Combining Philosophers

All the ideas for Robert Audi, Bernecker / Dretske and M Fitting/R Mendelsohn

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


81 ideas

4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Each line of a truth table is a model [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / a. Symbols of ML
Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn]
We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn]
The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn]
The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / b. Terminology of ML
A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn]
Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn]
A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn]
A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn]
Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / c. Derivation rules of ML
S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn]
If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn]
If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn]
Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn]
Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn]
Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn]
Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn]
Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn]
Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn]
Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn]
T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn]
D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn]
B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn]
4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn]
4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / b. System K
The system K has no accessibility conditions [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
□P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn]
The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / e. System K4
The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn]
Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn]
The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn]
10. Modality / A. Necessity / 7. Natural Necessity
Because 'gold is malleable' is necessary does not mean that it is analytic [Audi,R]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
□ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn]
Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Perception, introspection, testimony, memory, reason, and inference can give us knowledge [Bernecker/Dretske]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
Beliefs are based on perception, memory, introspection or reason [Audi,R]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
Could you have a single belief on its own? [Audi,R]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
We can make certain of what we know, so knowing does not entail certainty [Audi,R]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
If you gradually remove a book's sensory properties, what is left at the end? [Audi,R]
Sense-data theory is indirect realism, but phenomenalism is direct irrealism [Audi,R]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
The concepts needed for a priori thought may come from experience [Audi,R]
Red and green being exclusive colours seems to be rationally graspable but not analytic [Audi,R]
12. Knowledge Sources / B. Perception / 3. Representation
How could I see a field and believe nothing regarding it? [Audi,R]
To see something as a field, I obviously need the concept of a field [Audi,R]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
Sense data imply representative realism, possibly only representing primary qualities [Audi,R]
Sense-data (and the rival 'adverbial' theory) are to explain illusions and hallucinations [Audi,R]
12. Knowledge Sources / B. Perception / 5. Interpretation
Perception is first simple, then objectual (with concepts) and then propositional [Audi,R]
12. Knowledge Sources / B. Perception / 7. Causal Perception
Causal theory says true perceptions must be caused by the object perceived [Bernecker/Dretske]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Virtually all rationalists assert that we can have knowledge of synthetic a priori truths [Audi,R]
The principles of justification have to be a priori [Audi,R]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
To remember something is to know it [Audi,R]
I might remember someone I can't recall or image, by recognising them on meeting [Audi,R]
You can acquire new knowledge by exploring memories [Bernecker/Dretske]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
Justification can be of the belief, or of the person holding the belief [Bernecker/Dretske]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
Justification is either unanchored (infinite or circular), or anchored (in knowledge or non-knowledge) [Audi,R]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
Internalism about justification implies that there is a right to believe something [Audi,R]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Foundationalism aims to avoid an infinite regress [Bernecker/Dretske]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
Infallible sensations can't be foundations if they are non-epistemic [Bernecker/Dretske]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
Maths may be consistent with observations, but not coherent [Audi,R]
It is very hard to show how much coherence is needed for justification [Audi,R]
A consistent madman could have a very coherent belief system [Audi,R]
13. Knowledge Criteria / C. External Justification / 1. External Justification
Consistent accurate prediction looks like knowledge without justified belief [Audi,R]
Justification is normative, so it can't be reduced to cognitive psychology [Bernecker/Dretske]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
A reliability theory of knowledge seems to involve truth as correspondence [Audi,R]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
'Reliable' is a very imprecise term, and may even mean 'justified' [Audi,R]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Modern arguments against the sceptic are epistemological and semantic externalism, and the focus on relevance [Bernecker/Dretske]
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
Predictions are bound to be arbitrary if they depend on the language used [Bernecker/Dretske]
16. Persons / C. Self-Awareness / 4. Errors in Introspection
We can be ignorant about ourselves, for example, our desires and motives [Audi,R]
18. Thought / C. Content / 6. Broad Content
Semantic externalism ties content to the world, reducing error [Bernecker/Dretske]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Actions are not mere effects of reasons, but are under their control [Audi,R]