Combining Philosophers

All the ideas for Peter B. Lewis, Michael Potter and Vann McGee

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41 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter]
     Full Idea: The circularity in a definition where the property being defined is used in the definition is now known as 'impredicativity'. ...Some cases ('the tallest man in the room') are unproblematic, as they pick him out, and don't conjure him into existence.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 07 'Impred')
     A reaction: [part summary]
3. Truth / A. Truth Problems / 2. Defining Truth
The Identity Theory says a proposition is true if it coincides with what makes it true [Potter]
     Full Idea: The Identity Theory of truth says a proposition is true just in case it coincides with what makes it true.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 23 'Abs')
     A reaction: The obvious question is how 'there are trees in the wood' can somehow 'coincide with' or 'be identical to' the situation outside my window. The theory is sort of right, but we will never define the relationship, which is no better than 'corresponds'.
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
It has been unfortunate that externalism about truth is equated with correspondence [Potter]
     Full Idea: There has been an unfortunate tendency in the secondary literature to equate externalism about truth with the correspondence theory.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 65 'Truth')
     A reaction: Quitee helpful to distinguish internalist from externalist theories of truth. It is certainly the case that robust externalist views of truth have unfortunately been discredited merely because the correspondence account is inadequate.
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
     Full Idea: Set theory has three roles: as a means of taming the infinite, as a supplier of the subject-matter of mathematics, and as a source of its modes of reasoning.
     From: Michael Potter (Set Theory and Its Philosophy [2004], Intro 1)
     A reaction: These all seem to be connected with mathematics, but there is also ontological interest in set theory. Potter emphasises that his second role does not entail a commitment to sets 'being' numbers.
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
Usually the only reason given for accepting the empty set is convenience [Potter]
     Full Idea: It is rare to find any direct reason given for believing that the empty set exists, except for variants of Dedekind's argument from convenience.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 04.3)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: There is at least one limit level [Potter]
     Full Idea: Axiom of Infinity: There is at least one limit level.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 04.9)
     A reaction: A 'limit ordinal' is one which has successors, but no predecessors. The axiom just says there is at least one infinity.
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
Nowadays we derive our conception of collections from the dependence between them [Potter]
     Full Idea: It is only quite recently that the idea has emerged of deriving our conception of collections from a relation of dependence between them.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 03.2)
     A reaction: This is the 'iterative' view of sets, which he traces back to Gödel's 'What is Cantor's Continuum Problem?'
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
     Full Idea: We group under the heading 'limitation of size' those principles which classify properties as collectivizing or not according to how many objects there are with the property.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 13.5)
     A reaction: The idea was floated by Cantor, toyed with by Russell (1906), and advocated by von Neumann. The thought is simply that paradoxes start to appear when sets become enormous.
4. Formal Logic / G. Formal Mereology / 1. Mereology
Mereology elides the distinction between the cards in a pack and the suits [Potter]
     Full Idea: Mereology tends to elide the distinction between the cards in a pack and the suits.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1)
     A reaction: The example is a favourite of Frege's. Potter is giving a reason why mathematicians opted for set theory. I'm not clear, though, why a pack cannot have either 4 parts or 52 parts. Parts can 'fall under a concept' (such as 'legs'). I'm puzzled.
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
We can formalize second-order formation rules, but not inference rules [Potter]
     Full Idea: In second-order logic only the formation rules are completely formalizable, not the inference rules.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 01.2)
     A reaction: He cites Gödel's First Incompleteness theorem for this.
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
Validity is explained as truth in all models, because that relies on the logical terms [McGee]
     Full Idea: A model of a language assigns values to non-logical terms. If a sentence is true in every model, its truth doesn't depend on those non-logical terms. Hence the validity of an argument comes from its logical form. Thus models explain logical validity.
     From: Vann McGee (Logical Consequence [2014], 4)
     A reaction: [compressed] Thus you get a rigorous account of logical validity by only allowing the rigorous input of model theory. This is the modern strategy of analytic philosophy. But is 'it's red so it's coloured' logically valid?
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter]
     Full Idea: Natural deduction systems generally depend on conditional proof, but for Frege everything is asserted unconditionally. The modern turnstile |- is allowed to have antecedents, and hence to represent inference rather than Frege's judgement sign |---.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 03 'Axioms')
     A reaction: [compressed] Shockingly, Frege's approach seems more psychological than the modern approach. I would say that the whole point of logic is that it has to be conditional, because the truth of the antecedents is irrelevant.
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Deductivism can't explain how the world supports unconditional conclusions [Potter]
     Full Idea: Deductivism is a good account of large parts of mathematics, but stumbles where mathematics is directly applicable to the world. It fails to explain how we detach the antecedent so as to arrive at unconditional conclusions.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 12 'Deduc')
     A reaction: I suppose the reply would be that we have designed deductive structures which fit our understanding of reality - so it is all deductive, but selected pragmatically.
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Natural language includes connectives like 'because' which are not truth-functional [McGee]
     Full Idea: Natural language includes connectives that are not truth-functional. In order for 'p because q' to be true, both p and q have to be true, but knowing the simpler sentences are true doesn't determine whether the larger sentence is true.
     From: Vann McGee (Logical Consequence [2014], 2)
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Second-order variables need to range over more than collections of first-order objects [McGee]
     Full Idea: To get any advantage from moving to second-order logic, we need to assign to second-order variables a role different from merely ranging over collections made up of things the first-order variables range over.
     From: Vann McGee (Logical Consequence [2014], 7)
     A reaction: Thus it is exciting if they range over genuine properties, but not so exciting if you merely characterise those properties as sets of first-order objects. This idea leads into a discussion of plural quantification.
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
     Full Idea: A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 01.1)
     A reaction: Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth).
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
An ontologically secure semantics for predicate calculus relies on sets [McGee]
     Full Idea: We can get a less ontologically perilous presentation of the semantics of the predicate calculus by using sets instead of concepts.
     From: Vann McGee (Logical Consequence [2014], 4)
     A reaction: The perilous versions rely on Fregean concepts, and notably Russell's 'concept that does not fall under itself'. The sets, of course, have to be ontologically secure, and so will involve the iterative conception, rather than naive set theory.
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logically valid sentences are analytic truths which are just true because of their logical words [McGee]
     Full Idea: Logically valid sentences are a species of analytic sentence, being true not just in virtue of the meanings of their words, but true in virtue of the meanings of their logical words.
     From: Vann McGee (Logical Consequence [2014], 4)
     A reaction: A helpful link between logical truths and analytic truths, which had not struck me before.
Modern logical truths are true under all interpretations of the non-logical words [Potter]
     Full Idea: In the modern definition, a 'logical truth' is true under every interpretation of the non-logical words it contains.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 19 'Frege's')
     A reaction: What if the non-logical words are nonsense, or are used inconsistently ('good'), or ambiguously ('bank'), or vaguely ('bald'), or with unsure reference ('the greatest philosopher' becomes 'Bentham')? What qualifies as an 'interpretation'?
5. Theory of Logic / K. Features of Logics / 3. Soundness
Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee]
     Full Idea: Soundness theorems are seldom very informative, since typically we use informally, in proving the theorem, the very same rules whose soundness we are attempting to establish.
     From: Vann McGee (Logical Consequence [2014], 5)
     A reaction: [He cites Quine 1935]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
     Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8)
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee]
     Full Idea: One of the culminating achievements of Euclidean geometry was categorical axiomatisations, that describe the geometric structure so completely that any two models of the axioms are isomorphic. The axioms are second-order.
     From: Vann McGee (Logical Consequence [2014], 7)
     A reaction: [He cites Veblen 1904 and Hilbert 1903] For most mathematicians, categorical axiomatisation is the best you can ever dream of (rather than a single true axiomatisation).
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
     Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms).
     From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2)
     A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying.
6. Mathematics / C. Sources of Mathematics / 7. Formalism
The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter]
     Full Idea: Gödel's theorem does not refute formalism outright, because the committed formalist need not recognise the metalinguistic notion of truth to which the theorem appeals.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 45 'Log')
     A reaction: The theorem was prior to Tarski's account of truth. Potter says Gödel avoided explicit mention of truth because of this problem. In general Gödel showed that there are truths outside the formal system (which is all provable).
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Why is fictional arithmetic applicable to the real world? [Potter]
     Full Idea: Fictionalists struggle to explain why arithmetic is applicable to the real world in a way that other stories are not.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 21 'Math')
     A reaction: We know why some novels are realistic and others just the opposite. If a novel aimed to 'model' the real world it would be even closer to it. Fictionalists must explain why some fictions are useful.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter]
     Full Idea: The word 'concrete' is often used as the negative of 'abstract', with the slightly odd consequence that desires and hallucinations are thereby classified as concrete.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 12 'Numb')
     A reaction: There is also the even more baffling usage of 'abstract' for the most highly generalised mathematics, leaving lower levels as 'concrete'. I favour the use of 'generalised' wherever possible, rather than 'abstract'.
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
A relation is a set consisting entirely of ordered pairs [Potter]
     Full Idea: A set is called a 'relation' if every element of it is an ordered pair.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 04.7)
     A reaction: This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related.
8. Modes of Existence / A. Relations / 4. Formal Relations / c. Ancestral relation
'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter]
     Full Idea: From the successor function we can deduce its ancestral, the 'greater than' relation, which is a strict total ordering of the natural numbers. (Frege did not mention this, but Dedekind worked it out, when expounding definition by recursion).
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 07 'Def')
     A reaction: [compressed]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
     Full Idea: The argument that the relation of dependence is well-founded ...is a version of the classical arguments for substance. ..Any conceptual scheme which genuinely represents a world cannot contain infinite backward chains of meaning.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3)
     A reaction: Thus the iterative conception of set may imply a notion of substance, and Barwise's radical attempt to ditch the Axiom of Foundation (Idea 13039) was a radical attempt to get rid of 'substances'. Potter cites Wittgenstein as a fan of substances here.
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
     Full Idea: A collection has a determinate number of members, whereas a fusion may be carved up into parts in various equally valid (although perhaps not equally interesting) ways.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1)
     A reaction: This seems to sum up both the attraction and the weakness of mereology. If you doubt the natural identity of so-called 'objects', then maybe classical mereology is the way to go.
10. Modality / A. Necessity / 1. Types of Modality
Priority is a modality, arising from collections and members [Potter]
     Full Idea: We must conclude that priority is a modality distinct from that of time or necessity, a modality arising in some way out of the manner in which a collection is constituted from its members.
     From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3)
     A reaction: He is referring to the 'iterative' view of sets, and cites Aristotle 'Metaphysics' 1019a1-4 as background.
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
A material conditional cannot capture counterfactual reasoning [Potter]
     Full Idea: What the material conditional most significantly fails to capture is counterfactual reasoning.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 04 'Sem')
     A reaction: The point is that counterfactuals say 'if P were the case (which it isn't), then Q'. But that means P is false, and in the material conditional everything follows from a falsehood. A reinterpretation of the conditional might embrace counterfactuals.
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
Fichte, Schelling and Hegel rejected transcendental idealism [Lewis,PB]
     Full Idea: Fichte, Schelling and Hegel were united in their opposition to Kant's Transcendental Idealism.
     From: Peter B. Lewis (Schopenhauer [2012], 3)
     A reaction: That is, they preferred genuine idealism, to the mere idealist attitude Kant felt that we are forced to adopt.
Fichte, Hegel and Schelling developed versions of Absolute Idealism [Lewis,PB]
     Full Idea: At the University of Jena, Fichte, Hegel and Schelling critically developed aspects of Kant's philosophy, each in his own way, thereby giving rise to the movement known as Absolute Idealism, see reality as universal God-like self-consciousness.
     From: Peter B. Lewis (Schopenhauer [2012], 2)
     A reaction: Is asking how anyone can possibly have believed such a bizarre and ridiculous idea a) uneducated, b) stupid, c) unimaginative, or d) very sensible? It sounds awfully like Spinoza's concept of God. Also Anaxagoras.
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter]
     Full Idea: Knowledge might result from a reliable and an unreliable process. ...Is something knowledge if you were told it by a drunken schoolteacher?
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 66 'Rel')
     A reaction: Nice example. The listener must decide which process to rely on. But how do you decide that, if not by assessing the likely truth of what you are being told? It could be a bad teacher who is inspired by drink.
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
Traditionally there are twelve categories of judgement, in groups of three [Potter]
     Full Idea: The traditional categorisation of judgements (until at least 1800) was as universal, particular or singular; as affirmative, negative or infinite; as categorical, hypothetical or disjunctive; or as problematic, assertoric or apodictic.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 02 'Trans')
     A reaction: Arranging these things in neat groups of three seems to originate with the stoics. Making distinctions like this is very much the job of a philosopher, but arranging them in neat equinumerous groups is intellectual tyranny.
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter]
     Full Idea: Frege's mirroring principle (that the structure of thoughts mirrors that of language) has the uncomfortable consequence that since the phrase 'the concept "horse"' is saturated, it cannot refer to something unsaturated, which includes concepts.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 16 'Conc')
19. Language / C. Assigning Meanings / 4. Compositionality
'Direct compositonality' says the components wholly explain a sentence meaning [Potter]
     Full Idea: Some authors urge the strong notion of 'direct compositionality', which requires that the content of a sentence be explained in terms of the contents of the component parts of that very sentence.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 05 'Sem')
     A reaction: The alternative is that meaning is fully explained by an analysis, but that may contain more than the actual components of the sentence.
Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter]
     Full Idea: Compositionality is best seen as saying the semantic value of a string is explained by the strings lower down its parsing tree. It is unimportant whether a string is always parsed in terms of its own substrings.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 05 'Sem')
     A reaction: That is, the analysis must explain the meaning, but the analysis can contain more than the actual ingredients of the sentence (which would be too strict).
Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter]
     Full Idea: The principle of compositionality is more popular among philosophers of logic than of language, because the subtle context-sensitivity or ordinary language makes providing a compositional semantics for it a daunting challenge.
     From: Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 21 'Lang')
     A reaction: Logicians love breaking complex entities down into simple atomic parts. Linguistics tries to pin down something much more elusive.
19. Language / F. Communication / 2. Assertion
A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee]
     Full Idea: If our linguistic conventions entitle us to assert a sentence, they thereby make it true, because of the maxim that 'truth is the norm of assertion'.
     From: Vann McGee (Logical Consequence [2014], 8)
     A reaction: You could only really deny that maxim if you had no belief at all in truth, but then you can assert anything you like (with full entitlement). Maybe you can assert anything you like as long as it doesn't upset anyone? Etc.