Combining Texts
Ideas for
'Parmenides', 'Axiomatic Theories of Truth' and 'Nominalism and Substitutional Quantifiers'
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18 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 / A. Overview of Logic / 7. Second-Order Logic
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10794
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The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)]
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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 / F. Referring in Logic / 1. Naming / a. Names
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10786
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Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)]
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10788
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Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)]
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5. Theory of Logic / G. Quantification / 1. Quantification
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10799
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Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)]
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5. Theory of Logic / G. Quantification / 2. Domain of Quantification
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10790
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Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)]
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10791
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Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)]
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5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
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10785
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Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)]
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10795
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Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)]
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10798
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A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)]
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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 / 3. Antinomies
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13986
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Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle]
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14150
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Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato]
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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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