But an empty set is nevertheless a concrete object? — Wayfarer
I understand, I just meant to point out that if all possible (logically consistent/coherent) universes are equally real as the one we live in, correspondence theory of truth becomes identical to coherence theory of truth — litewave
I had the idea it was with land title claims and the tallying of agricultural output in Sumeria and Egypt. Land holdings had to be calculated across very irregular shapes, There was a recent discovery about this https://cosmosmagazine.com/science/mathematics/babylonian-tablet-trigonometry-pythagorean-triplets/ — Wayfarer
To simplify the discussion, let’s use a right-angled triangle with shorter perpendicular side s, longer perpendicular side l, and diagonal d, such that s² + l² = d² .
Columns two and three of Plimpton 322 simply contain values for s and d respectively for the series of Pythagorean triples. Column four is just a list of the numbers 1 to 15, so we can remember which row we’re up to. But column one represents the ratio d² / l², and since we’re given the value of d in column three, we can calculate l, and voila … a complete Pythagorean triple (s,l,d) is revealed! — cosmosmagazine.com
Every consistent description of a world corresponds to a real world. — litewave
Isn't that begging the question? By the way if a world has to be qualified with real as you do in "...a real world", it suggests that worlds can be unreal. Care to expand and elaborate. — TheMadFool
If what matters most according to the correspondence theory of truth, is the accurate portrayal of a particular or general 'state of affairs' - through language - of reality, — Shawn
and therefore what can be platonically described as the mind's eye — Shawn
From a retired mathematician who still dabbles with it, — jgill
That sequence of electronic dots has a kind of "physical" existence but is still in a way non-physical. How does this fit into the current discussion? — jgill
As I said, I think that all possible worlds are just as real as our world because I don't see any ontological difference between possible and real worlds. — litewave
What's impossible to you? — TheMadFool
Mathematics corresponds to the structure of reality (and omits the qualities that fill the structure). — litewave
And what is the ontological (existential) difference between a possible universe and a "real" universe? I think none, so all possible universes exist and descriptions of all possible universes correspond to reality. — litewave
When P matches R, there's a correspondence and then we can claim P is true. — TheMadFool
...so an empty collection would be the simplest concrete object. — litewave
A concept/property is an object that is not a collection but it has instances in collections. — litewave
Every consistent description of a world corresponds to a real world. — litewave
You appear to still be using "simples" - so you assume there is a "lowest level", and speak of "smallest parts".
But what is to count as a simple, as the atom from which you derive the world? Whatever you choose will be arbitrary - we might choose otherwise. — Banno
...Can you provide an indubitable account of what that "correspondence" consists in?
That's the core problem for correspondence. — Banno
The smallest parts, empty sets, are obviously "simples" in the sense that they have no parts. — litewave
Yes! Anything can count as a simple....any collection is also a "simple" in the sense that the collection as a whole is an indivisible/unstructured thing that stands in parthood relations to other things that are its parts. — litewave
A proposition describes an object by affirming that the object has certain properties. If the object really has those properties then the proposition is true - that's how a proposition corresponds to reality. — litewave
If this were so, then since in some possible world you didn't write that post; and since all possible universes exist and descriptions of all possible universes correspond to reality, you really didn't wright that post.
How will you avoid such inconsistency?
You have set the scope of "...exists" across all possible world instead of within the scope of each possible world, and that results in inconsistency. — Banno
Even though many descriptions of a universe by mathematicians don't correspond to our universe, they correspond to other possible universes. — litewave
...so an empty collection would be the simplest concrete object. — litewave
As Wayfarer impied, what is concrete about an empty set? — Banno
A concept/property is an object that is not a collection but it has instances in collections. — litewave
This is at odds with extensional logic, in which a property is a collection of objects; so "...is red" is the collection of red things. — Banno
But then all you have done is claim that anything could be true. — Banno
The point is surely to sort out the way things actually are from the way things might be. — Banno
Anything that is consistently defined and thus identical to itself. — litewave
...appears incompatible with...It is useful to sort out the way things are in our world from the way things are in other possible worlds. — litewave
...all possible universes exist and descriptions of all possible universes correspond to reality. — litewave
My reading of the correspondence theory of truth requires two essential components:
1. An actual reality. Call this R
2. A proposition about that actual reality. Call this P
When P matches R, there's a correspondence and then we can claim P is true. — TheMadFool
...and yet to understand empty sets one needs all the paraphernalia of set theory. SO if they are to form the "simples" of a logical system, it is only by presuposing set theory. Which is not all that simple. — Banno
..and? That does not explain the "correspondence" in the correspondence theory of truth. Indeed, while correspondence is about what is the case, you've moved to affirmation, which is distinct, and quite different. One can after all affirm things that are not true. — Banno
We agree that it is true in this possible world that you wrote the post; it is not true in some other possible world? — Banno
So do you think mathematical statements are true in this possible world because they are true in some possible world? — Banno
Then if it is true that in some possible world you dd not write that post, wouldn't it be true in this possible world, too? — Banno
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