There is an oldmeta-philosophical worry: very roughly, metaphysical theories have no observational consequences and so the study of metaphysics has no value. The worry has been around in some form since the rise of logical positivism in the early twentieth century but has seen a bit of a renaissance recently. In this paper, I provide an apology for metaphysics in the face of this kind of concern. The core of the argument is this: pure mathematics detaches from science in much the same manner as metaphysics and yet it is valuable nonetheless. The source of value enjoyed by pure mathematics extends to metaphysics as well. Accordingly, if one denies that metaphysics has value, then one is forced to deny that puremathematics has value. The argument places an added burden on the sceptic of metaphysics. If one truly believes that metaphysics is worthless (as some philosophers do), then one must give up on pure mathematics as well.

中文翻译：

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形而上学的形式道歉

存在着一种旧的超哲学的担忧：非常笼统地说，形而上学理论没有观察结果，因此形而上学的研究没有任何价值。自从二十世纪初逻辑实证主义兴起以来，这种担忧已经以某种形式出现，但是最近又出现了一些复兴。在本文中，面对这种关注，我为形而上学道歉。论据的核心是：纯粹的数学与形而上学几乎完全脱离了科学，但它仍然是有价值的。纯数学享有的价值之源也延伸到形而上学。因此，如果人们否认形而上学具有价值，那么人们就不得不否认纯粹数学具有价值。该论点给形而上学的怀疑者增加了负担。