Monday, January 18, 2016

We are not alone among language users

This argument is valid:

  1. All semantic truths are knowable to members of the community of language users.
  2. There are semantic truths that are not knowable to human language users.
  3. Therefore, there is at least one non-human language user.
There is some reason to accept (1) in light of the conventionality of language. Premise (2) is going to be quite controversial. I justify it by means of a standard argument for epistemicism. Consider Queen Elizabeth II. There are 88 statements of the form:
  • Elizabeth was not old at age n but she was old at age n+1
where n ranges from 1 to 88. It's a straightforward matter of classical logic to show that if all 88 statements are false, then:
  1. Elizabeth was old at age 1 or Elizabeth is not old at age 89.
But (4) is clearly false: Her Majesty is old now at age 89, and she surely wasn't old at age one. So, at least one of the 88 statements is false. This means that there is a sharp transition from being not old to being old. But it is clear that no matter what we find out about our behavior, biology and other relevant things, we can't know exactly where that transition lies. It seems very plausible that the relevant unknowable fact about the transition is a semantic fact. Hence, (2) is true.

The most plausible candidate for the non-human language user who is capable of knowing such semantic facts is God. God could institute the fundamental semantic facts of human language and thereby know them.

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5 comments:

  1. AnonymousJanuary 19, 2016 at 8:58 AM

    I think this is wrong. The word "old" is simply not well defined, and the "straightforward matter of classical logic" implicitly includes the assumption that your terms are well defined. They are not, and so your conclusion is not valid.

    Of course, as I've commented before, in reality no terms are ever well defined.

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  2. Heath WhiteJanuary 20, 2016 at 10:57 AM

    But (4) is clearly false.... So, at least one of the 88 statements is false. This means that there is a sharp transition.... Hence, (2) is true.

    It follows from the first two claims that there is a sharp transition, only if there is a sharp transition from "true" to "false." If truth is a vague predicate, like being old, then the argument fails and (2) is unsupported.

    And I think it pretty clearly has to be the case that "'Fa' is true" is vague iff F is vague. So the argument is question-begging.

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  3. AnonymousJanuary 20, 2016 at 11:08 AM

    It also occurs to me that your support for the first premise undermines your support for the second, and your support for the second undermines your support for the first.

    If we accept that all semantic truths are knowable because of the conventionality of language, we should immediately accept that all semantic truths are knowable to human beings, because the language we know is a human convention. The consequence is that if we want to say there is a sharp transition, it is knowable, but we have to set it ourselves by convention, e.g. you become old exactly when you reach age 60. (Of course this will in fact run into problems as well, when you realize that we cannot define an instant of time with infinite precision. But it makes no difference for the argument here.)

    Likewise, if we accept that there is a sharp transition which we cannot know, then we should deny that this is a convention, and thus we no longer have any reason to accept the first premise, unless we already know that God exists.

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  4. Alexander R PrussJanuary 20, 2016 at 11:32 AM

    Heath:

    Good point.

    But I can make this work without truth, at the expense of 88 additional premises:
    If Elizabeth is not old at one and she is old at two, there is a sharp transition in being old.
    If Elizabeth is not old at two and she is old at three, there is a sharp transition in being old.
    ...

    I think these 88 premises are all very plausible. But classical logic yields a valid argument from the premises I gave in the post to the disjunction of the antecedents of the 88 additional premises, and hence by disjunction-elimination, it yields that there is a sharp transition in being old.

    One can also go through truth. By the T-schema:
    If Elizabeth is not old at one but old at two, it is true that Elizabeth is not old at one but old at two.
    ...
    So the disjunction of the consequents of these conditions is true. So at least one of the consequents is true.

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  5. Alexander R PrussJanuary 28, 2016 at 3:53 PM

    This stuff is at the center of a paper I just finished: http://alexanderpruss.com/papers/si.pdf

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