Combining Texts

All the ideas for 'The Common-Sense View of Reality', 'Number Determiners, Numbers, Arithmetic' and 'Logical Necessity'

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27 ideas

1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
Metaphysics is hopeless with its present epistemology; common-sense realism is needed [Colvin]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
The logic of metaphysical necessity is S5 [Rumfitt]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt]
There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt]
We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt]
5. Theory of Logic / D. Assumptions for Logic / 3. Contradiction
Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt]
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
An adjective contributes semantically to a noun phrase [Hofweber]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
Quantifiers for domains and for inference come apart if there are no entities [Hofweber]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber]
'2 + 2 = 4' can be read as either singular or plural [Hofweber]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Why is arithmetic hard to learn, but then becomes easy? [Hofweber]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber]
7. Existence / D. Theories of Reality / 2. Realism
We can only distinguish self from non-self if there is an inflexible external reality [Colvin]
Common-sense realism rests on our interests and practical life [Colvin]
7. Existence / D. Theories of Reality / 4. Anti-realism
If objects are doubted because their appearances change, that presupposes one object [Colvin]
Arguments that objects are unknowable or non-existent assume the knower's existence [Colvin]
The idea that everything is relations is contradictory; relations are part of the concept of things [Colvin]
10. Modality / A. Necessity / 3. Types of Necessity
A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A]
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt]
A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt]
Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt]
15. Nature of Minds / C. Capacities of Minds / 4. Objectification
Our minds are at their best when reasoning about objects [Hofweber]