# If a = b, then 1 = 2

Discussion in 'General Philosophy' started by Speakpigeon, Oct 6, 2019.

1. ### SpeakpigeonValued Senior Member

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Are you able to explain what would be illogical in the implication:

If a = b, then 1 = 2
EB

3. ### BaldeeeValued Senior Member

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From a syllogistic point of view, it is simply a non sequitur.

From a mathematical point of view, to get to the conclusion you would need to be dividing, somewhere along the line, by zero.

e.g. if a = b then a-b=0, and thus 1 (a-b) = 2 (a-b) or in effect 1 * 0 = 2 * 0.
Divide both sides by (a-b) and you get 1 = 2.

Alas, dividing by zero results in the answer being undefined, where the "logic" breaks down.

5. ### TheFroggerBannedValued Senior Member

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"IF!" That does not mean, "is."

7. ### SpeakpigeonValued Senior Member

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I know it is but saying it doesn't follow is no explanation.
EB

8. ### davewhite04Valued Senior Member

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It makes perfect sense in software programming.

EDIT: Misread question. How would it not make sense? What you are trying to achieve decides if it is illogical or not. What is the point?

9. ### James RJust this guy, you know?Staff Member

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There's nothing illogical about that. It might be a fragment of some kind of logical argument, for all we know.

Working with the information we're given, we don't know what "a" and "b" are. If a is 1 and b is 2, for instance, then it's a logically valid statement.

10. ### SpeakpigeonValued Senior Member

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You have only shown that even if we added the usual arithmetic axioms, the one particular proof you can think of would be invalid.
You haven't shown why it is a non sequitur.
We don't need to assume anything else but what the question says: If a = b, then 1 = 2. We only have to assume what the symbols "a", "b", "1", "2" and "=" all mean.
EB

11. ### SpeakpigeonValued Senior Member

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I'm asking you to explain why "If a = b, then 1 = 2" would be illogical.
EB

12. ### SpeakpigeonValued Senior Member

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???
A fragment?
You think the complete argument could be for example "If 1 = 2, then if a = b, then 1 = 2"?!
You think I am just playing stupid games or what?!
Yes, that's exactly what I asked. Why can't you stick to that?
So, you've just proven a different argument.
Funny how you systematically choose to reply to a different question than the one I asked!
Sure, if Trump was a good man, the world would be different. Anything else?
So, derail. Bravo.
EB

13. ### Gawdzilla SamaValued Senior Member

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"a" is the output of motor #1
"b" is the output of motor #2.

a = b means they have the same output.

No need to constrain it to single integers with no context.

14. ### BaldeeeValued Senior Member

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If you wish to show a mathematical proof that doesn’t involve division by zero, feel free.
The only time the conclusion can be considered true is when 1x = 2x and you divide by x to arrive at the conclusion.
1x only = 2x when x is zero.
And the equation boils down to “one heap of nothing is the same as two heaps of nothing”.
It is possible for the premise to be true yet the conclusion false.
Thus it is invalid.
E.g. let a, b, and 1 all be “an apple”, and 2 be “not an apple”, and “=“ mean “is”.
You thus have the absurd: “if an apple is an apple, then an apple is not an apple”.
I.e. it is possible, under at least one interpretation of what the symbols mean, for the premise to be true yet the conclusion false.
Thus invalid.
Thus a non sequitur, as all formal fallacies are merely specific types of non sequitur.

15. ### davewhite04Valued Senior Member

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It wouldn't be, based on it actually working on my one example.

Is it illogical for everything? No.

16. ### James RJust this guy, you know?Staff Member

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Since you asked ... I think you have something of fixation for "stupid games" like this one. Most of the time, as far as I can tell, you seem intent on catching people out by setting up a scenario in which at some point you get to jump out of the bushes shouting "gotcha!"

Back to the topic.

Your original question in this thread, as you will recall, was "Are you able to explain what would be illogical in the implication: If a = b, then 1 = 2 ?"

I answered that question in full, saying that there is nothing necessarily illogical about that.

Obviously, you don't have a syllogism there. At best, you have a premise of a syllogism. Therefore, it is at best a fragment, like I said.

I stuck to it. You just didn't like the response I gave you, for whatever reason. Maybe you're disappointed you didn't get to jump out of the bushes at me or something. Who knows? What's obvious is that you're struggling to discuss your own topic in a civil manner. I don't know why that is.

Bravo.

17. ### SpeakpigeonValued Senior Member

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Thanks, all good to me.
EB

18. ### SpeakpigeonValued Senior Member

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Sorry, what example?!
EB

19. ### davewhite04Valued Senior Member

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i started writing the code but I... trust me it makes sense in software programming.

20. ### JeevesValued Senior Member

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The character a may equal the character b in several ways, none of which mean, require or imply that the two characters are interchangeable, as they are symbolic of different sounds.
Neither a nor b have any known or demonstrated relation to the numerals 1 and 2. Since these numerals are symbolic of distinct quantities, there is no sense in which they can be equal.
The proposition is both false in some or all of its particulars and nonsensical overall and has no utility in logic.

Write4U likes this.
21. ### Neddy BateValued Senior Member

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In the real world, 1 does not equal 2.

22. ### Write4UValued Senior Member

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a and b cannot have the same output. It is physically impossible. They are in different spacetime coordinates and that alone creates a "difference".

Claiming perfect equality is sloppy science.

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