Gian-Carlo Rota who, if you didn’t know it, held a professorship for mathematics and philosophy took the opportunity of a Synthese special edition to condemn mathematical philosophy before it was invented.
His basic argument is that mathematics is essentially clear and philosophy is not. Therefore any aspiration for clarity is damaging to philosophy. He also accuses mathematical philosophers of math envy.
Rota certainly was not shy with words, so I don’t want to withhold the following gems from you.
The fake philosophical terminology of mathematical logic has misled philosophers into believing that mathematical logic deals with the truth in the philosophical sense. But this is a mistake. Mathematical logic does not deal with the truth, but only with the game of truth.
Once swayed by the promises of formal rigor in philosophy in my young years, but now considering myself cured, I find this observation convincing.
But it even gets better.
The fake philosophical terminology of mathematical logic has misled philosophers into believing that mathematical logic deals with the truth in the philosophical sense. But this is a mistake. Mathematical logic does not deal with the truth, but only with the game of truth.
or
The prejudice that a concept must be precisely defined in order to be meaningful, or that an argument must be precisely stated in order to make sense, is one of the most insidious of the twentieth century. The best-known expression of this prejudice appears at the end of Ludwig Wittgenstein’s Tractatus, and the author’s later writings, in particular Philosophical Investigations, is a loud and repeated retraction of his earlier gaffe.
Looked at from the vantage point of ordinary experience, the ideal of precision appears preposterous. Our everyday reasoning is not precise, yet it is effective. Nature itself, from the cosmos to the gene, is approximate and inaccurate.
The concepts of philosophy are among the least precise. The mind, perception, memory, cognition, are words that do not have any fixed or clear meaning. Yet, they do have meaning. We misunderstand these concepts when we force them to be precise.
Mark Wilson would applaud and I am left to wonder what my friends at the MCMP will make of this.
Behind Rota’s philippic there is a trove of original arguments. He for example thinks that definitions and theorems in Mathematics justify each other in a circular way. The good definitions are those that allow interesting theorems to be proved and interesting theorems in turn motivate those definitions. And this makes sense because for him proofs are only a way of presenting mathematical facts.
I don’t want to take from your joy of reading “The pernicious influence of mathematics upon philosophy” on a sleepless night any further, so I will give Rota the last word.
The old problems of philosophy, such as mind and matter, reality, perception, are least likely to have ‘solutions’. In fact, we would be hard put to spell out what might be acceptable as a ‘solution’. The term ‘solution’ is borrowed from mathematics, and tacitly presupposes an analogy between problems of philosophy and problems of mathematics that is seriously misleading.