Combining Philosophers

All the ideas for Rescher,N/Oppenheim,P, E.J. Lemmon and Stephen Mumford

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123 ideas

1. Philosophy / D. Nature of Philosophy / 6. Hopes for Philosophy
Science studies phenomena, but only metaphysics tells us what exists [Mumford]
2. Reason / A. Nature of Reason / 1. On Reason
Many forms of reasoning, such as extrapolation and analogy, are useful but deductively invalid [Mumford]
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]
7. Existence / A. Nature of Existence / 1. Nature of Existence
For Humeans the world is a world primarily of events [Mumford]
7. Existence / D. Theories of Reality / 2. Realism
Modest realism says there is a reality; the presumptuous view says we can accurately describe it [Mumford]
7. Existence / D. Theories of Reality / 4. Anti-realism
Anti-realists deny truth-values to all statements, and say evidence and ontology are inseparable [Mumford]
8. Modes of Existence / B. Properties / 3. Types of Properties
Dispositions and categorical properties are two modes of presentation of the same thing [Mumford]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Categorical predicates are those unconnected to functions [Mumford]
Categorical properties and dispositions appear to explain one another [Mumford]
There are four reasons for seeing categorical properties as the most fundamental [Mumford]
8. Modes of Existence / B. Properties / 7. Emergent Properties
A lead molecule is not leaden, and macroscopic properties need not be microscopically present [Mumford]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
Dispositions are attacked as mere regularities of events, or place-holders for unknown properties [Mumford]
Properties are just natural clusters of powers [Mumford]
8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived
If dispositions have several categorical realisations, that makes the two separate [Mumford]
Dispositions are classifications of properties by functional role [Mumford]
I say the categorical base causes the disposition manifestation [Mumford]
8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties
All properties must be causal powers (since they wouldn't exist otherwise) [Mumford]
Intrinsic properties are just causal powers, and identifying a property as causal is then analytic [Mumford]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
Dispositions can be contrasted either with occurrences, or with categorical properties [Mumford]
Dispositions are ascribed to at least objects, substances and persons [Mumford]
Unlike categorical bases, dispositions necessarily occupy a particular causal role [Mumford]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / b. Dispositions and powers
If dispositions are powers, background conditions makes it hard to say what they do [Mumford]
Maybe dispositions can replace powers in metaphysics, as what induces property change [Mumford]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / c. Dispositions as conditional
Orthodoxy says dispositions entail conditionals (rather than being equivalent to them) [Mumford]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
Dispositions are not just possibilities - they are features of actual things [Mumford]
There could be dispositions that are never manifested [Mumford]
8. Modes of Existence / C. Powers and Dispositions / 7. Against Powers
If every event has a cause, it is easy to invent a power to explain each case [Mumford]
Traditional powers initiate change, but are mysterious between those changes [Mumford]
Categorical eliminativists say there are no dispositions, just categorical states or mechanisms [Mumford]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
A 'porridge' nominalist thinks we just divide reality in any way that suits us [Mumford]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
If properties are clusters of powers, this can explain why properties resemble in degrees [Mumford]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
Substances, unlike aggregates, can survive a change of parts [Mumford]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
Many artefacts have dispositional essences, which make them what they are [Mumford]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
How can we show that a universally possessed property is an essential property? [Mumford]
10. Modality / B. Possibility / 3. Combinatorial possibility
Maybe possibilities are recombinations of the existing elements of reality [Mumford]
Combinatorial possibility has to allow all elements to be combinable, which seems unlikely [Mumford]
Combinatorial possibility relies on what actually exists (even over time), but there could be more [Mumford]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
Truth-functional conditionals can't distinguish whether they are causal or accidental [Mumford]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
Dispositions are not equivalent to stronger-than-material conditionals [Mumford]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Nomothetic explanations cite laws, and structural explanations cite mechanisms [Mumford]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
General laws depend upon the capacities of particulars, not the other way around [Mumford]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
If fragile just means 'breaks when dropped', it won't explain a breakage [Mumford]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
Maybe dispositions can replace the 'laws of nature' as the basis of explanation [Mumford]
To avoid a regress in explanations, ungrounded dispositions will always have to be posited [Mumford]
Subatomic particles may terminate explanation, if they lack structure [Mumford]
14. Science / D. Explanation / 4. Explanation Doubts / a. Explanation as pragmatic
Ontology is unrelated to explanation, which concerns modes of presentation and states of knowledge [Mumford]
26. Natural Theory / B. Natural Kinds / 4. Source of Kinds
Natural kinds, such as electrons, all behave the same way because we divide them by dispositions [Mumford]
26. Natural Theory / C. Causation / 1. Causation
Causation interests us because we want to explain change [Mumford]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Singular causes, and identities, might be necessary without falling under a law [Mumford]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
We can give up the counterfactual account if we take causal language at face value [Mumford]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
It is only properties which are the source of necessity in the world [Mumford]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
In the 'laws' view events are basic, and properties are categorical, only existing when manifested [Mumford]
There are four candidates for the logical form of law statements [Mumford]
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
Without laws, how can a dispositionalist explain general behaviour within kinds? [Mumford]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
Dretske and Armstrong base laws on regularities between individual properties, not between events [Mumford]
Pure regularities are rare, usually only found in idealized conditions [Mumford]
Regularity laws don't explain, because they have no governing role [Mumford]
It is a regularity that whenever a person sneezes, someone (somewhere) promptly coughs [Mumford]
Would it count as a regularity if the only five As were also B? [Mumford]
Regularities are more likely with few instances, and guaranteed with no instances! [Mumford]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
If the best system describes a nomological system, the laws are in nature, not in the description [Mumford]
The best systems theory says regularities derive from laws, rather than constituting them [Mumford]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
Laws of nature are necessary relations between universal properties, rather than about particulars [Mumford]
If laws can be uninstantiated, this favours the view of them as connecting universals [Mumford]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
The necessity of an electron being an electron is conceptual, and won't ground necessary laws [Mumford]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
Laws of nature are just the possession of essential properties by natural kinds [Mumford]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
Some dispositions are so far unknown, until we learn how to manifest them [Mumford]
To distinguish accidental from essential properties, we must include possible members of kinds [Mumford]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
The Central Dilemma is how to explain an internal or external view of laws which govern [Mumford]
You only need laws if you (erroneously) think the world is otherwise inert [Mumford]
There are no laws of nature in Aristotle; they became standard with Descartes and Newton [Mumford]