| 2014 | Identity and Existence in Logic |
| 1.5 | p.59 | 18763 | Basic variables in second-order logic are taken to range over subsets of the individuals |
| 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. |
| 1.5 | p.60 | 18764 | The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles |
| 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. |
| 1.6 | p.60 | 18765 | Individuation was a problem for medievals, then Leibniz, then Frege, then Wittgenstein (somewhat) |
| 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. |
| 2.1 | p.63 | 18766 | 's is non-existent' cannot be said if 's' does not designate |
| 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'. |
| 2.3 | p.67 | 18767 | Free logics has terms that do not designate real things, and even empty domains |
| 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. |
| 2.5 | p.71 | 18768 | We cannot pick out a thing and deny its existence, but we can say a concept doesn't correspond |
| 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. |
| 2.6 | p.72 | 18769 | Do mathematicians use 'existence' differently when they say some entity exists? |
| 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...). |
| 2.6 | p.74 | 18770 | We can distinguish 'ontological' from 'existential' commitment, for different kinds of being |
| 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. |
| 2.6 | p.74 | 18771 | Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities |
| 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! |