In <C-2dnY1u28kdULvMnZ2dnUVZ_jWdnZ2d@giganews.com>, on 02/21/2013 at 07:44 PM, fom <fomJUNK@nyms.net> said:
>My point is that the very syntax of a first-order language can be >recognized as a minimal Hausdorff topology as soon as one places a >mutually exclusive bivalent truth functionality onto its symbols.
Only in the context of another system for which you have developed all of the machinery.
>Moreover, you cannot divorce this structure from a logic intended >as a deductive calculus because what makes it interpretable as a >deductive calculus is its relationship to the truth-conditions of >interpretations.
We have no choice; we need a deductive calculus to derive the theorems of Topology. Only once we have done so can we apply Topology to a different deductive calculus.
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