By Gregory Landini
A new approach to examining Frege's notations that clings to the trendy view that phrases and well-formed formulation are any disjoint syntactic different types. in this new procedure, we will eventually learn Frege's notations of their unique shape revealing striking new ideas to a number of the amazing difficulties of examining his philosophy.
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Additional info for Frege’s Notations: What They Are and How They Mean
In virtue of these characteristic functions we may speak of a transcription into Frege’s concept-script of the wffs of modern predicate calculus. In the above, we have wffs Fx and Gx and these are certainly not terms. But there are terms fx and gx in Frege’s concept-script that represent them (respectively) in such a way that by attachment of Frege’s turnstile one creates a wfff of the system. Thus proper transcription requires 38 Frege’s Notations the use of the turnstile and demands that we respect the difference between a term and a wff.
These are consequences of a thoroughgoing development of my logical views. Formerly, I distinguished two components in that whose external form is a declarative sentence: (1) the acknowledgment of truth, (2) the content that is acknowledged to be true. ’ This is now split for me into what I call ‘thought’ and ‘truth-value’, as a consequence of distinguishing sense and denotation of a sign. These passages reveal conclusively that Frege had not yet made the transition to general function terms in his Grundlagen and that there is no analog of Grundgestze’s horizontal stroke in it.
Xntn)). This is not a comprehension principle because ψ(t1, ... tn) is a predicate variable. However, when paired with a rule of uniform substitution, we can uniformly substitute wffs A(ζ1t1, ... , ζntn) for ψ(t1, ... tn)(x1t1, ... , xntn) and thereby arrive at any instance of a schematic comprehension principle Russell CPt. The Russellian notation of simple types tracks the Fregean levels in a convenient way. As we see, it also allows a very versatile way of representing simple types of relations, including inhomogeneous relations, such as ϕ(o, (o)).