# How can a false premise still produce a Strong Inductive Argument?

For brevity, I abbreviate: FP = False Premise, SIA = Strong Inductive Argument.

Source: A Concise Introduction to Logic (12 Ed, 2014) by Patrick J. Hurley

[p 46:] These four examples show that in general the strength or weakness of an inductive argument results not from the actual truth or falsity of the premises and conclusion, but from the probabilistic support the premises give to the conclusion.

[p 49:] For both deductive and inductive arguments, two separate questions need to be answered: (1) Do the premises support the conclusion? (2) Are all the premises true?
To answer the first question we begin by assuming the premises to be true. Then, for deductive arguments we determine whether, in light of this assumption, it necessarily follows that the conclusion is true. If it does, the argument is valid; if not, it is invalid. For inductive arguments we determine whether it probably follows that the conclusion is true. If it does, the argument is strong; if not, it is weak. For inductive arguments we keep in mind the requirements that the premises actually support the conclusion and that they not ignore important evidence.

I already understand and so ask not about the quote above. 1. How can a FP still constitute a SIA?

I am confused by these 2 cases (out of a total of 4) that appear paradoxical:
2. 'False premise and Probably true conclusion': How is this possible?
3. 'False premise and Probably false conclusion': How is this possible?

1. If the determination of Strongness needs the extra step of assuming true a FP, then how can the argument be judged 'Strong'?
If a FP were truly Strong, then you needed not this extra step of assuming true a FP!
At least the diction and use of 'Strong' disturbs me.

PS: Etymology helped me to perceive the similarity between Validity (in deduction) and Strongness (in induction), because the etymon of 'valid' (valere) means 'to be strong'. So Validity and Soundness meant the same thing etymologically, except that now the former applies to deduction and the latter induction.

• In logic there is a difference between valid and sound arguments, the latter may be valid (i.e. 100% strong) while having false premises. This is just a probabilistic version of it. – Conifold Dec 16 '15 at 1:49
• @Conifold Thank you; I do understand your reference to deduction. – Accounting Dec 16 '15 at 3:39

The author is using the term "strong" for inductive arguments as an analogous concept to the term "valid" for deductive arguments.

Remember that the definition of validity (at least the one generally used in introductory courses) is that an argument's form is valid if it is the case that it cannot have true premises and a false conclusion. This, in turn, makes it truth-preserving and means that if the premises are true, then the conclusion must also be true.

Calling an inductive argument strong is somewhat analogous in that this is saying (in a slightly more nebulous way) that the premises would very likely lead to the truth of the conclusion.

But in both cases, this structural feature does not mean the conclusion is true. In the case of a valid deductive argument, it means either that the conclusion is true or at least one premise is false. For a strong inductive argument, it means that barring some fact to the contrary, there is much evidence to suggest that conclusion would arrive from those premises, IF these premises were assumed true.

The key is to keep this analogy in mind and as such not to focus on dictionary definitions of "strong" or for that matter "valid" that differ from their technical usage in philosophy and critical thinking.

• Thank you. Please reverse my change if necessary, but is my change necessary to your answer? You DO need to assume the FP true? – Accounting Jan 13 '16 at 23:11

I think the point is that in logic we don't care about the actual truth or falsity of propositions in the real world, only about the validity of the arguments (whether the move from one proposition to another preserves truth). An argument is strong if the conclusion follows from the premises, regardless their truth value.

If you give one or two of "these four examples" referred to (p.46) I might confirm that it is what they mean.

• Sorry for the delay; I forgot to reply to your answer. The 'examples' refer to Table 1.2 on p 50. Google links to it. Google Books features it verbatim here. It is reproduced also here. Can you read these? – Accounting Jan 13 '16 at 23:14