Combining Philosophers

All the ideas for Leslie H. Tharp, Keith Lehrer and Zoltn Gendler Szab

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25 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer]
     Full Idea: Some philosophers (e.g Plato) begin with an account of reality, and then appended an account of how we can know it, ..but Descartes turned the tables, insisting that we must first decide what we can know.
     From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.2)
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer]
     Full Idea: An analysis is always relative to some objective. It makes no sense to simply demand an analysis of goodness, knowledge, beauty or truth, without some indication of the purpose of the analysis.
     From: Keith Lehrer (Theory of Knowledge (2nd edn) [2000], I p.7)
     A reaction: Your dismantling of a car will go better if you know what a car is for, but you can still take it apart in ignorance.
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
What is a singleton set, if a set is meant to be a collection of objects? [Szabó]
     Full Idea: The relationship between an object and its singleton is puzzling. Our intuitive conception of a set is a collection of objects - what are we to make of a collection of a single object?
     From: Zoltán Gendler Szabó (Nominalism [2003], 4.1)
     A reaction: The ontological problem seems to be the same as that of the empty set, and indeed the claim that a pair of entities is three things. For logicians the empty set is as real as a pet dog, but not for me.
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.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things [Szabó]
     Full Idea: It is better not to include in the definition of abstract entities that they ontologically depend on their concrete correlates. Note: ..but they may depend on the totality of concreta; maybe 'the supervenience of the abstract' is part of ordinary thought.
     From: Zoltán Gendler Szabó (Nominalism [2003], 2.2)
     A reaction: [the quoted phrase is from Gideon Rosen] It certainly seems unlikely that the concept of the perfect hexagon depends on a perfect hexagon having existed. Human minds have intervened between the concrete and the abstract.
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Justification is coherence with a background system; if irrefutable, it is knowledge [Lehrer]
     Full Idea: Justification is coherence with a background system which, when irrefutable, converts to knowledge.
     From: Keith Lehrer (Consciousness,Represn, and Knowledge [2006])
     A reaction: A problem (as the theory stands here) would be whether you have to be aware that the coherence is irrefutable, which would seem to require a pretty powerful intellect. If one needn't be aware of the irrefutability, how does it help my justification?
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Geometrical circles cannot identify a circular paint patch, presumably because they lack something [Szabó]
     Full Idea: The vocabulary of geometry is sufficient to identify the circle, but could not be used to identify any circular paint patch. The reason must be that the circle lacks certain properties that can distinguish paint patches from one another.
     From: Zoltán Gendler Szabó (Nominalism [2003], 2.2)
     A reaction: I take this to be support for the traditional view, that abstractions are created by omitting some of the properties of physical objects. I take them to be fictional creations, reified by language, and not actual hidden entities that have been observed.
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
Generalization seems to be more fundamental to minds than spotting similarities [Lehrer]
     Full Idea: There is a level of generalization we share with other animals in the responses to objects that suggest that generalization is a more fundamental operation of the mind than the observation of similarities.
     From: Keith Lehrer (Consciousness,Represn, and Knowledge [2006])
     A reaction: He derives this from Reid (1785) - Lehrer's hero - who argued against Hume that we couldn't spot similarities if we hadn't already generalized to produce the 'respect' of the similarity. Interesting. I think Reid must be right.
16. Persons / C. Self-Awareness / 1. Introspection
All conscious states can be immediately known when attention is directed to them [Lehrer]
     Full Idea: I am inclined to think that all conscious states can be immediately known when attention is directed to them.
     From: Keith Lehrer (Consciousness,Represn, and Knowledge [2006])
     A reaction: This strikes me as a very helpful suggestion, for eliminating lots of problem cases for introspective knowledge which have been triumphally paraded in recent times. It might, though, be tautological, if it is actually a definition of 'conscious states'.
18. Thought / E. Abstraction / 5. Abstracta by Negation
Abstractions are imperceptible, non-causal, and non-spatiotemporal (the third explaining the others) [Szabó]
     Full Idea: In current discussions, abstract entities are usually distinguished as 1) in principle imperceptible, 2) incapable of causal interaction, 3) not located in space-time. The first is often explained by the second, which is in turn explained by the third.
     From: Zoltán Gendler Szabó (Nominalism [2003], 2.2)
     A reaction: Szabó concludes by offering 3 as the sole criterion of abstraction. As Lewis points out, the Way of Negation for defining abstracta doesn't tell us very much. Courage may be non-spatiotemporal, but what about Alexander the Great's courage?