Question

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Reverend Jim

Basic definition is flawed

I've seen this statement made several times by Matt Dillahunty, and again here and I believe the statement, as explicitly stated, is misleading if not outright false. The statement is:

>If the premises are true, then the conclusion must be true.

I understand the intent, and I understand formal reasoning, but a counter-example is

  1. All humans are mortal.
  2. Earth is a planet.
  3. Therefore all dogs go to heaven.

It is obvious that the conclusion must relate to the preceding statements, and the premises must be related, but in logic, precision is paramount, and having such a basic statement such as "If the premises are true, then the conclusion must be true." is just sloppy. Is there a more precise wording of that statement?

asked on Thursday, Aug 14, 2025 03:50:15 PM by Reverend Jim

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Answers

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Mr. Wednesday
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You are correct. The premises being true is only one half of the equation, the other half is that the conclusion must be logically drawn from the premises. An argument which lacks the second half is a logical fallacy. The example you provided is a pretty classic example of a non sequitur . The premises are true, but they have nothing to do with the conclusion, therefore they do not prove the conclusion.

answered on Thursday, Aug 14, 2025 04:06:46 PM by Mr. Wednesday

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Bo Bennett, PhD
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You (or he) is missing an important part:

For the argument to be valid, if the premises are true, the conclusion must be true.”

This is true for deductive arguments.

answered on Thursday, Aug 14, 2025 04:01:57 PM by Bo Bennett, PhD

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Reverend Jim writes:

From ChatGPT:

A deductive argument is a type of reasoning where the conclusion is guaranteed to be true if the premises are true and the reasoning is valid.

Think of it like a math proof or a carefully built domino chain:

If the first statements (premises) are correct,
and the steps from them to the conclusion follow strict logical rules,
then the conclusion must be correct—no exceptions.

So I still don't see anything that precludes two unrelated premises and an unrelated conclusion as there was no definition of "logical rules". Forgive my being so pedantic but more than 50 years as a computer programmer has conditionend me to be unambiguous. I fully (I think) understand the rules of logic even if my undergraduate course in logic is long in the past. I'm just trying to nail down a precise statement of what constitutes a valid deductive argument.

I apologize for the inadvertant down-vote. I was looking for the reply link (couldn't find it) and the up/down buttons did not have a tool tip indicating what they were for.

I'm looking forward to many interesting hours reading your book.

posted on Thursday, Aug 14, 2025 04:15:09 PM
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Bo Bennett, PhD writes:
[To Reverend Jim]

Not a problem, Jim.

Perhaps it is a "given" in logic that the conclusion must follow from the premises. The somewhat sloppy shorthand you referred to is often used to explain the difference between a valid and sound argument. When you say "It is obvious that the conclusion must relate to the preceding statements, and the premises must be related, but in logic, precision is paramount," I would agree - in logic classes, but in casual online debate, especially when both parties claim to be well versed in logic, leaving that out is acceptable.

[ login to reply ] posted on Thursday, Aug 14, 2025 04:50:41 PM
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Reverend Jim writes:
[To Bo Bennett, PhD]

Thnks for the clarity. Now back to the book.

[ login to reply ] posted on Thursday, Aug 14, 2025 05:06:36 PM
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Kaiden writes:

[To Reverend Jim]

You say, “I'm just trying to nail down a precise statement of what constitutes a valid deductive argument.”

A deductive argument is an argument that is intended by the person giving the argument to be such that it impossible for the premises to be true and the conclusion false. A valid deductive argument is a deductive argument that actually is such that it is impossible for the premises to be true and the conclusion false.

A deductive argument can be invalid. In which case, it is a bad deductive argument.  

You say, ‘So I still don't see anything that precludes two unrelated premises and an unrelated conclusion as there was no definition of "logical rules".’

It doesn’t preclude this, as you correctly see. A valid deductive argument can have unrelated premises and an unrelated conclusion. Due to the definition of validity, any argument whose premises are necessarily false is automatically a valid argument, regardless of whether the conclusion is “related” to the premises. This is because if an argument’s premises are necessarily false, then of course the argument is such that it is impossible for the premises to be true and the conclusion false. For instance “I am a boy and not a boy, therefore the sky is blue” is a valid argument. That is not a failure to “nail down” a precise statement of what it means to be valid, in my opinion, but rather that is an oddity of this nailed-down definition of validity.

[ login to reply ] posted on Friday, Aug 15, 2025 09:27:32 PM
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Bo Bennett, PhD writes:

Better way to phrase this is "For an argument to be valid, the truth of its premises must guarantee the truth of its conclusion."

posted on Thursday, Aug 14, 2025 04:39:37 PM
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Reverend Jim writes:
[To Bo Bennett, PhD]

The most recent post in this thread is from Kaiden but I don't see a "reply to" for his post so I'll just reply here.

I don't need any further clarification but I will add that my original question was to a statement made in Dr. Bennet's book. I mentioned Matt Dillahunty only to point out that I'd heard the same statement word for word from another person who has demonstrated knowledge and ability in reasoning.

I maintain that the statement as posted was poorly worded. Dr. Bennett has since posted a much clearer (to me) version. My 50 years as a professional programmer has resulted in a certain level of expertise in that field. In the area of logic, however, I am much less accomplished so I hope you will forgive that my original question was not as precise as it could have been. I asked it out of a desire for clarification. My studies in this area continue.

Thank you all for your feedback.

[ login to reply ] posted on Friday, Aug 15, 2025 09:45:40 PM
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Kaiden writes:
[To Reverend Jim]

Whatever clarity you needed from Dr. Bennett about his book, I’m glad you both have the issue settled now. Thank you both. 

 

[ login to reply ] posted on Saturday, Aug 16, 2025 09:58:25 AM
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Arlo
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As you suggest, a basic statement such as "If the premises are true, then the conclusion must be true." is just sloppy.  It’s a half truth and an example of something that appears commonly.  A proponent will make a statement that, in itself, is correct even if incomplete.  Then, the other party is encouraged to accept it as complete.  The statement is a necessary condition – I.e., if not true the conclusion isn’t supported.  At the same time, it’s not sufficient – I.e., not enough to make the conclusion true.

A more complete description might be to describe the argument as a
syllogism — a three-step method of framing an argument.  At the start is a “major premise​“ — something taken as fact. Next comes the ​“minor premise”, something building on the major premise and again accepted as true.  

Then, a conclusion​ is drawn from blending the major and minor premises.

Major: from A we get to B

Minor: from B we get to C

Conckusion: therefore, from A we can get to C.

Two conditions are needed for the conclusion to be valid:

1) premises must be true, and

2) premises must be linked and must lead to the conclusion.

just saying premises need to be true gets us part way there; but the links need to be there, too.

answered on Thursday, Aug 14, 2025 06:01:58 PM by Arlo

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Kaiden
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Hi Reverend Jim!

 

Your Question informs us that when Dillahunty says “if the premises are true, then the conclusion must be true”, he is doing so in an attempt to provide us with a definition of a certain word. Very unhelpfully, your Question leaves out any clarity on what the word is which Dillahunty was attempting to define. However, Dr. Bennett suggests that Dillahunty is attempting to define the word “valid.” In which case, Dillahunty is right and excellent, not flawed, not sloppy, not false or misleading. A basic definition of a valid argument is in fact “if the premises are true, then the conclusion must be true.” 

Some people here who Answered your question seem to think that Dillahunty’s statement was meant to be a blanket description about all arguments or all syllogisms. However, there is no context to support that thought. Your Question, too, seems to make the mistake of assuming that Dillahunty is defining the word “argument.”

 

Thank you, Reverend Jim.

From, Kaiden

answered on Friday, Aug 15, 2025 09:24:23 PM by Kaiden

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