Mathematical Method • Discussion 2

Re: Peirce ListAuke van Breemen

It seems to come down to:  never consider the textual production of a scientist only in itself, but also look at the reality the text tries to explain.

Dear Auke,


We interpret texts
in relation to
the object in view.


  • Eisele, C. (1982), “Mathematical Methodology in the Thought of Charles S. Peirce”, Historia Mathematica 9, pp. 333–341.  OnlinePDF.

ccc: CyberneticsOntolog • Peirce List (1) (2) (3)Structural ModelingSystems Science

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2 Responses to Mathematical Method • Discussion 2

  1. Bhupinder Singh Anand says:

    Dear Jon,

    I personally feel we may need to caution about the consequences, and dangers, of preferring Plato’s ‘knowledge as justified true belief’ over Piccinini’s ‘knowledge as factually grounded (evidence-based) belief’, in an age of ‘alternative facts’ for which we — at least those of my ilk and generation (born circa 1940) — must shoulder the main responsibility.

    Dangers we may have unknowingly belittled — even if not denied outright — and counter-intuitive consequences we may have not only uncritically welcomed, but passionately nurtured in our schools and universities, post Cantor, by assuming in classical mathematics, logic, philosophy, and the natural sciences, that the unspecified can be treated as specifiable without supporting evidence.

    The challenge, as I see it, is that of using Plato’s justified true beliefs, in what philosopher Markus Pantsar calls pre-formal mathematics, in order to arrive at factually grounded (evidence-based) beliefs in our usual systems of formal mathematics;  which can then be treated as knowledge only if they can, first, be interpreted as corresponding to Plato’s justified true belief under Tarski’s definitions of the satisfaction, and truth, of the formulas of a formal language under a well-defined interpretation and, second, categorically communicated.



  2. Александр Шкотин says:

    Is there any chance to make exception for proofs as they are mostly a text?

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