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All the ideas for 'Critique of Practical Reason', 'works' and 'Beginning Logic'

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91 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom is knowing the highest good, and conforming the will to it [Kant]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
What fills me with awe are the starry heavens above me and the moral law within me [Kant]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
Consistency is the highest obligation of a philosopher [Kant]
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Metaphysics is just a priori universal principles of physics [Kant]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
'Contradictory' propositions always differ in truth-value [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL
We write the conditional 'if P (antecedent) then Q (consequent)' as P→Q [Lemmon]
That proposition that either P or Q is their 'disjunction', written P∨Q [Lemmon]
We write the 'negation' of P (not-P) as ¬ [Lemmon]
We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P) [Lemmon]
If A and B are 'interderivable' from one another we may write A -||- B [Lemmon]
That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon]
The sign |- may be read as 'therefore' [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
A 'well-formed formula' follows the rules for variables, ¬, →, ∧, ∨, and ↔ [Lemmon]
The 'scope' of a connective is the connective, the linked formulae, and the brackets [Lemmon]
A 'substitution-instance' is a wff formed by consistent replacing variables with wffs [Lemmon]
A wff is 'inconsistent' if all assignments to variables result in the value F [Lemmon]
'Contrary' propositions are never both true, so that ¬(A∧B) is a tautology [Lemmon]
Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon]
A wff is 'contingent' if produces at least one T and at least one F [Lemmon]
'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon]
A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [Lemmon]
A wff is a 'tautology' if all assignments to variables result in the value T [Lemmon]
A 'theorem' is the conclusion of a provable sequent with zero assumptions [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL
∧I: Given A and B, we may derive A∧B [Lemmon]
CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon]
MPP: Given A and A→B, we may derive B [Lemmon]
RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon]
MTT: Given ¬B and A→B, we derive ¬A [Lemmon]
∨I: Given either A or B separately, we may derive A∨B [Lemmon]
∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon]
DN: Given A, we may derive ¬¬A [Lemmon]
A: we may assume any proposition at any stage [Lemmon]
∧E: Given A∧B, we may derive either A or B separately [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
'Modus tollendo ponens' (MTP) says ¬P, P ∨ Q |- Q [Lemmon]
'Modus ponendo tollens' (MPT) says P, ¬(P ∧ Q) |- ¬Q [Lemmon]
We can change conditionals into negated conjunctions with P→Q -||- ¬(P ∧ ¬Q) [Lemmon]
We can change conditionals into disjunctions with P→Q -||- ¬P ∨ Q [Lemmon]
De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon]
The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon]
We can change conjunctions into negated conditionals with P→Q -||- ¬(P → ¬Q) [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth-tables are good for showing invalidity [Lemmon]
A truth-table test is entirely mechanical, but this won't work for more complex logic [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 4. Soundness of PL
If any of the nine rules of propositional logic are applied to tautologies, the result is a tautology [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 5. Completeness of PL
Propositional logic is complete, since all of its tautologous sequents are derivable [Lemmon]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC
Write '(∀x)(...)' to mean 'take any x: then...', and '(∃x)(...)' to mean 'there is an x such that....' [Lemmon]
'Gm' says m has property G, and 'Pmn' says m has relation P to n [Lemmon]
The 'symbols' are bracket, connective, term, variable, predicate letter, reverse-E [Lemmon]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / b. Terminology of PC
Our notation uses 'predicate-letters' (for 'properties'), 'variables', 'proper names', 'connectives' and 'quantifiers' [Lemmon]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC
Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon]
With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [Lemmon]
UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon]
Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon]
Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / e. Existential quantifier ∃
'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Necessity cannot be extracted from an empirical proposition [Kant]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / a. Nature of intentionality
How does anything get outside itself? [Fodor, by Martin,CB]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
Is intentionality outwardly folk psychology, inwardly mentalese? [Lyons on Fodor]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
Are beliefs brains states, but picked out at a "higher level"? [Lyons on Fodor]
18. Thought / B. Mechanics of Thought / 6. Artificial Thought / a. Artificial Intelligence
Is thought a syntactic computation using representations? [Fodor, by Rey]
18. Thought / C. Content / 1. Content
Maybe narrow content is physical, broad content less so [Lyons on Fodor]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
Can pure reason determine the will, or are empirical conditions relevant? [Kant]
The will is the faculty of purposes, which guide desires according to principles [Kant]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
The sole objects of practical reason are the good and the evil [Kant]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
Only human reason can confer value on our choices [Kant, by Korsgaard]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
People cannot come to morality through feeling, because morality must not be sensuous [Kant]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Kant may rate two things as finally valuable: having a good will, and deserving happiness [Orsi on Kant]
An autonomous agent has dignity [Würde], which has absolute worth [Kant, by Pinkard]
The good will is unconditionally good, because it is the only possible source of value [Kant, by Korsgaard]
Good or evil cannot be a thing, but only a maxim of action, making the person good or evil [Kant]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Morality involves duty and respect for law, not love of the outcome [Kant]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
Our happiness is all that matters, not as a sensation, but as satisfaction with our whole existence [Kant]
Happiness is the condition of a rational being for whom everything goes as they wish [Kant]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
Morality is not about making ourselves happy, but about being worthy of happiness [Kant]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
The highest worth for human beings lies in dispositions, not just actions [Kant]
Virtue is the supreme state of our pursuit of happiness, and so is supreme good [Kant]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Moral law is holy, and the best we can do is achieve virtue through respect for the law [Kant]
23. Ethics / D. Deontological Ethics / 3. Universalisability
No one would lend money unless a universal law made it secure, even after death [Kant]
Universality determines the will, and hence extends self-love into altruism [Kant]
23. Ethics / D. Deontological Ethics / 5. Persons as Ends
Everyone (even God) must treat rational beings as ends in themselves, and not just as means [Kant]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
A holy will is incapable of any maxims which conflict with the moral law [Kant]
Reason cannot solve the problem of why a law should motivate the will [Kant]
25. Social Practice / F. Life Issues / 4. Suicide
A permanent natural order could not universalise a rule permitting suicide [Kant]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
Obligation does not rest on the existence of God, but on the autonomy of reason [Kant]
28. God / B. Proving God / 2. Proofs of Reason / c. Moral Argument
We have to postulate something outside nature which makes happiness coincide with morality [Kant]
Belief in justice requires belief in a place for justice (heaven), a time (eternity), and a cause (God) [Kant, by PG]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
To know if this world must have been created by God, we would need to know all other possible worlds [Kant]
28. God / B. Proving God / 3. Proofs of Evidence / c. Teleological Proof critique
Using God to explain nature is referring to something inconceivable to explain what is in front of you [Kant]
From our limited knowledge we can infer great virtues in God, but not ultimate ones [Kant]
28. God / C. Attitudes to God / 4. God Reflects Humanity
In all naturalistic concepts of God, if you remove the human qualities there is nothing left [Kant]