Combining Texts

All the ideas for 'Existence and Quantification', 'Regressive Method for Premises in Mathematics' and 'Life of Pythagoras'

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23 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
17641 Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell]
2. Reason / A. Nature of Reason / 6. Coherence
17638 If one proposition is deduced from another, they are more certain together than alone [Russell]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
17632 Non-contradiction was learned from instances, and then found to be indubitable [Russell]
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]
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 / K. Features of Logics / 1. Axiomatisation
17629 Which premises are ultimate varies with context [Russell]
17630 The sources of a proof are the reasons why we believe its conclusion [Russell]
17640 Finding the axioms may be the only route to some new results [Russell]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
17627 It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17628 Arithmetic was probably inferred from relationships between physical objects [Russell]
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]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
17637 The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
17639 Believing a whole science is more than believing each of its propositions [Russell]
14. Science / C. Induction / 2. Aims of Induction
17631 Induction is inferring premises from consequences [Russell]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
17633 The law of gravity has many consequences beyond its grounding observations [Russell]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
1515 Pythagoreans believe it is absurd to seek for goodness anywhere except with the gods [Iamblichus]