Deduction Induction Truth Kareem Khalifa Department of Philosophy

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Deduction, Induction, & Truth Kareem Khalifa Department of Philosophy Middlebury College

Deduction, Induction, & Truth Kareem Khalifa Department of Philosophy Middlebury College

Overview • • • The Central Issue Deductive Validity Inductive Strength Deductive Validity vs.

Overview • • • The Central Issue Deductive Validity Inductive Strength Deductive Validity vs. Inductive Strength Validity vs. Truth Exercises

The Central Issue • Recall: an argument is a set of propositions such that

The Central Issue • Recall: an argument is a set of propositions such that one member of that set, the conclusion, can be affirmed on the basis of the others, the premises. • What does it mean for a proposition to be “affirmed on the basis” of other propositions?

Deductive Validity: The Gold Star • If the premises guarantee the truth of the

Deductive Validity: The Gold Star • If the premises guarantee the truth of the conclusion, then the conclusion can always be affirmed on the basis of the premises. • In other words, there is no way that the premises could be true and the conclusion could be false. That’s a guarantee!

Example of a deductively valid argument • Premise: If Khalifa is a mammal, then

Example of a deductively valid argument • Premise: If Khalifa is a mammal, then Khalifa is warm-blooded. • Premise: Khalifa is a mammal. • Conclusion: Khalifa is warm-blooded.

Deductive Validity: The Official Definition • A deductive argument is valid when, if all

Deductive Validity: The Official Definition • A deductive argument is valid when, if all of its premises are true, its conclusion must be true. • This is the SINGLE MOST IMPORTANT CONCEPT IN THE CLASS!!!!! • Failure to define validity properly is an automatic 5 point penalty on anything you do! You’ll also be very confused if you don’t get this concept.

Inductive Strength • So, deductive validity describes one way in which a conclusion can

Inductive Strength • So, deductive validity describes one way in which a conclusion can be affirmed on the basis of its premises: the iron-clad guarantee. • However, we have many good arguments that do not provide such guarantees, for example…

 • All observed peaches have pits. So all peaches have pits. • Previously,

• All observed peaches have pits. So all peaches have pits. • Previously, when I flip the switch, the light goes on. So the next time I flip the switch, the light will go on. • My parents have told me my name is Kareem Khalifa. So my name really is Kareem Khalifa. • There is a strong correlation between smoking and lung cancer. So smoking causes lung cancer.

Deductive validity versus inductive strength • Recall: A deductive argument is valid when, if

Deductive validity versus inductive strength • Recall: A deductive argument is valid when, if all of its premises are true, its conclusion must be true. • Compare: An inductive argument is strong when, if all of its premises are true, its conclusion is probably true.

Why would we ever settle for inductive arguments? • Deductive arguments require certainty; but

Why would we ever settle for inductive arguments? • Deductive arguments require certainty; but we often have to reason with incomplete information. • Conclusions of deductive arguments contain no new information over and above their premises; we often have to reason in order to gain further information. • Much of our reasoning is sensitive to background knowledge. Only inductive reasoning allows us to adapt our reasons to changes in our background knowledge. • These considerations need to be weighed against the inherent risk involved in inductive inference.

Invalid vs. Inductively strong arguments • Deductive validity: no way the premises are true

Invalid vs. Inductively strong arguments • Deductive validity: no way the premises are true and the conclusion is false. • Deductive invalidity: some way the premises are true and the conclusion is false. • Inductively strong: unlikely that the premises are true and the conclusion is false. • So inductively strong arguments are deductively invalid arguments. How do we distinguish them?

Possible replies • Copi & Cohen: Deductive arguments (valid or invalid) claim to be

Possible replies • Copi & Cohen: Deductive arguments (valid or invalid) claim to be valid; inductive arguments (strong or weak) claim to be strong. (30) • My preference: It doesn’t matter. If the argument is invalid, be aware of – How it is possible that conclusion is false when premises are true; AND – How probable it is that the conclusion is false when premises are true. • You should be considering this regardless of what the argument claims to do!

Validity versus truth • Recall: a deductive argument is valid when, if its premises

Validity versus truth • Recall: a deductive argument is valid when, if its premises are true, its conclusion must be true. • This does not say that valid arguments actually have true premises or true conclusions. • Validity only concerns the connection between premises and conclusion. But weak things can be connected by something strong.

Implications for logic • Propositions are true/false; arguments are valid/invalid. – This is an

Implications for logic • Propositions are true/false; arguments are valid/invalid. – This is an important conceptual point. • Deductive logic can tell us if a conclusion necessarily follows from a set of premises, but it cannot tell us if the premises and/or conclusions are true/false. – That’s why there are disciplines other than logic! • There can be valid arguments with false premises and/or false conclusions. – We saw this last class.

Exercise 1 • Valid, 1 true prem, 1 false prem, false concl. – If

Exercise 1 • Valid, 1 true prem, 1 false prem, false concl. – If Khalifa is a lizard, then Khalifa is a reptile. – Khalifa is a lizard. – Khalifa is a reptile.

Exercise 2 • Valid, 1 true prem, 1 false prem, true concl – If

Exercise 2 • Valid, 1 true prem, 1 false prem, true concl – If Khalifa is a koala, then Khalifa is a mammal. – Khalifa is a koala. – So Khalifa is a mammal.

Exercise 3 • Invalid, two true prems, false concl – If Khalifa is a

Exercise 3 • Invalid, two true prems, false concl – If Khalifa is a human, then Khalifa is a mammal. – If Khalifa is a mammal, then Khalifa is warmblooded. – So, Khalifa is not a human.

Exercise 4 • Invalid, two true prems, true concl – If Khalifa is a

Exercise 4 • Invalid, two true prems, true concl – If Khalifa is a human, then Khalifa is a mammal. – If Khalifa is a mammal, then Khalifa is warmblooded. – Khalifa is right-handed.

Exercise 5 • Valid, with 2 false prems, true concl – If Khalifa is

Exercise 5 • Valid, with 2 false prems, true concl – If Khalifa is an amoeba, then Khalifa is a vertebrate. – Khalifa is an amoeba. – So Khalifa is a vertebrate.

Exercise 6 • Invalid, two false prems, true concl – There are exactly two

Exercise 6 • Invalid, two false prems, true concl – There are exactly two students in PHIL 0180. – Middlebury tuition costs two dollars. – 2+2=4.

Exercise 7 • Invalid, 1 true prem, 1 false prem, true concl – If

Exercise 7 • Invalid, 1 true prem, 1 false prem, true concl – If Khalifa is a reptile, then Khalifa is a vertebrate. – If Khalifa is a vertebrate, then Khalifa is warmblooded. – So Khalifa is a vertebrate.

Exercise 8 • Valid, true prems, true concl—called a SOUND argument – If Khalifa

Exercise 8 • Valid, true prems, true concl—called a SOUND argument – If Khalifa is a human, then Khalifa is a mammal. – Khalifa is a human. – So Khalifa is a mammal.