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According to the article written by Sven Ove Hansson, which was published in The Bulletin of Symbolic Logic:

Some philosophers consider texts that make use of logical or mathematical notation as non-philosophical and not worth reading, whereas others consider non-formal treatments as-at best-useful preparations for the real work to be done in a formal language......At the same time, formalization encounters an internal resistance in philosophy that is not present in these other disciplines.

Other writers call philosophers who are skeptical about formalization in philosophy simply "anti-formalists". But who are these anti-formalists? And is there any movement or school of thought in academic philosophy known as anti-formalism?

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    I do not think so... There is the so-called "analytic" tradition of modern philosophy (mainly English speaking) from Frege, Russell and on, that makes use of "formal logic" in the discussion of philosophical problems. – Mauro ALLEGRANZA May 3 '17 at 11:11
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    "Anti-formalist" does not refer to a specific "school": at most, it can refer to philosopher smainly of the modern "continental" tradiciton that do not consider useful to apply formal logic methods to the discussion of phil problems. – Mauro ALLEGRANZA May 3 '17 at 11:13
  • Sven Ove Hansson seems active in the use of formal methods. – Mauro ALLEGRANZA May 3 '17 at 11:15
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    In (analytic) philosophy of language the term "anti-formalism" is used to describe philosophers like Wittgenstein, Austin, and more recently Rorty, who were generally skeptical of mathematical and formal approaches to natural language. According to Schwartz's Brief History of Analytic Philosophy the trend is "no longer fashionable". – Conifold May 3 '17 at 17:54
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As mentioned in the comments, formalism in philosophy is strongly associated with the Anglo-American tradition of analytic philosophy. This term is widely understood in opposition to continental philosophy. Although the latter term encompasses a wide range of traditions, much of which pre-date modern analytic philosophy as such, they almost all contradict the formalization of analytical philosophy in some fundamental way. As the Wikipedia article on continental philosophy highlights, they generally emphasize the limits of scientific knowledge and the importance of context and experience.

As for more direct and explicit critiques of formalism, there are some. For example, see "The Phenomenological Critique of Formalism: Responsibility and the Life-World" by Učník et al. (2004).

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