John S, Jerry C, List,
In what senses might this be a fair claim? Every version of temporal logic, dynamic logic, etc. can be mapped to first-order logic with explicit quantifiers that range over time: The claim might hold for some formal systems (i.e., mathematical) of deductive logic, but does it hold for all? Peirce seems to suggest that second order intentional logics can't be mapped onto what we call first-order predicate logics with quantifies. The formalization of hypostatic abstraction (e.g., the introduction of a lamba operator) presents features that go beyond what is found in the first order type of system. Are all of the features the modal systems in the EG amenable to treatment in terms of the quantifiers in first order predicate calculus? I don't know. When we move from formal (i.e., mathematical) systems of deductive logic, to the normative theory of ampliative inferences by induction and abduction, I would think that the claim does not hold. The mappings will not preserve the ampliative character of the inference patterns. If the arrangement of the premisses and conclusions in the ampliative inference patterns are transformed into inferences that fit deductive patterns, then some kind of mapping may be possible so long as those arguments are translated into one or another formal system. The problems can be made apparent, I would think, if we tried to specify the postulates, definitions and axioms that form the starting points for such formal systems. Can the underlying commitments for ampliative kinds of inferences be stated in the terms of such a set of formal postulates, definitions and axioms in a mathematical system? --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: Jerry LR Chandler <[email protected]> Sent: Monday, November 21, 2016 9:36 AM To: Peirce List Cc: John F Sowa Subject: Re: [PEIRCE-L] Time, Topology, Differential Logic List, John: I was a bit surprised by this statement. On Nov 15, 2016, at 10:52 AM, John F Sowa <[email protected]<mailto:[email protected]>> wrote: Every version of temporal logic, dynamic logic, etc. can be mapped to first-order logic with explicit quantifiers that range over time: I am thinking of chemical and biological phenomena such as enzyme catalysis, biological reproduction and other "emergent" phenomena that require ampliative logics. Cheers Jerry
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