[W:444:664] Logic 101: How To Properly Reason

gfm7175 · Aug 30, 2018

This thread was inspired by a many-pages-long discussion in another thread about the "begging the question" fallacy and how it actually works.

Lesson #1: What Is Validity

A deductive argument is "valid" if it is formed in a way which it would be impossible for the premises to be true and the conclusion be false. In other words, if the premises are true, then the conclusion is guaranteed to be true.

Lesson #2: How To Test Validity

Step #1: Assume that all premises are true, whether they are true or not.

Step #2: Ask yourself if the conclusion can still be false, given the truths of the premises.

Step #3: If the conclusion can be false, then the argument is invalid. If the conclusion can't be false, then the argument is valid.

What you will notice is that "validity" concerns itself with the form/structure of the argument, NOT the content of it. Thus, an argument can be valid even if its premises are false.

Lesson #3: What Makes An Argument Sound

Step #1: Establish and accept the premises as truth. At this point, the argument is "factually correct".

Step #2: Apply Lessons #1-2 to determine whether the "factually correct" argument is valid or invalid.

Step #3: If the argument is determined to be both "factually correct" and "valid", then the argument is "sound".

Lesson #4: Various Examples of Lessons #1-3

Example #1: If P, then Q... P... Therefore, Q

If I have a cat, I have a pet... I have a cat... Therefore, I have a pet

This argument is logically valid, and if the premises are "factually correct", then the argument is logically "sound".

If pigs fly, hell has frozen over... Pigs fly... Therefore, hell has frozen over.

This argument is logically valid. It is NOT, however, logically "sound" (because it is "factually incorrect").

Example #2: If P, then Q... Q... Therefore, P

If I have a cat, then I have a pet... I have a pet... Therefore, I have a cat.

This argument is logically invalid. Even if the argument is "factually correct", the conclusion doesn't follow from the premises. I could instead have a dog, fish, turtle, snake, etc...

Example #3: If P, then Q... Not Q... Therefore, Not P

If I have a cat, then I have a pet... I do not have a pet... Therefore, I do not have a cat.

This argument is logically valid. If the premises are "factually correct", then the argument is logically "sound".

Example #4: If P, then Q... Not P... Therefore, Not Q

If I have a cat, then I have a pet... I do not have a cat... Therefore, I do not have a pet.

This argument is logically invalid. Even if the argument is "factually correct", the conclusion doesn't follow from the premises. I could instead have a dog, fish, turtle, snake, etc...

Example #5: Not P... If Q, then P... Therefore, Not P

It is not the case that Yoda is green... If Darth Vader is Luke's dad, then Yoda is green... Therefore, it is not the case that Darth Vader is Luke's dad.

This argument is logically "valid". However, it is NOT logically "sound" (as it is "factually incorrect").

Example #6: P... Therefore P

I am a microwave... Therefore, I am a microwave.

This argument is logically "valid". However, it is NOT logically "sound" (as it is "factually incorrect").

God exists... Therefore, God exists.

This argument is logically "valid", and may or may not be logically "sound" (as it may or may not be "factually correct"). Using this argument as a "proof" is a logical fallacy [begging the question], but the argument IS a logically valid argument through the Proof of Identity axiom, so the argument itself is NOT a fallacy.

Lesson #5: Extra Credit

The foundation of logic is, surprisingly enough, circular reasoning... How is this so??!! Through use of axioms... Why??!! Because axioms themselves are circular reasoning (in other words, P... therefore P)

Hopefully this "Logic 101" course will prove beneficial to y'all as y'all make future assertions on Debate Politics...

Best wishes,
gfm7175

gfm7175 · Aug 30, 2018

Re: Logic 101: How To Properly Reason

NOTE

I just noticed that in Example #5, I made a typing error and put "Therefore, Not P" instead of "Therefore, Not Q"

"Therefore, Not Q" is what I meant to type in Example #5...

<alt>doxygen · Aug 30, 2018

Re: Logic 101: How To Properly Reason

Here's a text description for those who might prefer that form:

Introduction to Argument
Structure of a Logical Argument
Whether we are consciously aware of it or not, our arguments all follow a certain basic structure. They begin with one or more premises, which are facts that the argument takes for granted as the starting point. Then a principle of logic is applied in order to come to a conclusion. This structure is often illustrated symbolically with the following example:

Premise1: If A = B, Premise2: and B = C Logical connection: Then (apply principle of equivalence) Conclusion: A = C

In order for an argument to be considered valid the logical form of the argument must work – must be valid. A valid argument is one in which, if the premises are true, then the conclusion must be true also. However, if one or more premise is false then a valid logical argument may still lead to a false conclusion. A sound argument is one in which the logic is valid and the premises are true, in which case the conclusion must be true.

Also it is important to note that an argument may use wrong information, or faulty logic to reach a conclusion that happens to be true. An invalid or unsound argument does not necessarily prove the conclusion false. Demonstrating that an argument is not valid or not sound, however, removes it as support for the truth of the conclusion – it means that the conclusion is not necessarily true.

Breaking down an argument into its components is a very useful exercise, for it enables us to examine both our own arguments and those of others and critically analyze them for validity. This is an excellent way of sharpening one’s thinking, avoiding biases, and making effective arguments.

https://www.theskepticsguide.org/resources/logical-fallacies

It's (IMO) very important to be up front with the definition of the terms (words) used in an argument. Many words have multiple definitions. Context matters.

Angel · Aug 30, 2018

Re: Logic 101: How To Properly Reason

A much needed thread, gfm. This member appreciates your intention.

Personally I am partial to arguments with a conditional premise. The validity of logical form is allowed to display without cavil about the truth of the conditional premise since that is assumed to be true for the sake of argument.

Conditionals and Arguments

https://www2.rivier.edu/faculty/dburgess/web/secondConditional.htm

https://philosophy.lander.edu/logic/conditional.html

devildavid · Aug 30, 2018

Re: Logic 101: How To Properly Reason

How do you establish that premises are true even if they are not? That is a logical failure.

Axioms are not derived by circular reasoning.

More research is needed by the OP to understand how to reason properly.

Class dismissed.

gfm7175 · Aug 31, 2018

Re: Logic 101: How To Properly Reason

devildavid said:
How do you establish that premises are true even if they are not? That is a logical failure.

You don't establish premises as true if they aren't true...

devildavid said:
Axioms are not derived by circular reasoning.

To make my OP "more correct-er" ... Multiple axioms (a set of axioms) are circular in nature. A single axiom is a declaration, a "given rule".

devildavid said:
More research is needed by the OP to understand how to reason properly.

Unsubstantiated claim of my "lack of comprehension" dismissed...

devildavid said:
Class dismissed.

I'm glad you aren't the teacher...

Angel · Aug 31, 2018

Re: Logic 101: How To Properly Reason

devildavid said:
...
More research is needed by the OP to understand how to reason properly.

Class dismissed.

Dismissal again?

Here's your homework:

If G, then B.
If B, then M.
Therefore, if G, then M.

Is this a valid argument?

RAMOSS · Aug 31, 2018

Re: Logic 101: How To Properly Reason

gfm7175 said:
You don't establish premises as true if they aren't true...

To make my OP "more correct-er" ... Multiple axioms (a set of axioms) are circular in nature. A single axiom is a declaration, a "given rule".

Unsubstantiated claim of my "lack of comprehension" dismissed...

I'm glad you aren't the teacher...

There are very many pieces of arguments where the problem with them are they can't show that a premise is true, nor the conclusion is true, yet many people hold onto those arguments very dearly. '

Angel · Sep 1, 2018

Re: Logic 101: How To Properly Reason

RAMOSS said:
There are very many pieces of arguments where the problem with them are they can't show that a premise is true, nor the conclusion is true, yet many people hold onto those arguments very dearly. '

There's a question up in #7 for you.

Anarchon · Sep 1, 2018

Re: Logic 101: How To Properly Reason

This thread will make most of the folks on this board run in terror. That said, great topic. :beer: :thumbs:

Angel · Sep 1, 2018

Re: Logic 101: How To Properly Reason

devildavid said:
... how to reason properly...

RAMOSS said:
There are very many pieces of arguments where the problem with them are they can't show that a premise is true, nor the conclusion is true, yet many people hold onto those arguments very dearly. '

Angel said:
...
If G, then B.
If B, then M.
Therefore, if G, then M.

Is this a valid argument?

Answer: YES

That argument is valid.

Now, for our logicians manque, here is the truth table for the valid argument quoted above.

What does this truth table tell you about the truth of the premises and conclusion of our valid argument above?

William Rea · Sep 2, 2018

Re: Logic 101: How To Properly Reason

devildavid said:
How do you establish that premises are true even if they are not? That is a logical failure.

Axioms are not derived by circular reasoning.

More research is needed by the OP to understand how to reason properly.

Class dismissed.

It's like they have learnt that algebra and can show that following the rules of it gives true answers but, they haven't figured out that substituting invalid values into the equations does not give a valid answer.

Anyway, hi everyone, still no signs of an 'immaterial' being produced? I'm shocked I tells ya!

EMNofSeattle · Sep 2, 2018

Re: Logic 101: How To Properly Reason

Angel said:
Dismissal again?

Here's your homework:

If G, then B.
If B, then M.
Therefore, if G, then M.

Is this a valid argument?

Yes, that is a hypothetical syllogism

Angel · Sep 2, 2018

Re: Logic 101: How To Properly Reason

Angel said:
Angel said:

If G, then B.
If B, then M.
Therefore, if G, then M.

Click to expand...

That argument is valid.

Now, for our logicians manque, here is the truth table for the valid argument quoted above.

What does this truth table tell you about the truth of the premises and conclusion of our valid argument above?

What the truth table tells us is that both premises and conclusion are true in every case except one. The one case in which premises and conclusion are false is the case where the antecedent is true (the antecedent is the "if" clause) and the consequent is false (the consequent is the clause that follows the antecedent).

"If P, then Q" is true for every value of P and Q except in the case where P is true and Q is false.

Angel · Sep 2, 2018

Re: Logic 101: How To Properly Reason

William Rea said:
...
Anyway, hi everyone, still no signs of an 'immaterial' being produced? I'm shocked I tells ya!

Hi, Mr Rea! Oh, yes, there have been many signs. Among the latest came at 1:49 AM today when you posted your post.

Angel · Sep 4, 2018

Re: Logic 101: How To Properly Reason

For example.

If God created the universe, then the universe enjoys Divine Warrant.

Whether used as a premise or deduced as a conclusion, there is only one way that this conditional statement is false, and that is if God created the universe and the universe does not enjoy Divine Warrant.

Capish?
D'you unnerstand?

Angel · Sep 4, 2018

Re: Logic 101: How To Properly Reason

And that's why

I ♥ Conditionals

gfm7175 · Sep 4, 2018

Re: Logic 101: How To Properly Reason

William Rea said:
It's like they have learnt that algebra and can show that following the rules of it gives true answers but, they haven't figured out that substituting invalid values into the equations does not give a valid answer.

I suggest you re-read the OP...

William Rea said:
Anyway, hi everyone, ...

deleted Red Herring... Hi!

Angel · Sep 5, 2018

Re: Logic 101: How To Properly Reason

Does this conditional argument pass muster?

If God created life on earth, then "there is a special Providence in the fall of a sparrow."
If "there is a special Providence in the fall of a sparrow," then life on earth is sacred.___
Therefore, if God created life on earth, then life on earth is sacred.

Angel · Sep 6, 2018

Re: Logic 101: How To Properly Reason

Angel said:
Does this conditional argument pass muster?

If God created life on earth, then "there is a special Providence in the fall of a sparrow."
If "there is a special Providence in the fall of a sparrow," then life on earth is sacred.___
Therefore, if God created life on earth, then life on earth is sacred.

What follows from the sacredness of life?
Any takers?

Namaste

Angel · Sep 7, 2018

Re: Logic 101: How To Properly Reason

Angel said:
What follows from the sacredness of life?

The morality of the universe.

Quag · Sep 7, 2018

Re: Logic 101: How To Properly Reason

Angel said:
Does this conditional argument pass muster?

If God created life on earth, then "there is a special Providence in the fall of a sparrow."
If "there is a special Providence in the fall of a sparrow," then life on earth is sacred.___
Therefore, if God created life on earth, then life on earth is sacred.

If God created life on earth then aliens were created by the devil
If the devil created aliens then tomatoes are aliens
Therefore if God created life on earth God did not create tomatoes.

Angel · Sep 7, 2018

Re: Logic 101: How To Properly Reason

Quag said:
If God created life on earth then aliens were created by the devil
If the devil created aliens then tomatoes are aliens
Therefore if God created life on earth God did not create tomatoes.

Invalid.

Quag · Sep 7, 2018

Re: Logic 101: How To Properly Reason

Angel said:
Invalid.

As valid as what you posted

Angel · Sep 7, 2018

Re: Logic 101: How To Properly Reason

Quag said:
As valid as what you posted

No, what I posted is a valid syllogism. What you posted is an invalid syllogism.
Both terms contained in my conclusion are contained in the premises.
Your conclusion contains a term that does not appear in the premises, namely, "God did not create tomatoes."

But gfm and I are delighted you enrolled in this class.
Namaste

[W:444:664] Logic 101: How To Properly Reason

gfm7175

gfm7175

<alt>doxygen

"I want MY WALL!"

Angel

devildavid

Phlegmatic

gfm7175

Angel

RAMOSS

Angel

Anarchon

Resident Voluntaryist

Angel

William Rea

EMNofSeattle

No Russian ever called me deplorable

Angel

Angel

Angel

Angel

gfm7175

Angel

Angel

Angel

Quag

Angel

Quag

Angel