Combining Philosophers

All the ideas for Speussipus, Diodorus Cronus and Marcus Rossberg

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


16 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg]
Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg]
There are at least seven possible systems of semantics for second-order logic [Rossberg]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Logical consequence is intuitively semantic, and captured by model theory [Rossberg]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
In proof-theory, logical form is shown by the logical constants [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg]
5. Theory of Logic / K. Features of Logics / 4. Completeness
Completeness can always be achieved by cunning model-design [Rossberg]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
A deductive system is only incomplete with respect to a formal semantics [Rossberg]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle]
10. Modality / A. Necessity / 10. Impossibility
From the necessity of the past we can infer the impossibility of what never happens [Diod.Cronus, by White,MJ]
10. Modality / B. Possibility / 1. Possibility
The Master Argument seems to prove that only what will happen is possible [Diod.Cronus, by Epictetus]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
Conditionals are true when the antecedent is true, and the consequent has to be true [Diod.Cronus]
19. Language / D. Propositions / 4. Mental Propositions
Thought is unambiguous, and you should stick to what the speaker thinks they are saying [Diod.Cronus, by Gellius]
28. God / C. Attitudes to God / 5. Atheism
Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero]