Combining Texts
Ideas for
'Mahaprajnaparamitashastra', 'The Philosophy of Mathematics' and 'Axiomatic Theories of Truth'
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10 ideas
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
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16333
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The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach]
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5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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9195
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Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
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5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
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16310
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A theory is some formulae and all of their consequences [Halbach]
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5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
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9186
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First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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9187
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Logical truths and inference are characterized either syntactically or semantically [Dummett]
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5. Theory of Logic / K. Features of Logics / 3. Soundness
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16342
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You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach]
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16341
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Normally we only endorse a theory if we believe it to be sound [Halbach]
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16344
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Soundness must involve truth; the soundness of PA certainly needs it [Halbach]
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5. Theory of Logic / L. Paradox / 1. Paradox
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16347
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Many new paradoxes may await us when we study interactions between frameworks [Halbach]
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5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
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16336
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The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach]
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