Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, J.L. Mackie and Leslie H. Tharp

unexpand these ideas     |    start again     |     specify just one area for these philosophers


29 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp]
     Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3)
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic is either for demonstration, or for characterizing structures [Tharp]
     Full Idea: One can distinguish at least two quite different senses of logic: as an instrument of demonstration, and perhaps as an instrument for the characterization of structures.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
     A reaction: This is trying to capture the proof-theory and semantic aspects, but merely 'characterizing' something sounds like a rather feeble aspiration for the semantic side of things. Isn't it to do with truth, rather than just rule-following?
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
Elementary logic is complete, but cannot capture mathematics [Tharp]
     Full Idea: Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Second-order logic isn't provable, but will express set-theory and classic problems [Tharp]
     Full Idea: The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp]
     Full Idea: In sentential logic there is a simple proof that all truth functions, of any number of arguments, are definable from (say) 'not' and 'and'.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §0)
     A reaction: The point of 'say' is that it can be got down to two connectives, and these are just the usual preferred pair.
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
The main quantifiers extend 'and' and 'or' to infinite domains [Tharp]
     Full Idea: The symbols ∀ and ∃ may, to start with, be regarded as extrapolations of the truth functional connectives ∧ ('and') and ∨ ('or') to infinite domains.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §5)
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
There are at least five unorthodox quantifiers that could be used [Tharp]
     Full Idea: One might add to one's logic an 'uncountable quantifier', or a 'Chang quantifier', or a 'two-argument quantifier', or 'Shelah's quantifier', or 'branching quantifiers'.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3)
     A reaction: [compressed - just listed for reference, if you collect quantifiers, like collecting butterflies]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp]
     Full Idea: Skolem deduced from the Löwenheim-Skolem theorem that 'the absolutist conceptions of Cantor's theory' are 'illusory'. I think it is clear that this conclusion would not follow even if elementary logic were in some sense the true logic, as Skolem assumed.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §7)
     A reaction: [Tharp cites Skolem 1962 p.47] Kit Fine refers to accepters of this scepticism about the arithmetic of infinities as 'Skolemites'.
The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
     Full Idea: The Löwenheim-Skolem property seems to be undesirable, in that it states a limitation concerning the distinctions the logic is capable of making, such as saying there are uncountably many reals ('Skolem's Paradox').
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
5. Theory of Logic / K. Features of Logics / 3. Soundness
Soundness would seem to be an essential requirement of a proof procedure [Tharp]
     Full Idea: Soundness would seem to be an essential requirement of a proof procedure, since there is little point in proving formulas which may turn out to be false under some interpretation.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
5. Theory of Logic / K. Features of Logics / 4. Completeness
Completeness and compactness together give axiomatizability [Tharp]
     Full Idea: Putting completeness and compactness together, one has axiomatizability.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §1)
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
If completeness fails there is no algorithm to list the valid formulas [Tharp]
     Full Idea: In general, if completeness fails there is no algorithm to list the valid formulas.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
     A reaction: I.e. the theory is not effectively enumerable.
5. Theory of Logic / K. Features of Logics / 6. Compactness
Compactness is important for major theories which have infinitely many axioms [Tharp]
     Full Idea: It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
     A reaction: An example of infinite axioms is the induction schema in first-order Peano Arithmetic.
Compactness blocks infinite expansion, and admits non-standard models [Tharp]
     Full Idea: The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
5. Theory of Logic / K. Features of Logics / 8. Enumerability
A complete logic has an effective enumeration of the valid formulas [Tharp]
     Full Idea: A complete logic has an effective enumeration of the valid formulas.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp]
     Full Idea: Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one.
     From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2)
     A reaction: The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job.
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
     Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles.
     From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro'
     A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture?
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / f. Ethical non-cognitivism
The 'error theory' of morals says there is no moral knowledge, because there are no moral facts [Mackie, by Engel]
     Full Idea: Mackie's 'error theory' of ethics says that if a fact is something that corresponds to a true proposition, there are actually no moral facts, hence no knowledge of what moral statements are about.
     From: report of J.L. Mackie (Ethics: Inventing Right and Wrong [1977]) by Pascal Engel - Truth §4.2
     A reaction: Personally I am inclined to think that there are moral facts (about what nature shows us constitutes a good human being), based on virtue theory. Mackie is a good warning, though, against making excessive claims. You end up like a bad scientist.
26. Natural Theory / C. Causation / 8. Particular Causation / a. Observation of causation
Some says mental causation is distinct because we can recognise single occurrences [Mackie]
     Full Idea: It is sometimes suggested that our ability to recognise a single occurrence as an instance of mental causation is a feature which distinguishes mental causation from physical or 'Humean' causation.
     From: J.L. Mackie (Causes and Conditions [1965], §9)
     A reaction: Hume says regularities are needed for mental causation too. Concentrate hard on causing a lightning flash - 'did I do that?' Gradually recovering from paralysis; you wouldn't just move your leg once, and know it was all right!
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Mackie tries to analyse singular causal statements, but his entities are too vague for events [Kim on Mackie]
     Full Idea: In spite of Mackie's announced aim of analysing singular causal statements, it is doubtful that the entities that he is concerned with can be consistently interpreted as spatio-temporally bounded individual events.
     From: comment on J.L. Mackie (Causes and Conditions [1965]) by Jaegwon Kim - Causes and Events: Mackie on causation §3
     A reaction: This is because Mackie mainly talks about 'conditions'. Nearly every theory I encounter in modern philosophy gets accused of either circular definitions, or inadequate individuation conditions for key components. A tough world for theory-makers.
26. Natural Theory / C. Causation / 8. Particular Causation / c. Conditions of causation
Necessity and sufficiency are best suited to properties and generic events, not individual events [Kim on Mackie]
     Full Idea: Relations of necessity and sufficiency seem best suited for properties and for property-like entities such as generic states and events; their application to individual events and states is best explained as derivative from properties and generic events.
     From: comment on J.L. Mackie (Causes and Conditions [1965]) by Jaegwon Kim - Causes and Events: Mackie on causation §4
     A reaction: This seems to suggest that necessity must either derive from laws, or from powers. It is certainly hard to see how you could do Mackie's assessment of necessary and sufficient components, without comparing similar events.
A cause is part of a wider set of conditions which suffices for its effect [Mackie, by Crane]
     Full Idea: The details of Mackie's analysis are complex, but the general idea is that the cause is part of a wider set of conditions which suffices for its effect.
     From: report of J.L. Mackie (Causes and Conditions [1965]) by Tim Crane - Causation 1.3.3
     A reaction: Helpful. Why does something have to be 'the' cause? Immediacy is a vital part of it. A house could be a 'fire waiting to happen'. Oxygen is an INUS condition for a fire.
Necessary conditions are like counterfactuals, and sufficient conditions are like factual conditionals [Mackie]
     Full Idea: A necessary causal condition is closely related to a counterfactual conditional: if no-cause then no-effect, and a sufficient causal condition is closely related to a factual conditional (Goodman's phrase): since cause-here then effect.
     From: J.L. Mackie (Causes and Conditions [1965], §4)
     A reaction: The 'factual conditional' just seems to be an assertion that causation occurred (dressed up with the logical-sounding 'since'). An important distinction for Lewis. Sufficiency doesn't seem to need possible-worlds talk.
The INUS account interprets single events, and sequences, causally, without laws being known [Mackie]
     Full Idea: My account shows how a singular causal statement can be interpreted, and how the corresponding sequence can be shown to be causal, even if the corresponding complete laws are not known.
     From: J.L. Mackie (Causes and Conditions [1965], §9)
     A reaction: Since the 'complete' laws are virtually never known, it would be a bit much to require that to assert causation. His theory is the 'INUS' account of causal conditions - see Idea 8333.
26. Natural Theory / C. Causation / 8. Particular Causation / d. Selecting the cause
A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition [Mackie]
     Full Idea: If a short-circuit causes a fire, the so-called cause is, and is known to be, an Insufficient but Necessary part of a condition which is itself Unnecessary but Sufficient for the result. Let us call this an INUS condition.
     From: J.L. Mackie (Causes and Conditions [1965], §1)
     A reaction: I'm not clear why it is necessary, given that the fire could have started without the short-circuit. The final situation must certainly be sufficient. If only one situation can cause an effect, then the whole situation is necessary.
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
Mackie has a nomological account of general causes, and a subjunctive conditional account of single ones [Mackie, by Tooley]
     Full Idea: For general causal statements Mackie favours a nomological account, but for singular causal statements he argued for an analysis in terms of subjunctive conditionals.
     From: report of J.L. Mackie (Causes and Conditions [1965]) by Michael Tooley - Causation and Supervenience 5.2
     A reaction: These seem to be consistent, by explaining each by placing it within a broader account of reality. Personally I think Ducasse gives the best account of how you get from the particular to the general (via similarity and utility).
The virus causes yellow fever, and is 'the' cause; sweets cause tooth decay, but they are not 'the' cause [Mackie]
     Full Idea: We may say not merely that this virus causes yellow fever, but also that it is 'the' cause of yellow fever; but we could only say that sweet-eating causes dental decay, not that it is the cause of dental decay (except in an individual case).
     From: J.L. Mackie (Causes and Conditions [1965], §3)
     A reaction: A bit confusing, but there seems to be something important here, concerning the relation between singular causation and law-governed causation. 'The' cause may not be sufficient (I'm immune to yellow fever). So 'the' cause is the only necessary one?
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
The propositions that God is good and omnipotent, and that evil exists, are logically contradictory [Mackie, by PG]
     Full Idea: There is a contradiction between the propositions that God is wholly good, God is omnipotent, and evil exists, and one of them has got to give way (assuming good eliminates evil, and omnipotence has no limit).
     From: report of J.L. Mackie (Evil and Omnipotence [1955], Pref.) by PG - Db (ideas)
Is evil an illusion, or a necessary contrast, or uncontrollable, or necessary for human free will? [Mackie, by PG]
     Full Idea: Perhaps evil is an illusion, or it is necessary for good to exist, or in humans it is required because we have free will, or God lacks the full power to control it, but none of these looks convincing.
     From: report of J.L. Mackie (Evil and Omnipotence [1955], §B) by PG - Db (ideas)