Why is ID so successful?

Upchurch said:
Indeed I do. It means to repeatedly add a given unit. In this particular case, I added one each time.
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Yes, and to the first unit you add the second unit, and so on and so forth.
 
Iacchus said:
Do the math!
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I have done. I've even taught it. In my professional opinion as both a lexicographer and as a mathematician, Upchurch is spot-on.

Now, tell us what "increment" means and how Upchurch has misused it.
 
The fact that 1 + 1 = 2 is self-evident. This is what makes it timeless.
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cyborg said:
If I want to define a mathmatics where 1+1!=2 I can do so. I can define any sort of mathmatics I want with any rules I want that lead to any sort of bizzare inferrations they may do. That you would choose such a childish example of something supposedly mathmatically 'timeless' indicates to me you really don't know that much about maths. [/B]
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I think perhaps Iacchus means to say that one object plus one object gives you two objects, regardless of base. It is this that he thinks is self-evident.

Iacchus, don't express things mathematically when you aren't discussing mathematics.

~~ Paul
 
Paul C. Anagnostopoulos said:
I think perhaps Iacchus means to say that one object plus one object gives you two objects, regardless of base.
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I'm quite certain that you are correct.

The concept, however, is still wrong. One object and another object does not mean there are two objects, regardless of the base. In base-2, you would have ten objects, not two.

If he were to say, however, that 1 + 1 = 2 is always true in base-3 and up, I would agree. It is implicit in the declaration of the base.
[fquote]It is this that he thinks is self-evident.[/fquote]Therein lies the paradox. "Self-evident" means that the subject (whatever it is) justifies its own truth. Despite being false, Iacchus finds it to be self-evidently* true.

Incidently, I also agree with cyborg's reposted comments above. In my example, I'm assuming standard rules of mathematics.



* is that a word?
 
The concept, however, is still wrong. One object and another object does not mean there are two objects, regardless of the base. In base-2, you would have ten objects, not two.
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Well no, 10 in base-2 is not ten as much as in base-16 10 is not ten either. It is pronounced one-zero and it's value is two and sixteen respectively. MY main point there was about the arbitariness of symbols and numerical representation.

However the stronger argument is that there is no reason I cannot formulate a logical system where by adding one object to another does not give two objects. Such a system may be of limited value but there is no logical reason why I cannot define it so. You may think "oh, in that case there's no REAL mathmatics that does this so my point stands." Wrong again my ignorant friend. I'll tell you why.

Consider geometry for a moment. Would you consider the shortest distance between two-points to always be a line? That two parallel lines never cross? Are these timeless? Yes you say? Dead wrong. There's a whole set of non-Ecludian geometry that deals exactly with such systems where parallel lines do meet and the shortest distance between two points is not a line. In fact Ecludian geometry may only be considered one particular case of an infinite number of possible geometries.
 
Upchurch said:
The concept, however, is still wrong. One object and another object does not mean there are two objects, regardless of the base. In base-2, you would have ten objects, not two.
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There is no "ten" in base 2, any more than there is a "two." You could state that you have one-zero (10) objects. :D

But there is no reason we have to force the question to be stridently mathematical. We can forget about bases and just ask whether, in the real world, it is self evident that one object along with another object gives us two objects, thinking of the words one and two merely as labels for object counts.

~~ Paul

Edited to add: Like Cyborg said.
 
Paul C. Anagnostopoulos said:
We can forget about bases and just ask whether, in the real world, it is self evident that one object along with another object gives us two objects, thinking of the words one and two merely as labels for object counts.
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If we use rabbits as the objects, 1+1 = bunches and bunches.
 
Mercutio said:
If we use rabbits as the objects, 1+1 = bunches and bunches.
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Or the Baldrick approach :

1 bean + 1 bean = some beans

or

1 bean + 1 bean = a very small casserole.
 
1 + 1 = 2

If you have one abstract unit, and add one equal abstract unit to it, you have two of them, is that sum sometimes wrong? Is this proposition not always truth; "System P is consistent if G is not provable within P"?
 
Re: 1 + 1 = 2

Peter Soderqvist said:
If you have one abstract unit, and add one equal abstract unit to it, you have two of them, is that sum sometimes wrong?
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Yes. For example, if I have a lump of mud and stick another lump of mud to it, I don't have two lumps of mud; I have a single, larger, lump of mud. (If you don't like mud, I can do the same thing with a lump of peanut butter.)

If I have a cold room and I add a space heater to it, I get a warm room. If I add another space heater to it, I don't get two warm rooms -- or even necessarily a warmer room.

If I have one happy cat on my lap, and someone adds another happy cat on my lap, I probably now have zero[ happy cats.

And if I have a cup of water and I add a cup of alcohol to it, the resulting solution isn't two cups of liquid.

Of course, if I have a brick and add another brick to it, that does indeed make two bricks.

But why should our hypothetical "abtract units" be defined to -- or indeed, self-evidently have the properties of bricks, instead of lumps of mud or happy cats?


Is this proposition not always truth; "System P is consistent if G is not provable within P"?
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Yes, that proposition is sometimes incorrect. For example, I can develop an inconsistent system where the Godel sentence for that system is not even expressible within the system, and therefore not provable.
 
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