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All the ideas for 'works', 'On Multiplying Entities' and 'Identity and Existence in Logic'

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14 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
8207 The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine]
     Full Idea: It is the quest for system and simplicity that has kept driving the scientist to posit further entities as values of his variables. By positing molecules, Boyles' law of gases could be assimilated into a general theory of bodies in motion.
     From: Willard Quine (On Multiplying Entities [1974], p.262)
     A reaction: Interesting that a desire for simplicity might lead to multiplications of entities. In fact, I presume molecules had been proposed elsewhere in science, and were adopted in gas-theory because they were thought to exist, not because simplicity is nice.
8208 In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine]
     Full Idea: In classical arithmetic, ratios were posited to make division generally applicable, negative numbers to make subtraction generally applicable, and irrationals and finally imaginaries to make exponentiation generally applicable.
     From: Willard Quine (On Multiplying Entities [1974], p.263)
     A reaction: This is part of Quine's proposal (c.f. Idea 8207) that entities have to be multiplied in order to produce simplicity. He is speculating. Maybe they are proposed because they are just obvious, and the generality is a nice side-effect.
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
18767 Free logics has terms that do not designate real things, and even empty domains [Anderson,CA]
     Full Idea: Free logics say 1) singular terms are allowed that do not designate anything that exists; sometimes 2) is added: the domain of discourse is allowed to be empty. Logics with both conditions are called 'universally free logics'.
     From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.3)
     A reaction: I really like the sound of this, and aim to investigate it. Karel Lambert's writings are the starting point. Maybe the domain of logic is our concepts, rather than things in the world, in which case free logic sounds fine.
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
18763 Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA]
     Full Idea: Under its now standard principal interpretation, the monadic predicate variables in second-order logic range over subsets of the domain on individuals.
     From: C. Anthony Anderson (Identity and Existence in Logic [2014], 1.5)
     A reaction: This is an interpretation in which properties are just sets of things, which is fine if you are a logician, but not if you want to talk about anything important. Still, we must play the game. Boolos introduced plural quantification at this point.
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
18771 Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA]
     Full Idea: Ontological quantifiers might just as well range over all the entities needed for the semantics. ...The minimal way would be to just stop calling '∃' an 'existential quantifier', and always read it as 'there is...' rather than 'there exists...'.
     From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.6)
     A reaction: There is no right answer here, but it seems to be the strategy adopted by most logicians, and the majority of modern metaphysicians. They just allow abstracta, and even fictions, to 'exist', while not being fussy what it means. Big mistake!
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
     Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
     From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
     A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.
7. Existence / A. Nature of Existence / 2. Types of Existence
18769 Do mathematicians use 'existence' differently when they say some entity exists? [Anderson,CA]
     Full Idea: A cursory examination shows that mathematicians have no aversion to saying that this-or-that mathematical entity exists. But is this a different sense of 'existence'?
     From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.6)
     A reaction: For those of us like me and my pal Quine who say that 'exist' is univocal (i.e. only one meaning), this is a nice challenge. Quine solves it by saying maths concerns sets of objects. I, who don't like sets, am puzzled (so I turn to fictionalism...).
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
8205 Explaining events just by bodies can't explain two events identical in space-time [Quine]
     Full Idea: An account of events just in terms of physical bodies does not distinguish between events that happen to take up just the same portion of space-time. A man's whistling and walking would be identified with the same temporal segment of the man.
     From: Willard Quine (On Multiplying Entities [1974], p.260)
     A reaction: We wouldn't want to make his 'walking' and his 'strolling' two events. Whistling and walking are different because different objects are involved (lips and legs). Hence a man is not (ontologically) a single object.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
18770 We can distinguish 'ontological' from 'existential' commitment, for different kinds of being [Anderson,CA]
     Full Idea: There are sensible ways to maike a distinction between different kinds of being. ..One need not fear that this leads to a 'bloated ontology'. ...We need only distinguish 'ontological commitment' from 'existential commitment'
     From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.6)
     A reaction: He speaks of giving fictional and abstract entities a 'lower score' in existence. I think he means the 'ontological' commitment to be the stronger of the two.
9. Objects / A. Existence of Objects / 4. Impossible objects
18766 's is non-existent' cannot be said if 's' does not designate [Anderson,CA]
     Full Idea: The paradox of negative existentials says that if 's' does not designate something, then the sentence 's is non-existent' is untrue.
     From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.1)
     A reaction: This only seems be a problem for logicians. Everyone else can happily say 'my coffee is non-existent'.
18768 We cannot pick out a thing and deny its existence, but we can say a concept doesn't correspond [Anderson,CA]
     Full Idea: Parmenides was correct - one cannot speak of that which is not, even to say that it is not. But one can speak of concepts and say of them that they do not correspond to anything real.
     From: C. Anthony Anderson (Identity and Existence in Logic [2014], 2.5)
     A reaction: [This summarises Alonso Church, who was developing Frege] This sounds like the right thing to say about non-existence, but then the same principle must apply to assertions of existence, which will also be about concepts and not things.
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
18765 Individuation was a problem for medievals, then Leibniz, then Frege, then Wittgenstein (somewhat) [Anderson,CA]
     Full Idea: The medieval philosophers and then Leibniz were keen on finding 'principles of individuation', and the idea appears again in Frege, to be taken up in some respects by Wittgenstein.
     From: C. Anthony Anderson (Identity and Existence in Logic [2014], 1.6)
     A reaction: I take a rather empirical approach to this supposed problem, and suggest we break 'individuation' down into its component parts, and then just drop the word. Discussions of principles of individuations strike me as muddled. Wiggins and Lowe today.
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
18764 The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles [Anderson,CA]
     Full Idea: In the Identity of Indiscernibles, one speaks about properties, and the notion of a property is by no means clearly fixed and formalized in modern symbolic logic.
     From: C. Anthony Anderson (Identity and Existence in Logic [2014], 1.5)
     A reaction: The unclarity of 'property' is a bee in my philosophical bonnet, in speech, and in metaphysics, as well as in logic. It may well be the central problem in our attempts to understand the world in general terms. He cites intensional logic as promising.
10. Modality / A. Necessity / 11. Denial of Necessity
8206 Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine]
     Full Idea: The need to add a note of necessity to 'all black crows are black' could be met by a generalisation over classes (what belongs to sets x and y belongs to y), or maybe be quantifying over possible particulars.
     From: Willard Quine (On Multiplying Entities [1974], p.262)
     A reaction: He dislikes the second strategy because 'unactualized particulars are an obscure and troublesome lot'. The second is the strategy of Lewis. I think necessity starts to creep back in as soon as you ask WHY a generalisation holds true.