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Ideas for 'Metaphysics', 'Reductive Theories of Modality' and 'Philosophy of Mathematics'

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30 ideas

5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10259 The two standard explanations of consequence are semantic (in models) and deductive [Shapiro]
5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens
10257 Intuitionism only sanctions modus ponens if all three components are proved [Shapiro]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10253 Either logic determines objects, or objects determine logic, or they are separate [Shapiro]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
22154 For Aristotle bivalence is a feature of reality [Aristotle, by Boulter]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
10251 The law of excluded middle might be seen as a principle of omniscience [Shapiro]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
10212 Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and' [Shapiro]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
10209 A function is just an arbitrary correspondence between collections [Shapiro]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
10268 Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10235 A sentence is 'satisfiable' if it has a model [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10239 The central notion of model theory is the relation of 'satisfaction' [Shapiro]
10240 Model theory deals with relations, reference and extensions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10214 Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro]
10238 The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10234 Any theory with an infinite model has a model of every infinite cardinality [Shapiro]
5. Theory of Logic / L. Paradox / 2. Aporiai
11265 Aporia 4: Does metaphysics just investigate pure being, or also the characteristics of being? [Aristotle, by Politis]
11270 Aporia 9: Is there one principle, or one kind of principle? [Aristotle, by Politis]
11271 Aporia 10: Do perishables and imperishables have the same principle? [Aristotle, by Politis]
11258 We must start with our puzzles, and progress by solving them, as they reveal the real difficulty [Aristotle]
11262 Aporia 1: is there one science of explanation, or many? [Aristotle, by Politis]
11263 Aporia 2: Does one science investigate both ultimate and basic principles of being? [Aristotle, by Politis]
11264 Aporia 3: Does one science investigate all being, or does each kind of being have a science? [Aristotle, by Politis]
11266 Aporia 5: Do other things exist besides what is perceptible by the senses? [Aristotle, by Politis]
11267 Aporia 6: Are the basic principles of a thing the kinds to which it belongs, or its components? [Aristotle, by Politis]
11268 Aporia 7: Is a thing's kind the most general one, or the most specific one? [Aristotle, by Politis]
11272 Aporia 11: Are primary being and unity distinct, or only in the things that are? [Aristotle, by Politis]
11269 Aporia 8: Are there general kinds, or merely particulars? [Aristotle, by Politis]
11273 Aporia 12: Do mathematical entities exist independently, or only in objects? [Aristotle, by Politis]
11274 Aporia 13: Are there kinds, as well as particulars and mathematical entities? [Aristotle, by Politis]
11276 Aporia 15: Are the causes of things universals or particulars? [Aristotle, by Politis]
11275 Aporia 14: Are ultimate causes of things potentialities, or must they be actual? [Aristotle, by Politis]