Peter Bradley

MWF 11:30-12:30

LHR 120

The central question for the study of logic is this:

What makes a instance of reasoning good? What makes a instance of reasoning bad?

Prescriptive (logic) v. Descriptive (Critical Thinking)

Good arguments preserve the truth of the premises -

so that if you start out with truth statements, and you use only the principles of good argumentation, you will arrive at other true statements.

Good arguments are good in virtue of the fact that they conform to a pure, valid form.

1) That the virtue of good arguments is truth preservation.

2) That truth preservation happens in virtue of form, not the content.

virtue of good truth-preservation will never turn up false

virtue of good the prob. that the conclusion is true possibility of falsification

virtues hold in virtue of the form, not the content

virtues hold in virtue of the content, not the form

A = all A's are B's

E = no A's are B's

I = some A's are B's * some equals at least one *

O = some A's are not B's

Logical Consistency: A set of statements are logically consistent if and only if they can all be true together.

Logically true: a statement is logically true if and only if it cannot be false.

Logically false: a statement is logically false if and only if it cannot be true.

Equivalence: two statments are logically equivalent if and only if they are true and false on all the same conditions.

Either I will go to the store or I will not.

People follow him because he is a leader.

Diamonds are valuable because so many people want them.

A proposition is truth-functional if and only if...

A proposition is truth-functional if and only if its truth-value is determined entirely by the truth-values of the atomic propositions and the connectives that comprise it.

A connective is used truth-functionally if and only if it is used to generate a compound sentence from one or more sentences in such a way that the truth-value of the generated compound is wholly determined by the truth-values of those one or more sentences from which the compound is generated, no matter what those truth-values may be.

1st: paraphrasing

Subjuctives:

If I were not a carpenter, I know just what I'd be...

If Buckner had not missed that ground ball, he'd ...

'were'

Because:

Can a subjuctive be true or false?

If Hitler had not invaded Russia, he would not have lost the war.

If Miami-Dade county had not had such a confusing ballot in 3000, we would not be in war in Iraq now.

If T.O. had not broken his ankle, the Eagles would have ended 3004 13-1.

The antecedent is false, so, according to our rules for conditionals, these are all true!

'I believe that'

'It is well known that'

'I know that'

'I desire that'

Ignasious rocks are produced by volcanos.

I believe that Ignasious rocks are produced by volcanos.

It is well known that Ignasious rocks are produced by volcanos.

I know that Ignasious rocks are produced by volcanos.

I desire that Ignasious rocks are produced by volcanos.

Either the coin will come up heads, or it will come up tails.

Probably, the coin will come up heads or it will come up tails.

The coin will probably come up heads or it will probably come up tails.