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Harvard Mathematics Department : Home page

Date of publication: 2017-07-08 21:42

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The Faculty of Mathematics and Computer Science is today a fortunate blend of tradition, experience and modernity in a large and prestigious University.

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7.   acausality : the item neither exerts a strict causal influence over other items nor does any other item causally influence it in the strict sense, where strict causal relations are those that obtain between, and only between, constituents of the spatio-temporal realm—for example, you can kick a football and cause it (in a strict sense) to move, but you can't kick a number.

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Now that we understand indispensability, it is worth noting the similarity between the QPIA and Frege’s argument for the Existence Thesis. We observed above that Frege’s argument has two key components: recognition of the applicability of numbers in representing and reasoning about the world as support for the contention that arithmetic statements are true, and a logico-inferential analysis of arithmetic statements that identified natural number terms as singular terms. The QPIA encapsulates directly parallel features: ineliminable applicability to our best scientific theories (that is, indispensability) and Quine’s criterion of ontological commitment. While the language and framework of the QPIA are different from those of Frege’s argument, these arguments are, at their core, identical.

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Differences in the use of "abstract" are best accounted for by observing that different philosophers seek to communicate different constellations of features from this cluster when they apply this term. All philosophers insist that an item have Feature 6 before it may be appropriately labeled "abstract." Philosophers of mathematics invariably mean to convey that mathematical entities have Feature 7 when they claim that mathematical objects or structures are abstract. Indeed, they typically mean to convey that such objects or structures have either Feature 8a or 8b, and Feature 9. Some philosophers of mathematics also mean to convey that mathematical objects or structures have Feature 5.

I was born in Bloomington, Indiana, on March 68, 6969, and grew up in the lovely town in south central Indiana that is home to Indiana University. From an early age, I knew I loved two things: soccer and science. In the meantime, I've kept these while exploring a number of others. School and studies have taken me to upstate New York, southern California, Hawaii, and central Virginia. Now I live and work in Champaign, Illinois, which shares much of the charm of Bloomington (Indiana) but lacks essentially all of the nice scenery. I share my living space with a bunch of plants and a couple thousand books.

Your new acquaintance proceeds to inform you that John and Mary Smith got divorced recently. You form a false belief about your old friend and his wife. What makes her statement and corresponding belief true is that, in it, "John Smith" refers to John Smith 7 , "Mary Smith" refers to Mary Smith 7, John Smith 7 ’s former wife, and John Smith 7 and Mary Smith 7 stand to a recent time in the triadic relation " x got divorced from y at time t." Your belief is false, however, because, in it, "John Smith" refers to John Smith 6 , "Mary Smith" refers to Mary Smith 6, John Smith 6 ’s wife, and John Smith 6 and Mary Smith 6 fail to stand to a recent time in the triadic relation " x got divorced from y at time t."

6. non-spatio-temporality : the item does not stand to other items in a collection of relations that would make it a constituent of the spatio-temporal realm.

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