I know this is an old post, but I cannot but point out the trickery. For one "+" does not mean "combined with" in the context of cardinal numbers. Second, the set whose members are the two individual lumps of clay has a cardinality of 2. Third, a lump of clay and the material it consists in are not the same objects and do not even belong to comparable ontological categories. One is an individual, cohesive, countable object, the other one is stuff that is not countable. "Clay" is a mass term, "lump of clay" is a count term.Philosophy Explorer wrote:Try this. One lump of clay combined with one lump of clay is just one lump of clay.
PhilX
Is there a way to refute '1+1 = 2'?
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Re: Is there a way to refute '1+1 = 2'?
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Re: Is there a way to refute '1+1 = 2'?
A mathematical truth is only true with respect to its system of axioms, and is not true outside that system.
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Re: Is there a way to refute '1+1 = 2'?
Yes, but it is not a really interesting observation that different propositions can have different truth values. Sure, "1+1=2" can be interpreted differently in different contexts, but that's semantics. The point is that when you interpret the sentence "1+1=2" in the context of set theory / cardinal numbers, then you are entertaining a specific formal proposition involving specific formal concepts. The question has to do with how many truth values does (or can) that specific proposition have, otherwise we are just playing word games - or at least that is my understandingFan of Science wrote:There are actually mathematical systems that deal with adding one lump of clay to another lump and getting one lump. I don't have any personal experience with them, but know they exist from some of the math books I have read.
A mathematical truth is only true with respect to its system of axioms, and is not true outside that system.
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Re: Is there a way to refute '1+1 = 2'?
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Re: Is there a way to refute '1+1 = 2'?
Yes, there is. It is simply
1+1 <> 2.
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Re: Is there a way to refute '1+1 = 2'?
One one kilogram lump of clay plus one one kilogram lump of clay equals one two kilogram lump of clay.
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Re: Is there a way to refute '1+1 = 2'?
gamahucherpress.yellowgum.com/wp-conten ... ssible.pdf
1 number [2] + 1 number[3] = 1 number[5]
ie 1+1=1
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Re: Is there a way to refute '1+1 = 2'?
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Re: Is there a way to refute '1+1 = 2'?
You are comparing apples and oranges.gimal wrote:read Mathematics ends in contradiction.
gamahucherpress.yellowgum.com/wp-conten ... ssible.pdf
1 number [2] + 1 number[3] = 1 number[5]
ie 1+1=1
2 and 3 are different from each other. When you add them together, you get 5, which is different from 2 and different from 3. Yet you claim that they are the same things.
Just because they are numbers.
To you a number is a number is a number.
Well, numbers are different from each other. Different numbers, that is. Ignoring that is ignorant.
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Re: Is there a way to refute '1+1 = 2'?
If you can accept the notion that all things [in the Universe] are unique, then how can "2" exist?
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Re: Is there a way to refute '1+1 = 2'?
Not to mention that when you get to smaller subatomic particles, they are identical.
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Re: Is there a way to refute '1+1 = 2'?
It is only through our intellectual laziness and linguistic conventions that we make two possible, no?
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Re: Is there a way to refute '1+1 = 2'?
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Re: Is there a way to refute '1+1 = 2'?
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Re: Is there a way to refute '1+1 = 2'?
Have you previously asked that?I'll ask again. How is one straight line and another straight line somehow equal to that of a squiggly line?
The squiqqly line is this symbol '2', yes? And the straight line is this symbol - '1' - when not written by a French person. (They always make them look like '7').
I guess the answer is essentially the same as the answer to this question: Why does a whole load of squiggly lines created by one person on one side of the world cause a whole load of different squiggly lines to be generated by another person on another side of the world?
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