Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Phenomenology of Spirit' and 'Beginning Logic'

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81 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophy moves essentially in the element of universality [Hegel]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent
Philosophy aims to reveal the necessity and rationality of the categories of nature and spirit [Hegel, by Houlgate]
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Without philosophy, science is barren and futile [Hegel]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
Truth does not appear by asserting reasons and then counter-reasons [Hegel]
2. Reason / A. Nature of Reason / 8. Naturalising Reason
The structure of reason is a social and historical achievement [Hegel, by Pinkard]
2. Reason / A. Nature of Reason / 9. Limits of Reason
Truth does not come from giving reasons for and against propositions [Hegel]
3. Truth / D. Coherence Truth / 1. Coherence Truth
The true is the whole [Hegel]
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
That proposition that both P and Q is their 'conjunction', written P∧Q [Lemmon]
The sign |- may be read as 'therefore' [Lemmon]
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]
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
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]
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]
∧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]
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]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
I develop philosophical science from the simplest appearance of immediate consciousness [Hegel, by Hegel]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
The Absolute is not supposed to be comprehended, but felt and intuited [Hegel]
In the Absolute everything is the same [Hegel]
Genuine idealism is seeing the ideal structure of the world [Hegel, by Houlgate]
Being is Thought [Hegel]
12. Knowledge Sources / B. Perception / 1. Perception
Experience is immediacy, unity, forces, self-awareness, reason, culture, absolute being [Hegel, by Houlgate]
12. Knowledge Sources / B. Perception / 5. Interpretation
Hegel tried to avoid Kant's dualism of neutral intuitions and imposed concepts [Hegel, by Pinkard]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
Consciousness derives its criterion of knowledge from direct knowledge of its own being [Hegel]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / b. Essence of consciousness
Consciousness is shaped dialectically, by opposing forces and concepts [Hegel, by Aho]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / c. Parts of consciousness
Consciousness is both of objects, and of itself [Hegel]
16. Persons / A. Concept of a Person / 4. Persons as Agents
Hegel claims knowledge of self presupposes desire, and hence objects [Hegel, by Scruton]
16. Persons / E. Rejecting the Self / 2. Self as Social Construct
For Hegel knowledge of self presupposes objects, and also a public and moral social world [Hegel, by Scruton]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
23. Ethics / F. Existentialism / 6. Authentic Self
The in-itself must become for-itself, which requires self-consciousness [Hegel]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
Human nature only really exists in an achieved community of minds [Hegel]
Modern life needs individuality, but must recognise that human agency is social [Hegel, by Pinkard]
25. Social Practice / E. Policies / 5. Education / d. Study of history
History is the progress of the consciousness of freedom [Hegel]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
The movement of pure essences constitutes the nature of scientific method [Hegel]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
Science confronts the inner necessities of objects [Hegel]
28. God / B. Proving God / 1. Proof of God
The God of revealed religion can only be understood through pure speculative knowledge [Hegel]
28. God / C. Attitudes to God / 4. God Reflects Humanity
God is the essence of thought, abstracted from the thinker [Hegel, by Feuerbach]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Hegel made the last attempt to restore Christianity, which philosophy had destroyed [Hegel, by Feuerbach]