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Sounds like some of the uninteresting ones do. But yeah, if we ignore all the counterexamples to your claim the only claims left are ones which agree with you. Not sure what that's supposed to prove, but I guess it is one way to win an argument.
You're really not getting it, are you?
Every branch of mathematics I'm familiar with that includes "2", "4", "+", and "=" has the equality "2 + 2 = 4",
Feel free to list any counterexamples you might have.
If it "follows inexorably from his assumptions," then it is a true statement of the form A => B, not simply a fictional statement. Conversely, if it's fictional, it cannot "follow inexorably."
I'm having trouble reconciling those two statements.
as far as I know, no branch of mathematics whatsoever has the inequality "2 + 2 != 4".
Feel free to list any counterexamples you might have.
For example, 2 + 2 = 2 if you define + the correct way.
I don't see why not. If Holmes lives at 221B Baker Street, then it is inexorably true that his home is near Regents Park.
The Pythagorean Theorem is true, or it is false.
But in the real world, the best we have is provisional acceptance, unless and until someone writes a better story.
That table defines a set of equalities and implied inequalities on the set {0, 1, 2, 3}. Since the table doesn't contain 4, the inequality 2 + 2 != 4 is not included, as I said.
I'm not aware of any branch of mathematics that has 2 + 2 = 2
Hardly, because in fiction we can rewrite the geography of London. Nothing in fiction is inexorably true.
So it's a case where 2+2=4 isn't true.
Now you do - it's an example of a bitwise logical operator. I mentioned that in my original reply.
Just like we can create different systems of math on a whim. What's your point?
Ayer would have it that in the context of decimal arithmetic, 2 + 2 = 4 is a factually significant statement in that it is verifiable (it has a truth value); however (like all such mathematical statements) it is tautological, as it is true by definition.
Which is not quite the same as 2 + 2 != 4 being true.
That would be a logical "or" or "and" then, which are not usually written with a "+".
With respect, that's the entire point of the thread. The fictionalist account says that we can create different systems of mathematics on a whim. The Platonist, logicist, and empiricist accounts say that we are constrained by some form of external reality.
What makes you think that it's possible to create different systems of mathematics on a whim?
And if we could, why on earth would you expect anything about the resulting system to be "inexorably true"?
So? You were looking for examples of cases where 2+2=4 weren't true. Moving the goalposts to try and weasel your way
Proof of this claim?
Then the latter camps are obviously wrong, assuming you're describing them correctly.
The fact that people do exactly that.
But if you mean given to us as a magical gift from god, no.
That reminds me of the old joke:
"... Finally, having derived the desired result, he looks up at the student and says, 'Yes, as I thought, it is obvious.' "
The onus of proof is on you. You're the one claiming that the mathematics community uses "+" to mean bitwise "and" or "or."
Create different systems of mathematics on a whim? Hardly.
I can't remember saying that, either.
And I note that you're now starting to back away from the fictionalist account to having mathematics be "true" in some sense, such as being "useful for mapping to explanations about how reality behaves."
Hey, you made the claim.
In boolean logic, 2 + 2 = 2.
Or this one, which explicitly explains what the + sign is used for : http://www.ee.surrey.ac.uk/Projects/CAL/digital-logic/formsdef/index.html. I told you how to find this stuff in my last post, but I'm happy to hand-hold you to more examples if you need them.
Who cares what the mental state of mathematicians are at the time they're creating new math? Please explain how any of that matters to the discussion at hand.
Just like we can create different systems of math on a whim. What's your point?
I answered "other" on your poll rather than "fictionalist".
I picked other - the meaning of 2 + 2 = 4 depends on which arbitrary system of math you're assuming when you write it. There are any number of different meanings depending on which you pick, and in many of those cases the sentence contains either undefined terms or is simply false.
Math is just a more formal language, better at communicating some ideas than natural language. Kinda like your fictionalism idea, except that it obviously has some connection to the real world since it can be used to describe things.
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