Combining Texts

All the ideas for 'Logical Consequence', 'Paradoxes of the Infinite' and 'Natural Minds'

expand these ideas     |    start again     |     specify just one area for these texts


16 ideas

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 / 1. Set Theory
An aggregate in which order does not matter I call a 'set' [Bolzano]
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 / 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 / a. The Infinite
A truly infinite quantity does not need to be a variable [Bolzano]
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]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / d. Secondary qualities
The taste of chocolate is a 'finer-grained' sensation than the taste of sweetness [Polger]
16. Persons / B. Nature of the Self / 1. Self and Consciousness
The mind and the self are one, and the mind-self is a biological phenomenon [Polger]
17. Mind and Body / C. Functionalism / 5. Teleological Functionalism
Teleological functions explain why a trait exists; causal-role functions say what it does [Polger]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Identity theory says consciousness is an abstraction: a state, event, process or property [Polger]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
A mummified heart has the teleological function of circulating blood [Polger]
Teleological notions of function say what a thing is supposed to do [Polger]