Essential Deduction

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Essential Deduction

• Techniques of
• Constructing Formal Expressions
• Evaluating Attempts to Create
• Valid Arguments

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Consider these arguments...
If Thos. Paine advocates it then somebody
questions it. Thos Paine advocates it.
Therefore, somebody will question it.
If Thos. Paine advocates it then somebody
questions it. Somebody is questioning it.
Therefore, Thos. Paine must be advocating
it.
Note One argument is better than another if it's
more reliable. Is one of these arguments better
than the other?
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Consider using claim variables...
A claim variable is a letter or other symbol that
stands for a claim, or proposition.
For example... P - Thomas Paine advocates it. Q -
Somebody questions it. R - Paul Revere advocates
it.
In the box above, P, Q, and R are claim variables
representing three different sentences.
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Consider these arguments formally...
We'll use these variables... P - Thomas Paine
advocates it. Q - Somebody questions it.
If P then Q P Therefore, Q
If P then Q Q Therefore, P
One argument form is better than the other if it
is more reliable. Is one of these argument forms
better than the other?
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Modus Ponens
If P then Q P Therefore, Q
Modus Ponens is a valid deductive form. Any
argument that is in this form and has true
premises will have a true conclusion.
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IMPORTANT POINT A valid deduction is perfectly
reliable. This means that if the premises of an
argument are true, the conclusion must be true.
And that's pretty much all it means. "Valid" is
a word that describes reliable logic. It does
not mean the premises are actually true.
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Affirming the Consequent
If P then Q Q Therefore, P
Affirming the Consequent is an invalid form. An
argument that is in this form and has true
premises may or may not have a true conclusion.
Invalid arguments are not completely reliable.
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Modus Tollens
If P then Q Q Therefore, P
Modus Tollens is a valid deductive form. Any
argument that is in this form and has true
premises will have a true conclusion. The ""
means "not".
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Denying the Antecedent
If P then Q P Therefore, Q
Denying the Antecedent is an invalid form. An
argument that is in this form and has true
premises may or may not have a true conclusion.
Invalid arguments are not completely reliable.
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Chain Argument
If P then Q If Q then R So, if P
then R
The Chain Argument is a valid deductive form.
Any argument that is in this form (including any
number of premises, as long as they can be
arranged as a chain) and has true premises will
have a true conclusion.
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Reversed Conclusion Chain Argument
If P then Q If Q then R So, if R
then P
The Reversed Conclusion Chain Argument is an
invalid (i.e., unreliable) form. An argument
that is in this form may have true premises and
(unlike a valid form) still have a false
conclusion.