. For these transsexuals, it is perfectly conceivable that some of are of the feminine gender. If I were attracted to and dated such a transsexual, then would I be gay or bisexual, or at least not straight? I cannot say. And, I suspect this is because our conceptual scheme fails to capture the multifaceted reality of sexual preference.
Moreover, even if we try to understand sexual preference on the continuum of bisexuality, homosexuality and heterosexuality, we’d still be getting a distorted viewpoint. For here, at least on the traditionally used continuums, the divergence of preference in sex and gender is not recognized. And even if it were, we'd need to account for the different conceptions of masculinity within the different cultures. A case in point: You'd find me quite resistant to identify young South Korean men as generally consistent with "the" contemporary western viewpoint of masculinity.
Thursday, October 28, 2010
Sunday, October 10, 2010
Revisiting that pesky material implication
Consider this:
(1) If I roll an even number, it will land 6.
Presuming an unbiased conventional die, it seems appropriate to attribute my degree of confidence as 1/3, since there are only 3 instances of even number and only 1 of those 3 is a 6.
But now consider (1) as a material conditional. There are now only 2 ways which (1) can be false (from the die landing on 2 or 4). Thus, we say the degree of confidence in its truth is 4/6, which yields 2/3.
1/3 vs. 2/3
Two different degrees of confidence for a single statement. Is this a problem for the material implication?
(1) If I roll an even number, it will land 6.
Presuming an unbiased conventional die, it seems appropriate to attribute my degree of confidence as 1/3, since there are only 3 instances of even number and only 1 of those 3 is a 6.
But now consider (1) as a material conditional. There are now only 2 ways which (1) can be false (from the die landing on 2 or 4). Thus, we say the degree of confidence in its truth is 4/6, which yields 2/3.
1/3 vs. 2/3
Two different degrees of confidence for a single statement. Is this a problem for the material implication?
Saturday, October 9, 2010
Pesky material conditionals
I’ve always been suspicious about the ‘if’ as truth-functional within conventional logic. I herein give some classical examples as some grounds for my suspicion.
As we all know, a material implication is true in any other case where it is not the case that the antecedent is true and the consequent false. Thus, the statement, ‘If Toronto is the capital of Canada, then the moon is made of cheese’ is true, for both the antecedent and consequent are false. Yet, that certainly does not correspond well to our intuitions. Indeed, we’d think something quite to the contrary. Consider another: ‘if 2+2=4, then the moon is made of cheese.’ Here the antecedent is true while the consequent is false; and hence the conditional is true. But, again, this does not correspond well to our intuitions. Indeed, we want to say something to the contrary, since ‘if…then’ statements in English carry a sense relevance between the antecedent and the consequent while such no such relevance is found here.
Here’s another example:
If I win a massive lottery, then I will not pay off my school loan.
This conditional seems implausibly true. Indeed, my school loan is one of the first things I would pay off if I won a massive lottery. But, consider its truth as a material conditional. It’s almost certain that the antecedent is false. But if it’s false, then the truth of the conditional is secured. Thus, then, we have a confliction. Let’s consider another example:
Consider the negation of a conditional, ~(if p then q). On conventional logic, ~(if p then q) yields both p & ~q. In formal lingo, the impropriety of that which is yielded is far from obvious. So let me offer an example in English: ‘It is not the case that if you pray to God, then God exists.’ From this, we conclude: ‘Thus, you pray to God and it is not the case that God exists.’ By simplification, we assert: ‘Thus, it is not the case that God exists.’
Considering the above, if you are anything like me, the conclusion should strike you as absurd. Yet, the conclusion is exactly what we’d be committed to since conditionals are only false if their antecedents are true and the consequent is false.
Let’s try another: The ‘if’, in English, is not always transitive although it is in conventional logic, if p then q/ if q the r; if p then r. To see why this is problematic, contemplate this:
If Pat dies before the election, then Sean will win. If Sean wins, Pat will retire from public life after the election. Thus, is Pat dies before the election, then Pat will retire from public life after the election.
I could understand perfectly well what someone would mean by the two statements, and yet I’d never think the conclusion is what they’d be logically committed as per hypothetical syllogism. It’s absurd, I think. There is also a more humorous example to consider as well:
If I put sugar in my coffee, it will taste good. Therefore, if I put both sugar in my coffee and feces in my coffee, it will taste good.
This is valid. The last statement follows from the first since it is true that 'if p then q'; 'if (p&r) then q', whatever r may be. But surely we wouldn’t want to make this conclusion from the first statement. It’s just wrong. It’s funny, but wrong.
There have been attempts to help remedy these problems. Grice has argued something in opposition to my suspicions, and there have been conditional logics as well as relevance logic. I reject the first two as implausible or insufficient, and I have trouble with the third since it denies the disjunctive syllogism.
I’ll write about relevance logic some other time.
Cheers,
As we all know, a material implication is true in any other case where it is not the case that the antecedent is true and the consequent false. Thus, the statement, ‘If Toronto is the capital of Canada, then the moon is made of cheese’ is true, for both the antecedent and consequent are false. Yet, that certainly does not correspond well to our intuitions. Indeed, we’d think something quite to the contrary. Consider another: ‘if 2+2=4, then the moon is made of cheese.’ Here the antecedent is true while the consequent is false; and hence the conditional is true. But, again, this does not correspond well to our intuitions. Indeed, we want to say something to the contrary, since ‘if…then’ statements in English carry a sense relevance between the antecedent and the consequent while such no such relevance is found here.
Here’s another example:
If I win a massive lottery, then I will not pay off my school loan.
This conditional seems implausibly true. Indeed, my school loan is one of the first things I would pay off if I won a massive lottery. But, consider its truth as a material conditional. It’s almost certain that the antecedent is false. But if it’s false, then the truth of the conditional is secured. Thus, then, we have a confliction. Let’s consider another example:
Consider the negation of a conditional, ~(if p then q). On conventional logic, ~(if p then q) yields both p & ~q. In formal lingo, the impropriety of that which is yielded is far from obvious. So let me offer an example in English: ‘It is not the case that if you pray to God, then God exists.’ From this, we conclude: ‘Thus, you pray to God and it is not the case that God exists.’ By simplification, we assert: ‘Thus, it is not the case that God exists.’
Considering the above, if you are anything like me, the conclusion should strike you as absurd. Yet, the conclusion is exactly what we’d be committed to since conditionals are only false if their antecedents are true and the consequent is false.
Let’s try another: The ‘if’, in English, is not always transitive although it is in conventional logic, if p then q/ if q the r; if p then r. To see why this is problematic, contemplate this:
If Pat dies before the election, then Sean will win. If Sean wins, Pat will retire from public life after the election. Thus, is Pat dies before the election, then Pat will retire from public life after the election.
I could understand perfectly well what someone would mean by the two statements, and yet I’d never think the conclusion is what they’d be logically committed as per hypothetical syllogism. It’s absurd, I think. There is also a more humorous example to consider as well:
If I put sugar in my coffee, it will taste good. Therefore, if I put both sugar in my coffee and feces in my coffee, it will taste good.
This is valid. The last statement follows from the first since it is true that 'if p then q'; 'if (p&r) then q', whatever r may be. But surely we wouldn’t want to make this conclusion from the first statement. It’s just wrong. It’s funny, but wrong.
There have been attempts to help remedy these problems. Grice has argued something in opposition to my suspicions, and there have been conditional logics as well as relevance logic. I reject the first two as implausible or insufficient, and I have trouble with the third since it denies the disjunctive syllogism.
I’ll write about relevance logic some other time.
Cheers,
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