rough draft of paper given May 1, 2008
This is a paper that attempts to connect proof theory and the pragmatic semantics of inference to the philosophical notions of metaphysical necessity, analyticity, and a priori knowledge (pg2). The paper begins by reviewing the origins of author's particular brand of pragmatism, birthed by Wittgenstein's 'meaning is use' injunction but interpreted by Brandom as a normative exhortation: what x means is how one should use x e.g. in an assertion or denial (pg2-3). The pragmatic elements author borrows from Gentzen, where traditional forms of contradiction are read as 'self-defeating' (rather than, perhaps, metaphysically impossible). (pg3) The validity of logical consequence is that it gives license to inference; thus, author seeks to connect (or perhaps, underwrite) the semantics of a term with normative pragmatism in logic. (pg3-6)
There are three 'triangular' concepts in philosophy that author wants to connect together through his logic. They are:
-Metaphysical necessity (using modality)
-A priori knowability
-Analyticity, or the framework that underwrite analytic truth
Author gives a little history of these concepts in philosophy since Kant (pg6-8). Of keen interest was Kripke's version of necessary a posteriori. Author claims this is a kind of necessity but not as robust as we're accustomed to since it may be metaphysical but not epistemological. (pg8) Author thinks this prompts Davies & Humberstone to give a 'two-dimensional semantics' where there is a distinction in possible world semantics between: (pg8-9)
-When we consider what the actual world might be like (epistemic possibility)
-How other worlds are different from (or the same as) the actual one (metaphysical possibility)
Thus worlds that might be metaphysically impossible (1 dimension of necessity) might still be epistemically possible-- we don't know that it's impossible (yet, or at all). Author uses the work of Jackson and Chalmers to extend this discussion into the metaphysical/epistemic (Davies & Humberstone don't use that distinction when talking about their two dimensions of modality), but also believes that Chalmers gets it wrong on the value of this distinction between metaphysical modality and epistemic modality. Author also believes that 2-d semantics doesn't give a proper account of what a possible world is. (pg 9-10)
For a re-framing of the 2-d semantics, author turns to inferentialism. He tries to connect the a priori with considering what other worlds might be like (metaphysical possibility) independent of what we know is or isn't the case. Author considers this 'indicative supposition' (pg10-13). Then there is 'subjunctive supposition', which works when you're 'planning' action-- it doesn't matter what is metaphysically true or not, the only thing that matters is what you know or believe (epistemic possibility) (pg13-14). This connects to necessity in the Kripkean sense: H2O is necessarily water because of how we are going to treat H2O and water in all possible worlds... [?]
Author concludes with some summaries of his arguments and by acknowledging that his theory relies on cognitive psychology for its verification. (pg15)
-When we consider what the actual world might be like (epistemic possibility)
-How other worlds are different from (or the same as) the actual one (metaphysical possibility)
Thus worlds that might be metaphysically impossible (1 dimension of necessity) might still be epistemically possible-- we don't know that it's impossible (yet, or at all). Author uses the work of Jackson and Chalmers to extend this discussion into the metaphysical/epistemic (Davies & Humberstone don't use that distinction when talking about their two dimensions of modality), but also believes that Chalmers gets it wrong on the value of this distinction between metaphysical modality and epistemic modality. Author also believes that 2-d semantics doesn't give a proper account of what a possible world is. (pg 9-10)
For a re-framing of the 2-d semantics, author turns to inferentialism. He tries to connect the a priori with considering what other worlds might be like (metaphysical possibility) independent of what we know is or isn't the case. Author considers this 'indicative supposition' (pg10-13). Then there is 'subjunctive supposition', which works when you're 'planning' action-- it doesn't matter what is metaphysically true or not, the only thing that matters is what you know or believe (epistemic possibility) (pg13-14). This connects to necessity in the Kripkean sense: H2O is necessarily water because of how we are going to treat H2O and water in all possible worlds... [?]
Author concludes with some summaries of his arguments and by acknowledging that his theory relies on cognitive psychology for its verification. (pg15)
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