Question

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Is this logic correct?


In the following statement, the arithmetic is wrong, but is the logic correct? 

If 5+6=14
then
7+7<>14

asked on Saturday, May 08, 2021 09:55:42 AM by

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Answers

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Kaiden
1

Hi, Jim!

         The sentence you have presented, which uses the “if…then” connective, is a sometimes called a conditional sentence. A conditional sentence is neither logically valid nor logically invalid because validity and invalidity are properties of arguments, and a conditional sentence is not an argument. When it comes to a conditional sentence, what we may appropriately ask is whether it is true or false, but not whether it is valid or invalid.

         Is the conditional sentence that you presented true? Yes, it is. In truth-functional logic, a conditional sentence is false just in case its antecedent is true and its consequent is false. But the antecedent of your conditional is false. It is false that 5+6=14. So, the conditional is true.  

         Suppose that you did reformulate the sentence into an argument instead of a conditional sentence…

Premise one: 5+6=14

Conclusion: 7+7<>14

         Is this argument valid? Yes, it is. An argument is valid just in case it is impossible that all of the premises are true and the conclusion false. Mathematically, it is impossible for all of the premises of the above argument to be true. 5+6=14 cannot be true. Since it is impossible that all of the premises are true, it follows that it is impossible that all of the premises are true and the conclusion false. Therefore, the argument is valid.  

Outrageous, yes, I know. 

 

Thank you, Jim

From, Kaiden

answered on Saturday, May 08, 2021 07:02:07 PM by Kaiden

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account no longer exists writes:

Thank you, Kaiden.

posted on Saturday, May 08, 2021 08:48:44 PM
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Bill writes:

Kind of reminds me of non-Euclidean geometry. Which I don't really understand to start with. There is something called multi-valued logic, equally mind-bending. So who knows? Not me. 

posted on Sunday, May 09, 2021 02:35:49 PM
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Bo Bennett, PhD
1

Not enough information:

If A+B=C
then D+D <> C

We don't know what D is.

answered on Saturday, May 08, 2021 11:48:22 AM by Bo Bennett, PhD

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account no longer exists writes:

Hello Bo, as to  :  #I  f A+B=C , then D+D  : agree totally : we don't know what D is.

Now, I clicked on an email link which brought me here, telling me it was an answer to my question :
#2  "If 5+6=14, then 7+7<>14" : is this logic valid (even though the arithmetic is wrong).

Clearly #1 above is an answer to a different question. There appears to be a bit of confusion. Should I post the question (#2) again? Apologies for the confusion ... it's my first post.

 

 

posted on Saturday, May 08, 2021 12:37:54 PM
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Bo Bennett, PhD writes:
[To Jim]

You are welcome to just leave the question here to solicit different answer. If 5+6 = 14, then the numbers are simply placeholders for other numbers. This is why we use variables to make it more clear. We don't know what the number 7 represents in this example, so we cannot know if 7+7 <> 14. So it is the answer to the question, but perhaps someone has a different answer that I am missing.

[ login to reply ] posted on Saturday, May 08, 2021 01:24:03 PM
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account no longer exists writes:

[To Bo]

Thank you. Just to clarify, the numbers are normal numbers, base-10 system with their normal values. It's the IF-->THEN that's in question, in other words, even thought the arithmetic is wrong, is the conclusion valid.

posted on Saturday, May 08, 2021 05:35:01 PM
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Bo Bennett, PhD writes:
[To Jim]

If numbers are base-10 normal values, then 5+6 would not equal 14. Both can't be true simultaneously. If 5+6=14, then we must be in a universe where where these numbers represent something other than base-10 normal values, in which case, we don't have enough information to know if 7+7 <> 14 follows. So you can say this would be a non sequitur .

[ login to reply ] posted on Saturday, May 08, 2021 05:42:51 PM
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TrappedPrior (RotE) writes:
[To Bo Bennett, PhD]

If we assume the Western, patriarchal ways of knowing, of course. From an intersectional viewpoint, 5+6 could equal 14.

[ login to reply ] posted on Saturday, May 08, 2021 06:14:33 PM
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Bo Bennett, PhD writes:
[To Rationalissimo]

Of course, I am such a white western male. :)

[ login to reply ] posted on Saturday, May 08, 2021 06:45:16 PM