Abstract
In this contribution we sketch a propositional logical system designed to represent reasoning with philosophical categories. This should be of relative interest, at least, for two reasons. In first place, the proposed system attempts to formalize the notion of category mistake; and, in second place, the system provides a formal alternative to regulate reasoning involving categories, since the propositional systems typically used to represent reasoning are unable to do that, thus allowing the introduction of category mistakes.
Highlights
INTRODUCTIONTo give an idea of the scope of this contribution, we would like to begin with a particular re-interpretation of proposition 4.112 from Wittgenstein’s
To give an idea of the scope of this contribution, we would like to begin with a particular re-interpretation of proposition 4.112 from Wittgenstein’s ___Tractatus: the object of a logical system is the logical elucidation of inference
We look forward the elucidation of inference; in particular, our main goal is to sketch a propositional logical system designed to represent reasoning with philosophical categories
Summary
To give an idea of the scope of this contribution, we would like to begin with a particular re-interpretation of proposition 4.112 from Wittgenstein’s. Its syntax is defined by two rules: i) if φ∈VAR, φ is a well formed formula (wff) of Lp; and ii) if φ and ψ are wffs of Lp, ¬φ and φ∧ψ are wffs of Lp. its semantics is composed by a domain of truth values, D={1, 0}, where 1 stands for the designated value and 0 for the anti-designated value; and a function of interpretation that maps the variables to truth values, f:VARD, so that for all φ∈VAR, either f(φ)=1 or f(φ)=0, and for no φ∈VAR, f(φ)=1 and f(φ)=0. Its semantics is composed by a domain of truth values, D={1, 0}, where 1 stands for the designated value and 0 for the anti-designated value; and a function of interpretation that maps the variables to truth values, f:VARD, so that for all φ∈VAR, either f(φ)=1 or f(φ)=0, and for no φ∈VAR, f(φ)=1 and f(φ)=0 Given this function, a valuation vLp is defined in such way that vLp(φ)=f(φ), vLp(¬φ)=1−vLp(φ), and vLp(φ∧ψ)=min(vLp(φ),vLp(ψ)), defining negation and conjunction.
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