Combining Texts

All the ideas for 'Rationality in Action', 'Philosophy' and 'First-Order Modal Logic'

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89 ideas

2. Reason / A. Nature of Reason / 1. On Reason
Entailment and validity are relations, but inference is a human activity [Searle]
Theory involves accepting conclusions, and so is a special case of practical reason [Searle]
2. Reason / A. Nature of Reason / 8. Naturalising Reason
Rationality is built into the intentionality of the mind, and its means of expression [Searle]
Rationality is the way we coordinate our intentionality [Searle]
3. Truth / A. Truth Problems / 4. Uses of Truth
Truth is what unites, and the profound truths create a community [Jaspers]
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]
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]
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]
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 / A. Overview of Logic / 1. Overview of Logic
If complex logic requires rules, then so does basic logic [Searle]
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]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
In real reasoning semantics gives validity, not syntax [Searle]
7. Existence / C. Structure of Existence / 5. Supervenience / b. Types of supervenience
Users of 'supervenience' blur its causal and constitutive meanings [Searle]
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 / 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 / 4. Belief / c. Aim of beliefs
A belief is a commitment to truth [Searle]
We can't understand something as a lie if beliefs aren't commitment to truth [Searle]
Our beliefs are about things, not propositions (which are the content of the belief) [Searle]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
Thinking must involve a self, not just an "it" [Searle]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
Reasons can either be facts in the world, or intentional states [Searle]
13. Knowledge Criteria / C. External Justification / 1. External Justification
In the past people had a reason not to smoke, but didn't realise it [Searle]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
Causes (usually events) are not the same as reasons (which are never events) [Searle]
16. Persons / A. Concept of a Person / 2. Persons as Responsible
Being held responsible for past actions makes no sense without personal identity [Searle]
16. Persons / A. Concept of a Person / 3. Persons as Reasoners
Giving reasons for action requires reference to a self [Searle]
A 'self' must be capable of conscious reasonings about action [Searle]
An intentional, acting, rational being must have a self [Searle]
16. Persons / A. Concept of a Person / 4. Persons as Agents
Action requires a self, even though perception doesn't [Searle]
16. Persons / B. Nature of the Self / 1. Self and Consciousness
Selfs are conscious, enduring, reasonable, active, free, and responsible [Searle]
A self must at least be capable of consciousness [Searle]
16. Persons / B. Nature of the Self / 4. Presupposition of Self
The self is neither an experience nor a thing experienced [Searle]
16. Persons / B. Nature of the Self / 5. Self as Associations
The bundle must also have agency in order to act, and a self to act rationally [Searle]
16. Persons / F. Free Will / 2. Sources of Free Will
Freedom needs knowledge, the possibility of arbitrariness, and law [Jaspers]
16. Persons / F. Free Will / 4. For Free Will
I am aware that freedom is possible, and the freedom is not in theory, but in seeking freedom [Jaspers]
Free will is most obvious when we choose between several reasons for an action [Searle]
Rational decision making presupposes free will [Searle]
We freely decide whether to make a reason for action effective [Searle]
20. Action / C. Motives for Action / 1. Acting on Desires
Preferences can result from deliberation, not just precede it [Searle]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
We don't accept practical reasoning if the conclusion is unpalatable [Searle]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
The essence of humanity is desire-independent reasons for action [Searle]
Only an internal reason can actually motivate the agent to act [Searle]
20. Action / C. Motives for Action / 4. Responsibility for Actions
My freedom increases as I broaden my vision of possiblities and motives [Jaspers]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
If it is true, you ought to believe it [Searle]
If this is a man, you ought to accept similar things as men [Searle]
23. Ethics / B. Contract Ethics / 3. Promise Keeping
Promises hold because I give myself a reason, not because it is an institution [Searle]
23. Ethics / D. Deontological Ethics / 2. Duty
'Ought' implies that there is a reason to do something [Searle]
23. Ethics / F. Existentialism / 1. Existentialism
My helplessness in philosophising reveals my being, and begins its upsurge [Jaspers]
The struggle for Existenz is between people who are equals, and are utterly honest [Jaspers]
Once we grasp freedom 'from' things, then freedom 'for' things becomes urgent [Jaspers]
23. Ethics / F. Existentialism / 6. Authentic Self
Mundane existence is general, falling under universals, but Existens is unique to individuals [Jaspers]
We want the correct grasp on being that is neither solipsism nor absorption in the crowd [Jaspers]
'Existenz' is the potential being, which I could have, and ought to have [Jaspers]
23. Ethics / F. Existentialism / 7. Existential Action
Every decision I make moves towards or away from fulfilled Existenz [Jaspers]