Combining Texts

All the ideas for 'Existence and Quantification', 'Quodlibeta' and 'What is Cantor's Continuum Problem?'

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20 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
5745 Quine says quantified modal logic creates nonsense, bad ontology, and false essentialism [Melia on Quine]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
8789 Various strategies try to deal with the ontological commitments of second-order logic [Hale/Wright on Quine]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
7. Existence / A. Nature of Existence / 3. Being / b. Being and existence
16966 Philosophers tend to distinguish broad 'being' from narrower 'existence' - but I reject that [Quine]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
16965 All we have of general existence is what existential quantifiers express [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
16963 Existence is implied by the quantifiers, not by the constants [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / c. Commitment of predicates
16964 Theories are committed to objects of which some of its predicates must be true [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
4216 Express a theory in first-order predicate logic; its ontology is the types of bound variable needed for truth [Quine, by Lowe]
18966 Ontological commitment of theories only arise if they are classically quantified [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
14490 You can be implicitly committed to something without quantifying over it [Thomasson on Quine]
7. Existence / E. Categories / 1. Categories
16961 In formal terms, a category is the range of some style of variables [Quine]
8. Modes of Existence / B. Properties / 8. Properties as Modes
16641 Whiteness does not exist, but by it something can exist-as-white [Aquinas]
11. Knowledge Aims / A. Knowledge / 2. Understanding
22170 Senses grasp external properties, but the understanding grasps the essential natures of things [Aquinas]
12. Knowledge Sources / A. A Priori Knowledge / 3. Innate Knowledge / a. Innate knowledge
22169 Initial universal truths are present within us as potential, to be drawn out by reason [Aquinas]
12. Knowledge Sources / B. Perception / 3. Representation
22168 Minds take in a likeness of things, which activates an awaiting potential [Aquinas]