Combining Philosophers

All the ideas for George Engelbretsen, E.J. Lemmon and Julien Offray de La Mettrie

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75 ideas

3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
If facts are the truthmakers, they are not in the world [Engelbretsen]
There are no 'falsifying' facts, only an absence of truthmakers [Engelbretsen]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
Traditional term logic struggled to express relations [Engelbretsen]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen]
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]
We write the 'negation' of P (not-P) as [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 '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]
Two propositions are 'equivalent' if they mirror one another's truth-value [Lemmon]
A wff is a 'tautology' if all assignments to variables result in the value T [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]
'Subcontrary' propositions are never both false, so that A∨B is a tautology [Lemmon]
'Contrary' propositions are never both true, so that (A∧B) is a tautology [Lemmon]
A wff is 'contingent' if produces at least one T and at least one F [Lemmon]
A 'implies' B if B is true whenever A is true (so that A→B is tautologous) [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
RAA: If assuming A will prove B∧B, then derive A [Lemmon]
A: we may assume any proposition at any stage [Lemmon]
MTT: Given B and A→B, we derive A [Lemmon]
DN: Given A, we may derive A [Lemmon]
∧I: Given A and B, we may derive A∧B [Lemmon]
∧E: Given A∧B, we may derive either A or B separately [Lemmon]
MPP: Given A and A→B, we may derive B [Lemmon]
∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon]
∨I: Given either A or B separately, we may derive A∨B [Lemmon]
CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
We can change conditionals into negated conjunctions with P→Q -||- (P ∧ Q) [Lemmon]
'Modus ponendo tollens' (MPT) says P, (P ∧ Q) |- Q [Lemmon]
De Morgan's Laws make negated conjunctions/disjunctions into non-negated disjunctions/conjunctions [Lemmon]
We can change conjunctions into negated conditionals with P→Q -||- (P → Q) [Lemmon]
The Distributive Laws can rearrange a pair of conjunctions or disjunctions [Lemmon]
'Modus tollendo ponens' (MTP) says P, P ∨ Q |- Q [Lemmon]
We can change conditionals into disjunctions 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]
Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon]
UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon]
Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon]
With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro [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 / A. Overview of Logic / 2. History of Logic
Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
The paradoxes of material implication are P |- Q → P, and P |- P → Q [Lemmon]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical syntax is actually close to surface linguistic form [Engelbretsen]
Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Existence and nonexistence are characteristics of the world, not of objects [Engelbretsen]
7. Existence / D. Theories of Reality / 7. Facts / a. Facts
Facts are not in the world - they are properties of the world [Engelbretsen]
7. Existence / E. Categories / 4. Category Realism
Individuals are arranged in inclusion categories that match our semantics [Engelbretsen]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
The imagination alone perceives all objects; it is the soul, playing all its roles [La Mettrie]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
When falling asleep, the soul becomes paralysed and weak, just like the body [La Mettrie]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
The soul's faculties depend on the brain, and are simply the brain's organisation [La Mettrie]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Man is a machine, and there exists only one substance, diversely modified [La Mettrie]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
All thought is feeling, and rationality is the sensitive soul contemplating reasoning [La Mettrie]
18. Thought / B. Mechanics of Thought / 6. Artificial Thought / a. Artificial Intelligence
With wonderful new machines being made, a speaking machine no longer seems impossible [La Mettrie]
19. Language / B. Reference / 2. Denoting
Terms denote objects with properties, and statements denote the world with that property [Engelbretsen]
19. Language / D. Propositions / 1. Propositions
'Socrates is wise' denotes a sentence; 'that Socrates is wise' denotes a proposition [Engelbretsen]
19. Language / F. Communication / 3. Denial
Negating a predicate term and denying its unnegated version are quite different [Engelbretsen]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
The sun and rain weren't made for us; they sometimes burn us, or spoil our seeds [La Mettrie]
27. Natural Reality / G. Biology / 3. Evolution
There is no abrupt transition from man to animal; only language has opened a gap [La Mettrie]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
There is no clear idea of the soul, which should only refer to our thinking part [La Mettrie]