Combining Texts

All the ideas for 'The Evolution of Modern Metaphysics', 'First-Order Modal Logic' and 'The World as Will and Idea'

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89 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy considers only the universal, in nature as everywhere else [Schopenhauer]
Everyone is conscious of all philosophical truths, but philosophers bring them to conceptual awareness [Schopenhauer]
1. Philosophy / D. Nature of Philosophy / 8. Humour
Absurdity is incongruity between correct and false points of view [Schopenhauer]
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Metaphysics is the most general attempt to make sense of things [Moore,AW]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Metaphysics must understand the world thoroughly, as a principal source of knowledge [Schopenhauer]
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 / F. Referring in Logic / 3. Property (λ-) Abstraction
'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn]
7. Existence / A. Nature of Existence / 2. Types of Existence
Matter and intellect are inseparable correlatives which only exist relatively, and for each other [Schopenhauer]
7. Existence / D. Theories of Reality / 3. Reality
Schopenhauer, unlike other idealists, says reality is irrational [Schopenhauer, by Lewis,PB]
7. Existence / D. Theories of Reality / 4. Anti-realism
The knowing subject and the crude matter of the world are both in themselves unknowable [Schopenhauer]
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 / B. Certain Knowledge / 4. The Cogito
Descartes found the true beginning of philosophy with the Cogito, in the consciousness of the individual [Schopenhauer]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
Schopenhauer can't use force/energy instead of 'will', because he is not a materialist [Lewis,PB on Schopenhauer]
The world only exists in relation to something else, as an idea of the one who conceives it [Schopenhauer]
We know reality because we know our own bodies and actions [Schopenhauer]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Kant rightly separates appearance and thing-in-itself [Schopenhauer]
Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
Direct feeling of the senses are merely data; perception of the world comes with understanding causes [Schopenhauer]
12. Knowledge Sources / B. Perception / 5. Interpretation
All perception is intellectual [Schopenhauer]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
A consciousness without an object is no consciousness [Schopenhauer]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
We have hidden and unadmitted desires and fears, suppressed because of vanity [Schopenhauer]
16. Persons / C. Self-Awareness / 2. Knowing the Self
I know both aspects of my body, as representation, and as will [Schopenhauer]
16. Persons / E. Rejecting the Self / 4. Denial of the Self
It is as perverse to resent our individuality being replaced by others, as to resent the body renewing itself [Schopenhauer]
16. Persons / F. Free Will / 5. Against Free Will
We all regard ourselves a priori as free, but see from experience that character and motive compel us [Schopenhauer]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
Man's actions are not free, because they follow strictly from impact of motive on character [Schopenhauer]
20. Action / A. Definition of Action / 4. Action as Movement
Every true act of will is also at once and without exception a movement of the body [Schopenhauer]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
Schopenhauer was caught in Christian ideals, because he didn't deify his 'will' [Nietzsche on Schopenhauer]
Only the will is thing-in-itself, seen both in blind nature and in human action [Schopenhauer]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
If we were essentially intellect rather than will, our moral worth would depend on imagined motives [Schopenhauer]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
Schopenhauer is a chief proponent of aesthetic experience as 'disinterested' [Schopenhauer, by Janaway]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
A principal pleasure of the beautiful is that it momentarily silences the will [Schopenhauer]
21. Aesthetics / A. Aesthetic Experience / 6. The Sublime
The Sublime fights for will-less knowing, when faced with a beautiful threat to humanity [Schopenhauer, by Lewis,PB]
21. Aesthetics / C. Artistic Issues / 5. Objectivism in Art
Schopenhauer emphasises Ideas in art, unlike most romantics [Schopenhauer, by Lewis,PB]
21. Aesthetics / C. Artistic Issues / 6. Value of Art
The will-less contemplation of art brings a liberation from selfhood [Schopenhauer, by Gardner]
Man is more beautiful than anything else, and the loftiest purpose of art is to reveal his nature [Schopenhauer]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics
The only aim of our existence is to grasp that non-existence would be better [Schopenhauer]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
We should no more expect ethical theory to produce good people than aesthetics to produce artists [Schopenhauer]
22. Metaethics / B. Value / 1. Nature of Value / d. Subjective value
Every good is essentially relative, for it has its essential nature only in its relation to a desiring will [Schopenhauer]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Will casts aside each of its temporary fulfilments, so human life has no ultimate aim [Schopenhauer, by Scruton]
22. Metaethics / B. Value / 2. Values / e. Death
Most people would probably choose non-existence at the end of their life, rather than relive the whole thing [Schopenhauer]
22. Metaethics / B. Value / 2. Values / f. Altruism
Altruistic people make less distinction than usual between themselves and others [Schopenhauer]
22. Metaethics / B. Value / 2. Values / i. Self-interest
Only self-love can motivate morality, but that also makes it worthless [Schopenhauer]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
Happiness is the swift movement from desire to satisfaction, and then again on to desire [Schopenhauer]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
We can never attain happiness while our will is pursuing desires [Schopenhauer]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
Virtue must spring from an intuitive recognition that other people are essentially like us [Schopenhauer]
26. Natural Theory / A. Speculations on Nature / 1. Nature
The essence of nature is the will to life itself [Schopenhauer]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Christianity is a pessimistic religion, in which the world is equated with evil [Schopenhauer]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
Religion is the mythical clothing of the truth which is inaccessible to the crude human intellect [Schopenhauer]