Recap on last week. Causal generalisations. Arguments from analogy

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Recap on last week…

…evaluating inductive arguments….

….inductive generalisations and  causal generalisations…

…. arguments from analogy and authority

Inductive generalisations:

–  Is the premise true?

–  How large is the sample?

–  How representative is the sample?

–  Beware ‘informal’ heuristics – Is there a counterexample?

Causal generalisations:

–  Is the premise true?

–  How strong is the correlation?

–  Does the causal relation make sense or could it be accidental?

–  What causes what?

Arguments from analogy:

–  are the two things similar?

–  are they similar in respect of something relevant?

–  can we find a disanalogy?

Arguments from authority:

–  who exactly is the source of information?

–  is this source qualified in the appropriate area?

–  is the source impartial in respect of this claim?

–  do other experts make other claims?

This week we shall be looking at…

… the distinction between validity and truth…

…at why validity is important…

….and at evaluating deductive arguments

A good deductive argument is SOUND if and only if it:

(a)  is valid  

AND

(b)  has true premises  


Is the argument sound?

True premises

False premises

Valid

Invalid 

9

Is the argument sound?

True premises

False premises

Valid

Sound

Unsound

Invalid 

Unsound

Unsound

10

The truth of the premises is not a matter for logicians or those interested in critical reasoning….

….there are many ways in which we determine the truth or falsehood of premises…

…and these ways do not fall into the scope of a class on critical reasoning


Validity, on the other hand…

…is very much of interest to logicians…

…because validity preserves truth…

…if an argument is valid, then if its premises are true…

…we can be certain its conclusion is true Validity, in fact, is of interest to anyone…

…who is concerned about truth… …because we often don’t know the truth of our premises….

…and we often test the truth of our premises by…

… constructing valid arguments and..

…testing the truth of the conclusion

If we can show that…

…the conclusion of a valid argument is false…

…what do we thereby discover?

Hypothesis:  Smoking causes cancer

Prediction: if smoking causes cancer then every smoker will get cancer Test: each smoker gets cancer

All women are passive

Mrs. Thatcher is a woman

----------------------------------

Therefore Mrs. Thatcher is passive

So what is this relation of validity that everyone is so concerned with?

Here is the best theory that philosophers and mathematicians can come up with…

An arguments is valid…

… if and only if…

… there is no possible situation in which… 

…all its premises are true…

…. and its conclusion false Beware:  it is the possibility of the combination…

…of true premises and false conclusion…. 

….that is ruled out by an argument’s being valid…

(this is why validity preserves truth) Note: it is the possibility

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