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Logic & Scientific Philosophy

After Some Revisions… – Kelly

I awoke this morning to an extraordinarily kind comment from Mr. Stephen Downes, who tore my blog post to shreds.  Well, that is slightly dramatic.  He opened my eyes to just how little I actually knew about how to properly write fallacy and syllogism.  So, after some reiteration, explanation, and revision, here is a (hopefully) more accurate version of what I tried to say last night:

Someone with the last name 'Bryant' is in Africa.
I am Kelly Bryant.
Therefore, I am in Africa.

While the two premises are true, this argument is not sound.

A – Bryant
B – Africa
C – I (Kelly Bryant)

This categorical syllogism follows the form of:

Some ‘A’ is ‘B’.
‘C’ is an ‘A’.
Therefore, ‘C’ is a ‘B’.

The two premises are true, but the form is wrong, making the conclusion false.  The form is wrong because there are two particular premises.  This argument is not vaild or sound.  My sister, Stacey Bryant, is currently in Uganda, so it is truthful to say that ‘Someone with the last name Bryant is in Africa.’  My last name is clearly also Bryant, making the second premise also truthful.

This is where the categorical fault in logic takes place. To categorize accurately, you would need to use the form of Disjunctive Syllogism:

Either Kelly Bryant or Stacey Bryant is in Africa.
Kelly Bryant is in Port Coquitlam.
Therefore, Stacey Bryant is in Africa.

This argument is both valid and sound.

A: Kelly Bryant
B: Stacey Bryant
C: Uganda

A disjunctive syllogism uses the following form:

Either ‘A’ or ‘B’ is a ‘C’.
‘A’ is not a ‘C’.
Therefore, ‘B’ is a ‘C’.

Typically, the word ‘either’ and ‘or’ mean ‘either or both’, not ‘either but not both,’ which makes this argument more difficult to accurately prove.  However, I began with saying ‘either’, meaning ‘one or both’ is in Africa, but then went on to say that one of the terms was in Port Coquitlam, making it clearly not in Africa.  This proves that the other term must be in Africa.  ‘Kelly Bryant’ (A) is clearly not in Africa, and one of the terms must be in Africa, so that soundly concludes that ‘Stacey Bryant’ (B) must be in Africa.

Stacey Bryant hanging out by the Nile in Africa

Kelly Bryant taking a nap in Port Coquitlam

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Discussion

2 thoughts on “After Some Revisions… – Kelly

  1. Much better, and your formalizations are correct.

    This sentence is wrong, however: “The two premises are valid, making the conclusion valid, but not sound.”

    It’s a bit tricky.

    We use the words ‘valid’ and ‘sound’ only to describe *arguments* as a whole. We use the words ‘true’ and ‘false’ only to describe parts of arguments, and specifically, premises and the conclusion.

    So we would say ‘the two premises are true’, not ‘the two premises are valid’. We would say ‘the argument is sound’, not ‘the conclusion is sound’.

    Posted by Stephen Downes | October 4, 2012, 10:30 am

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