15 ideas
| 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. |
| 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. |
| 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! |
| 17435 | Objects do not naturally form countable units [Koslicki] |
| Full Idea: Objects do not by themselves naturally fall into countable units. | |
| From: Kathrin Koslicki (Isolation and Non-arbitrary Division [1997], 2.2) | |
| A reaction: Hm. This seems to be modern Fregean orthodoxy. Why did the institution of counting ever get started if the things in the world didn't demand counting? Even birds are aware of the number of eggs in their nest (because they miss a stolen one). |
| 17433 | We can still count squares, even if they overlap [Koslicki] |
| Full Idea: The fact that there is overlap does not seem to inhibit our ability to count squares. | |
| From: Kathrin Koslicki (Isolation and Non-arbitrary Division [1997], 2.2) | |
| A reaction: She has a diagram of three squares overlapping slightly at their corners. Contrary to Frege, these seems to depend on a subliminal concept of the square that doesn't depend on language. |
| 17439 | There is no deep reason why we count carrots but not asparagus [Koslicki] |
| Full Idea: Why do speakers of English count carrots but not asparagus? There is no 'deep' reason. | |
| From: Kathrin Koslicki (Isolation and Non-arbitrary Division [1997]) | |
| A reaction: Koslick is offering this to defend the Fregean conceptual view of counting, but what seems to matter is what is countable, and not whether we happen to count it. You don't need to know what carrots are to count them. Cooks count asparagus. |
| 17434 | We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki] |
| Full Idea: The reason we have a hard time counting the branches and the waves is because our concepts 'branches on the tree' and 'waves on the ocean' do not determine sufficiently precise boundaries: the concepts do not draw a clear invisible line around each thing. | |
| From: Kathrin Koslicki (Isolation and Non-arbitrary Division [1997], 2.2) | |
| A reaction: This is the 'isolation' referred to in Frege. |
| 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...). |
| 17436 | We talk of snow as what stays the same, when it is a heap or drift or expanse [Koslicki] |
| Full Idea: Talk of snow concerns what stays the same when some snow changes, as it might be, from a heap of snow to a drift, to an expanse. | |
| From: Kathrin Koslicki (Isolation and Non-arbitrary Division [1997], 2.2) | |
| A reaction: The whiteness also stays the same, but isn't stuff. |
| 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. |
| 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. |
| 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. |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |