Combining Philosophers
Ideas for Ralph Waldo Emerson, Volker Halbach and Keith Hossack
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16 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 / C. Ontology of Logic / 1. Ontology of Logic
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15652
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We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach]
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5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
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23628
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The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
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5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
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23627
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'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
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5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
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15651
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Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach]
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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 / 2. Descriptions / b. Definite descriptions
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10671
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Plural definite descriptions pick out the largest class of things that fit the description [Hossack]
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5. Theory of Logic / G. Quantification / 6. Plural Quantification
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10666
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Plural reference will refer to complex facts without postulating complex things [Hossack]
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10669
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Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack]
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10675
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A plural comprehension principle says there are some things one of which meets some condition [Hossack]
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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 / 5. Paradoxes in Set Theory / d. Russell's paradox
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10673
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Plural language can discuss without inconsistency things that are not members of themselves [Hossack]
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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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