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Proof-Normalisation and Truth by Definition

Citation: Gabbay, Michael (2008) Proof-Normalisation and Truth by Definition. ["eprint_fieldopt_thesis_type_phd" not defined] thesis, UNSPECIFIED.

In this thesis I defend an account of analyticity against some well known objections. I defend a view of analyticity whereby an analytic truth is true by definition, and that logical connectives may be defined by their inference rules. First I answer objections that the very idea of truth-by-definition is metaphysically flawed (things are true because of the world, not definition, it seems). More importantly, I respond to objections that no theory of definitions by inference rules (i.e. implicit definitions) can be given that does not allow spurious definitions (e.g. the `definition' of Prior's connective tonk). I shall argue that demanding normalisation (a.k.a. harmony) of definitional inference rules is a natural and well motivated solution to these objections. I conclude that a coherent account of implicit definition can be given as the basis of an account of analyticity. I then produce some logical results showing that we can give natural deduction rules for complex and interesting logical systems that satisfy a normal form theorem. In particular, I present a deduction system for classical logic that is harmonious (i.e. deductions in it normalise), and show how to extend and enhance it to include strict conditionals and empty reference. Also I discuss two areas where our reasoning and classical logic appear not to match: general conditional reasoning, and reasoning from contradictions. I present a general theory of conditionals (along the lines of Lewis' closest-possible-world account) and I suggest that the logic of conditionals is not entirely analytic. Also, I discuss issues surrounding the ex falso rule and conclude that everything really does follow from a contradiction. Finally I suggest a positive theory of when and how the implicit definitions are made that define our logical language.Mathematical Logic

Creators: Gabbay, Michael and
Subjects: Philosophy
Keywords: Proof-Normalisation, Truth, Analyticity, Logical Connectives, Inference Rules, Natural Deduction Rules, Conditionals, Contradictions, Lewis, Ex Falso Rule
Divisions: Institute of Philosophy
Collections: Thesis
London Philosophy PhD Theses
Theses and Dissertations
Dates:
  • 19 February 2008 (published)
Comments and Suggestions:
Description/Provenance: Submitted by Sophie Archer (sophie.archer@sas.ac.uk) on 2008-02-13T19:36:00Z No. of bitstreams: 1 Michael Gabbay - PhD Thesis.pdf: 888792 bytes, checksum: b05c0cf236ff33a13d49679f85c2b453 (MD5); Description/Provenance: Approved for entry into archive by Zoe Holman (zoe.holman@sas.ac.uk) on 2008-02-19T14:29:04Z (GMT) No. of bitstreams: 1 Michael Gabbay - PhD Thesis.pdf: 888792 bytes, checksum: b05c0cf236ff33a13d49679f85c2b453 (MD5); Description/Provenance: Made available in DSpace on 2008-02-19T14:29:04Z (GMT). No. of bitstreams: 1 Michael Gabbay - PhD Thesis.pdf: 888792 bytes, checksum: b05c0cf236ff33a13d49679f85c2b453 (MD5). Date accessioned: 2008-02-19T14:29:04Z; Date available: 2008-02-19T14:29:04Z; Date issued: 2008-02-19T14:29:04Z.

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