Fwd: NDPR Peter van Inwagen and William Lane Craig Do Numbers Exist? A Debate about Abstract Objects

[Doug Mounce]

Interesting review on the ontological foundations of regard to mathematical features. The collection of articles begins with the theological aseity (a word I just learned) 

" the question must then arise whether their [abstracta] non-existence is a matter of contingency or necessity. If the former, then abstracta could have existed, and if they had, presumably that would either have been as an effect of the will of God—contrary to their acausality—or independently of His will, contrary to His aseity. On the other hand, if abstracta necessarily don’t exist, that necessity may be construed as marking a limitation on God’s powers: He cannot make it otherwise."

The issue in logic, apart from theology, persists in that, " there is no such thing as stumbling across an abstract object—as one might, for example, stumble across a black swan on the banks of the Murray river in SE Australia, or a hitherto botanically undocumented species of orchid in Suffolk. Rather, when numbers, for example, are concerned, the question of existence needs to be understood as a theoretical question, in such a way that the question of commitment comes first: are we—or perhaps should we be—theoretically committed to the existence of numbers, and are the theories in question good, for whatever purpose—or perhaps even unavoidable?"

Balaguer gives a mixed review, but I recall recent discussion about Rahner and how Thomas classified those necessarily true propositions in logic that directly relate.  And yet, Thomas' advance on Platonism is not referenced.  

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Subject: NDPR Peter van Inwagen and William Lane Craig Do Numbers Exist? A Debate about Abstract Objects
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Notre Dame Philosophical Reviews

2025.06.4 View this Review Online   View Other NDPR Reviews

Peter van Inwagen and William Lane Craig, Do Numbers Exist? A Debate about Abstract Objects, with a Foreword by Mark Balaguer, Routledge 2024, 275pp., $35.95 (pbk), ISBN 9780367442767.

Reviewed by Reviewed by Crispin Wright, University of Stirling

This exchange is published in the Routledge series, Little Debates about Big Questions. Routledge characterises the intent of the series as comprising “Short, lively and accessible debates. . .[showcasing] diverse and deep answers. Pedagogical features include standard form arguments, section summaries, bolded key terms and principles, glossaries, and annotated reading lists.” Readers should accordingly be advised that this book actually offers not a “little debate” but a ramified exchange over some 275 pages, comprising three phases: an extended opening statement by each protagonist, a first round of replies by each, and then a second round of replies to the replies. With...

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