Combining Texts

All the ideas for 'Logical Consequence', 'A Free Will' and 'Knowledge and the Philosophy of Number'

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23 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / e. Late classical philosophy
In the third century Stoicism died out, replaced by Platonism, with Aristotelian ethics [Frede,M]
In late antiquity nearly all philosophers were monotheists [Frede,M]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
16. Persons / F. Free Will / 2. Sources of Free Will
The idea of free will achieved universal acceptance because of Christianity [Frede,M]
The Stoics needed free will, to allow human choices in a divinely providential cosmos [Frede,M]
For Christians man has free will by creation in God's image (as in Genesis) [Frede,M]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
There is no will for Plato or Aristotle, because actions come directly from perception of what is good [Frede,M]
29. Religion / A. Polytheistic Religion / 4. Dualist Religion
The Gnostic demiurge (creator) is deluded, and doesn't care about us [Frede,M]