Into the Wardrobe

AllanS:
Strictly speaking, 1+1=2 is a "lie" in the material world. Since no two material things are identical, it's impossible to add them together.

Xara:
Water? Sand? Air? Clones?

AllanS:
An apple plus and orange doesn't equal two bananas. You can only add identical things together. No two material things are identical in every way. If they were, they would be the same object (with identical atoms, identical history, identical position in space etc.)

Xara:
I wonder if you mean 1x + 1y ¬ 2z. Whereas what I am saying is 1x + 1x = 2x wherein 1 is not a descriptor of quality, but of quantity. Otherwise we would say 1x + 1x (3 lines meaning identical to) 2x.

AllanS:
You assume the very thing you're trying to prove. "Quantity" cannot exist in the material world since no two unit objects can be identical.

I see two distinct material objects in a bowl. They both call to mind the idea "APPLE" which, being ideal, I can add to make "2 APPLES". I then project this ideal truth back into the material world and say, quite brazenly, that I have 2 apples in the bowl.

Xara:
"Quantity" is, by it's very concept, something that exists in the material world. Platonic ideals cannot be measured.

When you talk about the Platonic ideal of "2" and the act of smuggling it into the real world, the reply must be that I am using the empirical form of the Platonic ideal to count those apples. Thus there are 2 apples.

There is an interesting article in the Canadian Journal of Philosophy pertaining to this topic. It is on the event of coincident entities, or in other words the idea of there being two entities in the same place at the same time. This of course is in reference to the question of identity and how one assigns identity to an entity.


For instance, there is an illustration used of the story of Theseus' ship. As such, Theseus sails in his vessels for years, all the while replacing parts of his ship. Hypothetically, there as another who is collecting the parts that Theseus' crew dispose of the ship. Ultimately, a new ship is built from the old parts from Theseus' ship. The question then posed is which is Theseus' ship since it is entirely replaced by new material and its ORIGINAL material is what comprises the 'new' ship. Logically then we could conceiveably have two entities of the same identity.

But even more, it is possible to have two entities of the same or different kind, residing in the same place; an empirical impossibility but a logical one. For example, suppose there is a road and we will call it route 8. Now route 8 merges at some point with another road, we will call it interstate 5, and then breaks off again unto its own. Now during this period, there are two roads in one place; and empirical impossibility but a logical fact.

So, in reference to this dilemma concerning quality and quantity and identity in the material world. If from a Platonic perspective one were to assign quantity to say an orange, then it depends on whether one is referencing the (F)orm of the orange or the sensually perceived representation, or shadow, of the orange. For as you can see from the examples I have provided, there is no solution save what sort of theory one subscribes to.

I'd say that numbers are possible answers to the question "how many?"; this may or may not help.

The confusion arises form the fact that numbers can be used either to signify actual objects, like apples or chickens, or they can be used to signify non-existant things -- i.e., "points." When you play a game such as Cribbage, or Uno, you count "points" to see who wins. There is no such thing as a "point," so what are you counting? With regard to "points," then, 1+1=2, end of report. In higher math numbers are used frequently to signify things that are both non-existant and impossible, such as "imaginary numbers," because these non-existant/impossible "things" are functional and necessary.

That, I presume, is why AlanS specified in the OP that 1+1=2 is a lie in the material world. In the physical world it is questionable; In quantum mechanics it can be disproved; in the metaphysical world it is absolute truth.

Maybe.

Pax Domini
Art

As one of those pesky Aristoltean realists, I really don't see what there is to debate. We can count things by what they have in common, even if it's just the fact of their thing-ness, or their unity. It's the latter, most likely, that people are confused about.

As for logical facts, "a thing which is cannot both be and not be at the same time in the same way." With all due respect, any so called logical facts which contradict this first principle of thought are nothing but sleight of hand.

Two questions:

Is it true that a horse is an animal?
Is it true that a cat is an animal?

If both are true, then 1 cat plus 1 horse are 2 animals, and the abstraction 1+1 = 2 from this sentence (and the plethora of others constructed in the same fashion) are true. This is what most people mean by 1+1 = 2. No one expects that the M&M's, pizzas, pets,a nd other things that they count are identical. The meaning of 1+1 = 2 is precisely the abstraction, therefore, of the notion of combination, separated from the issue of non-identity.



Now here are some problems:

The sentence 1x + 1x = 2x where x is a real object (e.g. 1 cat + 1 cat are 2 cats) is necessarily incomplete. I have to not say something about one or more of the cats, otherwise the sentence is false.

True: 1 cat + 1 cat = 2 cats.
Incomplete: Fluffy and Thumper are cats.

The issue of categories has been invoked to solve the problem, but it really just promotes it. What does it mean to say that a certain object is a horse? I happen to think that when it comes right down to it, most sentences are false or incomplete. Are horses large or small? Are swans white? Are people smart?


That having been said, it is impossible to say that no two objects are identical, and there is a possibility that certain phenomena of atomic physics (e.g. the Pauli Exclusion Principle) arise because one cannot force both intrinsic identicalness and locational identicalness on some kinds of objects at the same time. Electrons, for example, are supposed to all be intrinsically identical, therefore it is impossible to stack them in the same place, making their locations identical. This is why we don't fall to the center of the earth and why we cannot pass through walls. On the other hand, certain other kinds of objects ignore this rule, e.g. photons. This is what is called the fermion/boson distinction. (Bosons stack; fermions do not.)

This does not eliminate the problem of non-addibility that is being discussed, except possibly for bosons.



The point I want to finish with is this: unless every noun in your sentence is a proper noun, then your sentence is a kind of abstraction. All of mathematics is abstraction of this kind. Probably, sentences with direct pointers to individuals are implicit abstractions (e.g. "John is my father.") because they rely on understanding of abstract groups (here "fathers") to function. When you say 1+1 = 2 you have to lose definition of the objects involved, but exactly the same thing happens in most sentences, like "John is my father," "Cows are animals", and "God is good."

gosh...this doesnt have ANYTHING to do with does it?

/me waits for another thread that might

::Two objects have common thingy-ness inasmuch as they both conform to a common idea. It's the ideas were adding, not the objects.

Hey Allan.

Ideas are meaning about objects (forgive me if you tire of hearing me say this, but ideas are that by which we directly apprehend, not that which we directly apprehend), so that the idea that there are seperate objects which share existence is about those objects we have in mind. That is to say, two objects have common thing-ness in so far as the idea is drawn from the common thing-ness of the objects.

Robert said: there is an illustration used of the story of Theseus' ship.


Allan said...In the material temporal world, identical objects must have the same history. ie. They must be the same object. To talk of two identical objects is absurd.

Yes but material objects do not exhaust all objects that indeed exist. There are after all metaphysical objects. And this says nothing to the veritably infinite number of possible worlds that, whether exist theoretically or literally, could have all the same properties of one object in one world with those of one in another and as such are identical except for their being in another world.

Robert said: suppose there is a road and we will call it route 8. Now route 8 merges at some point with another road, we will call it interstate 5, and then breaks off again unto its own. Now during this period, there are two roads in one place; and empirical impossibility but a logical fact.


Allan said...Again, the two roads have different histories. Route 8 is 200 miles long, east-west. Interstate 5 is 500 miles long, north-south. Clearly, they cannot both exist in one place.

And yet this says nothing to the ‘current’ identification of the road. Sure, this route or that route have different histories, but let us say that route 8 when merging with interstate 5 ‘become’ route 9. In this instance, route 9 has the same history as the other two roads. And yet one can ‘refer to’ route 9 as being route 8 and interstate 5 at the same time. The histories of these two individual roads are only respective to their distinction from one another. When they are route 9, when referencing this patch of road, it is irrelevant to point to separate histories since what they culminate into this merge. If route 8 is 200 miles long e to w and I-5 500 miles long n to s, this says nothing to their separate identities. The point is that 100 miles down the road for route 8 and 250 miles down the road for I-5, they are route 9 at that point and still both r-8 and I-5. Their identity before this point does not help clarify the dilemma of their being two in one as a third identity.




Robert...as you can see from the examples I have provided, there is no solution save what sort of theory one subscribes to.


Allan said...You've lost me here.

What I mean here is that only by subscribing to a particular theory invested in solving the problems is there any relief from the issue. For instance, if I theorize that identity is obtained by way of a thing’s material cataloguing, then the problem of Theseus’ ship is solved by accepting the rebuilder’s claim; who took the actual pieces of the ship and made another ship.