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Ideas for 'Metaphysics', 'works' and 'Thinking About Logic'

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34 ideas

5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Not all validity is captured in first-order logic [Read]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
The non-emptiness of the domain is characteristic of classical logic [Read]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Semantics must precede proof in higher-order logics, since they are incomplete [Read]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
We should exclude second-order logic, precisely because it captures arithmetic [Read]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read]
Logical consequence isn't just a matter of form; it depends on connections like round-square [Read]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
For Aristotle bivalence is a feature of reality [Aristotle, by Boulter]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
For intuitionists excluded middle is an outdated historical convention [Brouwer]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
A theory is logically closed, which means infinite premisses [Read]
5. Theory of Logic / G. Quantification / 1. Quantification
Quantifiers are second-order predicates [Read]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
In second-order logic the higher-order variables range over all the properties of the objects [Read]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A logical truth is the conclusion of a valid inference with no premisses [Read]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Any first-order theory of sets is inadequate [Read]
5. Theory of Logic / K. Features of Logics / 6. Compactness
Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read]
Compactness does not deny that an inference can have infinitely many premisses [Read]
Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read]
Compactness makes consequence manageable, but restricts expressive power [Read]
5. Theory of Logic / L. Paradox / 2. Aporiai
Aporia 3: Does one science investigate all being, or does each kind of being have a science? [Aristotle, by Politis]
We must start with our puzzles, and progress by solving them, as they reveal the real difficulty [Aristotle]
Aporia 4: Does metaphysics just investigate pure being, or also the characteristics of being? [Aristotle, by Politis]
Aporia 1: is there one science of explanation, or many? [Aristotle, by Politis]
Aporia 2: Does one science investigate both ultimate and basic principles of being? [Aristotle, by Politis]
Aporia 5: Do other things exist besides what is perceptible by the senses? [Aristotle, by Politis]
Aporia 9: Is there one principle, or one kind of principle? [Aristotle, by Politis]
Aporia 6: Are the basic principles of a thing the kinds to which it belongs, or its components? [Aristotle, by Politis]
Aporia 7: Is a thing's kind the most general one, or the most specific one? [Aristotle, by Politis]
Aporia 8: Are there general kinds, or merely particulars? [Aristotle, by Politis]
Aporia 10: Do perishables and imperishables have the same principle? [Aristotle, by Politis]
Aporia 11: Are primary being and unity distinct, or only in the things that are? [Aristotle, by Politis]
Aporia 12: Do mathematical entities exist independently, or only in objects? [Aristotle, by Politis]
Aporia 13: Are there kinds, as well as particulars and mathematical entities? [Aristotle, by Politis]
Aporia 15: Are the causes of things universals or particulars? [Aristotle, by Politis]
Aporia 14: Are ultimate causes of things potentialities, or must they be actual? [Aristotle, by Politis]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
Self-reference paradoxes seem to arise only when falsity is involved [Read]