David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Synthese 167 (1):163 - 182 (2009)
An account of validity that makes what is invalid conditional on how many individuals there are is what I call a conditional account of validity. Here I defend conditional accounts against a criticism derived from Etchemendy’s well-known criticism of the model-theoretic analysis of validity. The criticism is essentially that knowledge of the size of the universe is non-logical and so by making knowledge of the extension of validity depend on knowledge of how many individuals there are, conditional accounts fail to reflect that the former knowledge is basic, i.e., independent of knowledge derived from other sciences. Appealing to Russell’s pre-Principia logic, I defend conditional accounts against this criticism by sketching a rationale for thinking that there are infinitely many logical objects.
|Keywords||Logical consequence Logical epistemology Russell|
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References found in this work BETA
Ludwig Wittgenstein (1922/1999). Tractatus Logico-Philosophicus. Dover Publications.
Hartry Field (1989). Realism, Mathematics & Modality. Basil Blackwell.
John Divers (2002). Possible Worlds. Routledge.
Bertrand Russell (1919/1993). Introduction to Mathematical Philosophy. Dover Publications.
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