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A disclaimer: I am not currently a fictionalist, but I find it remarkably interesting to consider. Fictionalists are not making claims about mathematical truth

A disclaimer: I am not currently a fictionalist, but I find it remarkably interesting to consider. Fictionalists are not making claims about mathematical truth; they are making claims about philosophical truth. When Colyvan (who I believe is not a fictionalist) describes fictionalism as an error theory of mathematical discourse, he does not mean that mathematicians incorrectly assign the label of mathematical truth to statements that are mathematically false, but rather that it is an error to conflate mathematical truth ("true in the story of mathematics") with philosophical truth. In other words, you and the fictionalists are in agreement on your first point. I don't quite understand your second point, or its justification. For example, would you consider the statement "All even primes greater than 2 are divisible by 1001" to be true, false, or meaningless? I think most people will agree that even primes greater than 2 do not exist. Fictionalists would assert that this statement is false; with my background in formal logic, I tend to believe that this statement is vacuously true. I would be interested in seeing an argument for the claim that this statement is meaningless.

ajkjk 10y ago
The argument of the paper (which I do not find compelling) seems to be that the sentence "all even primes greater than 2 are divisible by 1001" is 'false' because "the words prime, 2, divisible, and 1001" are undefined. (In the framework in which those words aren't undefined, then sure, we can talk about whether that sentence is true or false and have an interesting discussion. In formal logic it's definitely true. But that's not the discussion the article is interested in, as far as I can tell.) To which OP (and I, and I think most people..) would say: we accept that you're being clever by declaring that "outside of mathematics, these words are undefined". But calling a sentence with undefined terms "false" is absurd. Just call it "meaningless" until all the terms are defined. Then you avoid making statements like "'8+5=13' is false", which at first glance seems absurd, and at second glance seems like "you're saying things that are absurd to raise eyebrows instead of taking the easy alternative of saying things that are reasonable."
techbio 10y ago
Even while Captain Obvious is not wrong, eyes will rightly glaze over. Double negative--I'm not a mathematician, I paint, but Mom taught me right and wrong, two of the latter do not make a right. "All even primes greater than 2 are divisible by 1001." => "everything else in this analysis will be ignored" (because it's not math)
- cokernel 10y ago
  Could you clarify who "Captain Obvious" is?
  - douche 10y ago
    https://en.wikipedia.org/wiki/Captain_Obvious https://en.wikipedia.org/wiki/Captain_Obvious
  - techbio 10y ago
    The Wikipedia link is the reference I intended. "Captain Obvious" refers to the one in a group or conversation who states what everyone else knows, and as such impedes the group's progression toward their shared goals. Thanks, HN user "douche", you nailed it. Strange to me how folk wisdom is so unwelcome in a philosophy discussion. While not explicitly stated, the subtext appears to be putting my comment as the "Captain Obvious." I'll avoid commenting in this context in the future.

ajkjk 10y ago

The argument of the paper (which I do not find compelling) seems to be that the sentence "all even primes greater than 2 are divisible by 1001" is 'false' because "the words prime, 2, divisible, and 1001" are undefined. (In the framework in which those words aren't undefined, then sure, we can talk about whether that sentence is true or false and have an interesting discussion. In formal logic it's definitely true. But that's not the discussion the article is interested in, as far as I can tell.) To which OP (and I, and I think most people..) would say: we accept that you're being clever by declaring that "outside of mathematics, these words are undefined". But calling a sentence with undefined terms "false" is absurd. Just call it "meaningless" until all the terms are defined. Then you avoid making statements like "'8+5=13' is false", which at first glance seems absurd, and at second glance seems like "you're saying things that are absurd to raise eyebrows instead of taking the easy alternative of saying things that are reasonable."

techbio 10y ago

Even while Captain Obvious is not wrong, eyes will rightly glaze over. Double negative--I'm not a mathematician, I paint, but Mom taught me right and wrong, two of the latter do not make a right. "All even primes greater than 2 are divisible by 1001." => "everything else in this analysis will be ignored" (because it's not math)

cokernel 10y ago
Could you clarify who "Captain Obvious" is?
- douche 10y ago
  https://en.wikipedia.org/wiki/Captain_Obvious https://en.wikipedia.org/wiki/Captain_Obvious
- techbio 10y ago
  The Wikipedia link is the reference I intended. "Captain Obvious" refers to the one in a group or conversation who states what everyone else knows, and as such impedes the group's progression toward their shared goals. Thanks, HN user "douche", you nailed it. Strange to me how folk wisdom is so unwelcome in a philosophy discussion. While not explicitly stated, the subtext appears to be putting my comment as the "Captain Obvious." I'll avoid commenting in this context in the future.