木橋で風に吹かれ、書店に寄ってから、Starbucksで上記の入手文献をのんびり読む。
以下に、この文献でのBenacerrafさんに対する質問をすべて順に掲げ、最初の質問の返答内容をかいつまんで紹介してみよう。
Benacerrafさんは、この最初の質問に対する返答に一番力を入れておられるように感じられる。
Mark Crimmins
I wonder what you think of this line of thought. An ordinary speaker, long having used number-talk, turns to philosophy and encounters the ontological question of whether there (“really”) are numbers. Whatever else she thinks about this question, she does not regard her past usage, or the usage of her linguistic peers, as having expressed commitment to a position on the matter (even when they say things like “there are numbers between ten and twenty”). But if the literal meaning (and truth-conditions) of ordinary talk comes from the standard commitments of speakers, it seems to follow that the ontological question is a different question from that of the literal truth of “there are numbers” in English.
ここでCrimminsさんが言わんとしておられるのは、わかりやすく噛み砕いて補足すると、次のようなことであると思われる。
大まかに言えば、人が言っていることをその言葉に即して字義通りに捉えた場合に見られる存在論と、当人が積極的に「私はしかじかの存在論を取る」と公言する場合に見られる存在論とは、異なることが多い。前者は後者から帰結すると考えられるから、誰かの存在論を確定させる場合には、前者と後者の存在論を区別し、後者の存在論を当人の存在論として取るべきであろう。
Benacerrafさんはこれに反対の立場を取り、次のように述べている。
I argued in “Mathematical Truth” that there is a strong prima facie case for treating pairs of sentences like
1) There are at least three perfect numbers greater than 17.
2) There are at least three large cities older than New York.
as semantically alike, at least to then extent of attributing to their members a shared first-order structure and the parallel truth conditions that such treatment would entail. In so doing, I was implicitly denying what Mark is claiming −namely that the truth conditions of these sentences do not require the existence of the entities they name and over which they quantify. […] I would like nothing better than an intelligible and viable interpretation of these sentences that did not embroil us in the conundrums that appear to ensue when we treat them as semantically parallel. However, I don’t know of any that I find satisfactory.
そしてここでの難問に対する有望なアプローチについて次のように話しておられる。
In my opinion, the best candidate theory that has emerged in the intervening years [1965-2000] is some form of fictionalism. Do I find that totally satisfying? No, I do not.
ちなみに、次のZaltaさんの質問に答える中でBenacerrafさんは、数学的言明に対する意味論と認識論の不調和という難問について、有望な、あるいは何か貢献できるものを持っている別の立場として、Neo-Fregeanismを上げておられる。
しかしfictionalismとneo-fregeanismとでは、存在論上、正反対である…。Benacerrafさんにとっては、nominalisticにしろplatonisticにしろ、いずれでもいいから件の難問を解決できればよい、解決されてほしいと、pragmaticにお考えなのであろうか？
そのほかの質問は以下の通り。
Edward Zalta
Could you please briefly sketch your current view about the relationship between the meaning of mathematical sentences and our knowledge of mathematics?
Richard Zach
Your papers “What numbers could not be” (1965) and “Mathematical Truth” (1973) have significantly shaped the debate in the philosophy of mathematics for the last quarter century by setting out important questions that need to be answered by a satisfactory account of mathematical truth and knowledge. Among the many rival accounts proposed to address your questions, do you think a clear winner has emerged? What do you see as the most important open questions in the philosophy of mathematics?
Grigori Mints
Do you think logic is still important for philosophy?
The Dualist
In papers published in the 1990’s you revised some of your assertions from “Mathematical Truth” and “What Numbers Could Not Be.” Have your views changed further over the last few years?
The Dualist
If you were to edit a third edition of “Philosophy of Mathematics: Selected Readings” what new papers would you add?
The Dualist
Can you describe some of your current and future projects? In what ways do you hope your work might set the agenda for future philosophy of mathematics?
The Dualist
While undergraduates may have experience with natural science, English, Mathematics in high school, undergraduates rarely enter college with exposure to analytic philosophy. In your experience, what has been the best way for teachers to introduce students to analytic philosophy?
The Dualist
Do you have advice for students considering a career in philosophy?
