Combining Philosophers

All the ideas for Lynch,MP/Glasgow,JM, Anil Gupta and Brian Clegg

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40 ideas

2. Reason / D. Definition / 1. Definitions
Definitions usually have a term, a 'definiendum' containing the term, and a defining 'definiens' [Gupta]
     Full Idea: Many definitions have three elements: the term that is defined, an expression containing the defined term (the 'definiendum'), and another expression (the 'definiens') that is equated by the definition with this expression.
     From: Anil Gupta (Definitions [2008], 2)
     A reaction: He notes that the definiendum and the definiens are assumed to be in the 'same logical category', which is a right can of worms.
Notable definitions have been of piety (Plato), God (Anselm), number (Frege), and truth (Tarski) [Gupta]
     Full Idea: Notable examples of definitions in philosophy have been Plato's (e.g. of piety, in 'Euthyphro'), Anselm's definition of God, the Frege-Russell definition of number, and Tarski's definition of truth.
     From: Anil Gupta (Definitions [2008], Intro)
     A reaction: All of these are notable for the extensive metaphysical conclusions which then flow from what seems like a fairly neutral definition. We would expect that if we were defining essences, but not if we were just defining word usage.
2. Reason / D. Definition / 2. Aims of Definition
A definition needs to apply to the same object across possible worlds [Gupta]
     Full Idea: In a modal logic in which names are non-vacuous and rigid, not only must existence and uniqueness in a definition be shown to hold necessarily, it must be shown that the definiens is satisfied by the same object across possible worlds.
     From: Anil Gupta (Definitions [2008], 2.4)
The 'revision theory' says that definitions are rules for improving output [Gupta]
     Full Idea: The 'revision theory' of definitions says definitions impart a hypothetical character, giving a rule of revision rather than a rule of application. ...The output interpretation is better than the input one.
     From: Anil Gupta (Definitions [2008], 2.7)
     A reaction: Gupta mentions the question of whether such definitions can extend into the trans-finite.
2. Reason / D. Definition / 3. Types of Definition
A definition can be 'extensionally', 'intensionally' or 'sense' adequate [Gupta]
     Full Idea: A definition is 'extensionally adequate' iff there are no actual counterexamples to it. It is 'intensionally adequate' iff there are no possible counterexamples to it. It is 'sense adequate' (or 'analytic') iff it endows the term with the right sense.
     From: Anil Gupta (Definitions [2008], 1.4)
Traditional definitions are general identities, which are sentential and reductive [Gupta]
     Full Idea: Traditional definitions are generalized identities (so definiendum and definiens can replace each other), in which the sentential is primary (for use in argument), and they involve reduction (and hence eliminability in a ground language).
     From: Anil Gupta (Definitions [2008], 2.2)
Traditional definitions need: same category, mention of the term, and conservativeness and eliminability [Gupta]
     Full Idea: A traditional definition requires that the definiendum contains the defined term, that definiendum and definiens are of the same logical category, and the definition is conservative (adding nothing new), and makes elimination possible.
     From: Anil Gupta (Definitions [2008], 2.4)
2. Reason / D. Definition / 4. Real Definition
Chemists aim at real definition of things; lexicographers aim at nominal definition of usage [Gupta]
     Full Idea: The chemist aims at real definition, whereas the lexicographer aims at nominal definition. ...Perhaps real definitions investigate the thing denoted, and nominal definitions investigate meaning and use.
     From: Anil Gupta (Definitions [2008], 1.1)
     A reaction: Very helpful. I really think we should talk much more about the neglected chemists when we discuss science. Theirs is the single most successful branch of science, the paradigm case of what the whole enterprise aims at.
2. Reason / D. Definition / 6. Definition by Essence
If definitions aim at different ideals, then defining essence is not a unitary activity [Gupta]
     Full Idea: Some definitions aim at precision, others at fairness, or at accuracy, or at clarity, or at fecundity. But if definitions 'give the essence of things' (the Aristotelian formula), then it may not be a unitary kind of activity.
     From: Anil Gupta (Definitions [2008], 1)
     A reaction: We don't have to accept this conclusion so quickly. Human interests may shift the emphasis, but there may be a single ideal definition of which these various examples are mere parts.
2. Reason / D. Definition / 10. Stipulative Definition
Stipulative definition assigns meaning to a term, ignoring prior meanings [Gupta]
     Full Idea: Stipulative definition imparts a meaning to the defined term, and involves no commitment that the assigned meaning agrees with prior uses (if any) of the term
     From: Anil Gupta (Definitions [2008], 1.3)
     A reaction: A nice question is how far one can go in stretching received usage. If I define 'democracy' as 'everyone is involved in decisions', that is sort of right, but pushing the boundaries (children, criminals etc).
2. Reason / D. Definition / 11. Ostensive Definition
Ostensive definitions look simple, but are complex and barely explicable [Gupta]
     Full Idea: Ostensive definitions look simple (say 'this stick is one meter long', while showing a stick), but they are effective only because a complex linguistic and conceptual capacity is operative in the background, of which it is hard to give an account.
     From: Anil Gupta (Definitions [2008], 1.2)
     A reaction: The full horror of the situation is brought out in Quine's 'gavagai' example (Idea 6312)
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta]
     Full Idea: The basic principles governing truth are Truth Elimination (sentence A follows from ''A' is true') and the converse Truth Introduction (''A' is true' follows from A), which combine into Tarski's T-schema - 'A' is true if and only if A.
     From: Anil Gupta (Truth [2001], 5.1)
     A reaction: Introduction and Elimination rules are the basic components of natural deduction systems, so 'true' now works in the same way as 'and', 'or' etc. This is the logician's route into truth.
3. Truth / F. Semantic Truth / 2. Semantic Truth
A weakened classical language can contain its own truth predicate [Gupta]
     Full Idea: If a classical language is expressively weakened - for example, by dispensing with negation - then it can contain its own truth predicate.
     From: Anil Gupta (Truth [2001], 5.2)
     A reaction: Thus the Tarskian requirement to move to a metalanguage for truth is only a requirement of a reasonably strong language. Gupta uses this to criticise theories that dispense with the metalanguage.
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
A set is 'well-ordered' if every subset has a first element [Clegg]
     Full Idea: For a set to be 'well-ordered' it is required that every subset of the set has a first element.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13)
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
Set theory made a closer study of infinity possible [Clegg]
     Full Idea: Set theory made a closer study of infinity possible.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13)
Any set can always generate a larger set - its powerset, of subsets [Clegg]
     Full Idea: The idea of the 'power set' means that it is always possible to generate a bigger one using only the elements of that set, namely the set of all its subsets.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
     Full Idea: Axiom of Extension: Two sets are equal if and only if they have the same elements.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
Pairing: For any two sets there exists a set to which they both belong [Clegg]
     Full Idea: Axiom of Pairing: For any two sets there exists a set to which they both belong. So you can make a set out of two other sets.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
     Full Idea: Axiom of Unions: For every collection of sets there exists a set that contains all the elements that belong to at least one of the sets in the collection.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: There exists a set of the empty set and the successor of each element [Clegg]
     Full Idea: Axiom of Infinity: There exists a set containing the empty set and the successor of each of its elements.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
     A reaction: This is rather different from the other axioms because it contains the notion of 'successor', though that can be generated by an ordering procedure.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
Powers: All the subsets of a given set form their own new powerset [Clegg]
     Full Idea: Axiom of Powers: For each set there exists a collection of sets that contains amongst its elements all the subsets of the given set.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
     A reaction: Obviously this must include the whole of the base set (i.e. not just 'proper' subsets), otherwise the new set would just be a duplicate of the base set.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
     Full Idea: Axiom of Choice: For every set we can provide a mechanism for choosing one member of any non-empty subset of the set.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
     A reaction: This axiom is unusual because it makes the bold claim that such a 'mechanism' can always be found. Cohen showed that this axiom is separate. The tricky bit is choosing from an infinite subset.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
Axiom of Existence: there exists at least one set [Clegg]
     Full Idea: Axiom of Existence: there exists at least one set. This may be the empty set, but you need to start with something.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
Specification: a condition applied to a set will always produce a new set [Clegg]
     Full Idea: Axiom of Specification: For every set and every condition, there corresponds a set whose elements are exactly the same as those elements of the original set for which the condition is true. So the concept 'number is even' produces a set from the integers.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
     A reaction: What if the condition won't apply to the set? 'Number is even' presumably won't produce a set if it is applied to a set of non-numbers.
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
The ordered pair <x,y> is defined as the set {{x},{x,y}}, capturing function, not meaning [Gupta]
     Full Idea: The ordered pair <x,y> is defined as the set {{x},{x,y}}. This does captures its essential uses. Pairs <x,y> <u,v> are identical iff x=u and y=v, and the definition satisfies this. Function matters here, not meaning.
     From: Anil Gupta (Definitions [2008], 1.5)
     A reaction: This is offered as an example of Carnap's 'explications', rather than pure definitions. Quine extols it as a philosophical paradigm (1960:§53).
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The Liar reappears, even if one insists on propositions instead of sentences [Gupta]
     Full Idea: There is the idea that the Liar paradox is solved simply by noting that truth is a property of propositions (not of sentences), and the Liar sentence does not express a proposition. But we then say 'I am not now expressing a true proposition'!
     From: Anil Gupta (Truth [2001], 5.1)
     A reaction: Disappointed to learn this, since I think focusing on propositions (which are unambiguous) rather than sentences solves a huge number of philosophical problems.
Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta]
     Full Idea: An example of the Strengthened Liar is the following statement SL: 'Either SL is neither-true-nor-false or it is not true'. This raises a serious problem for any theory that assesses the paradoxes to be neither true nor false.
     From: Anil Gupta (Truth [2001], 5.4.2)
     A reaction: If the sentence is either true or false it reduces to the ordinary Liar. If it is neither true nor false, then it is true.
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
     Full Idea: Three views of mathematics: 'pure' mathematics, where it doesn't matter if it could ever have any application; 'real' mathematics, where every concept must be physically grounded; and 'applied' mathematics, using the non-real if the results are real.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.17)
     A reaction: Very helpful. No one can deny the activities of 'pure' mathematics, but I think it is undeniable that the origins of the subject are 'real' (rather than platonic). We do economics by pretending there are concepts like the 'average family'.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
An ordinal number is defined by the set that comes before it [Clegg]
     Full Idea: You can think of an ordinal number as being defined by the set that comes before it, so, in the non-negative integers, ordinal 5 is defined as {0, 1, 2, 3, 4}.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13)
Beyond infinity cardinals and ordinals can come apart [Clegg]
     Full Idea: With ordinary finite numbers ordinals and cardinals are in effect the same, but beyond infinity it is possible for two sets to have the same cardinality but different ordinals.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Transcendental numbers can't be fitted to finite equations [Clegg]
     Full Idea: The 'transcendental numbers' are those irrationals that can't be fitted to a suitable finite equation, of which π is far and away the best known.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
     Full Idea: The realisation that brought 'i' into the toolkit of physicists and engineers was that you could extend the 'number line' into a new dimension, with an imaginary number axis at right angles to it. ...We now have a 'number plane'.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.12)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
     Full Idea: It is a chicken-and-egg problem, whether the lack of zero forced forced classical mathematicians to rely mostly on a geometric approach to mathematics, or the geometric approach made 0 a meaningless concept, but the two remain strongly tied together.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
     Full Idea: As far as Kronecker was concerned, Cantor had built a whole structure on the irrational numbers, and so that structure had no foundation at all.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
     Full Idea: Paul Cohen showed that the Continuum Hypothesis is independent of the axioms of set theory.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15)
The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
     Full Idea: The 'continuum hypothesis' says that aleph-one is the cardinality of the rational and irrational numbers.
     From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14)
7. Existence / C. Structure of Existence / 3. Levels of Reality
A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow]
     Full Idea: It seems unavoidable that the facts about logically necessary relations between levels of facts are themselves logically distinct further facts, irreducible to the microphysical facts.
     From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C)
     A reaction: I'm beginning to think that rejecting every theory of reality that is proposed by carefully exposing some infinite regress hidden in it is a rather lazy way to do philosophy. Almost as bad as rejecting anything if it can't be defined.
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow]
     Full Idea: Logical supervenience, restricted to individuals, seems to imply strong reduction. It is said that where the B-facts logically supervene on the A-facts, the B-facts simply re-describe what the A-facts describe, and the B-facts come along 'for free'.
     From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C)
     A reaction: This seems to be taking 'logically' to mean 'analytically'. Presumably an entailment is logically supervenient on its premisses, and may therefore be very revealing, even if some people think such things are analytic.
7. Existence / D. Theories of Reality / 6. Physicalism
Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow]
     Full Idea: The root intuition behind nonreductive materialism is that reality is composed of ontologically distinct layers or levels. …The upper levels depend on the physical without reducing to it.
     From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], B)
     A reaction: A nice clear statement of a view which I take to be false. This relationship is the sort of thing that drives people fishing for an account of it to use the word 'supervenience', which just says two things seem to hang out together. Fluffy materialism.
The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow]
     Full Idea: Jessica Wilson (1999) says what makes physicalist accounts different from emergentism etc. is that each individual causal power associated with a supervenient property is numerically identical with a causal power associated with its base property.
     From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], n 11)
     A reaction: Hence the key thought in so-called (serious, rather than self-evident) 'emergentism' is so-called 'downward causation', which I take to be an idle daydream.