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From Logic to Practice

Gabriele Lolli, Marco Panza, and Giorgio Venturi, editors
Publication Date: 
Number of Pages: 
Boston Studies in the Philosophy and History of Science 308
[Reviewed by
Charles Ashbacher
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Writings in philosophy require a different mindset from the reader. Philosophers take what appear to be obvious and settled things, sometimes just a term or two, and turn them into a discussion taking up several pages. This book of papers generally follows that line, although there are a few unusual twists that will cause the non-philosopher to do a mental double-take.

For example, consider the opening line to chapter 5, “A Deflationary Account of the Truth of the Gödel Sentence G.”

According to deflationism, truth is a metaphysically thin property, redundant and dispensable, but useful as a generalization device. . .

I had never delved into deflationism before, this certainly got my attention, especially when it renders truth “dispensable.”

The title of chapter 13 is “On the Indispensable Premises of the Indispensability Argument” is another instance and it is quite interesting, somewhat less technical in structure than some of the other chapters.

There is also the occasional surprising statement that is, shall we say it, “inconsistent.” On the last page of chapter 6, which deals with “Rule Following and the Limits of Formalization” there is the phrase, “Now, we can well imagine a tortoise accepting modus ponens and demanding for more instructions for its application… ” My thought was, “where did that come from? Is this a new term?” No, it turns out to have been a reference to an actual tortoise that is attempting to do mathematics. It is just slow at it.

Without question, my favorite puzzler appears on page 115 and involves “Prior’s tonk.” There are a couple of expressions (one of which is labeled ∏) using this operator that are confusing. This is amusingly “explained” in the subsequent paragraph by the phrase “(as it is often said, the rules of tonk are not in harmony.)”

Focused much more on the philosophy of mathematics than it is on history, the papers here delve into the most fundamental questions, such as when we can apply the notion of truth or even when we can cast it aside. 

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, and teaching college classes. In his spare time, he reads about these things and helps his daughter in her lawn care business.