Are the premises of deductive arg's. founded upon inductive cases?...help is what I am in need of

Question

Let's take this example of a deductive argument:

P1: Monkeys like bananas.

P2: Lucy is a monkey.

C: Therefore, Lucy likes bananas.

Disregarding whether this argument is true or false, how does one formulate P1 (premise 1)? One cannot deduce that monkeys like bananas from reason alone. We know that monkeys like bananas from numerous cases of actually seeing, via sense experience, numerous monkeys eat bananas. However, aren't we using individual cases (of monkeys eating bananas) to base our P1? To compose an inductive argument:

Case: While at the zoo, I saw 28 out of the 30 monkeys eat bananas.

C: Therefore, monkeys like bananas.

Undoubtedly, the deductive argument seems more air-tight, that is, it's a better argument. But it still doesn't escape the reality, I think, that its P1 is based off inductive cases. But why? Aren't inductive arguments less likely to convey truth than deductive arguments? And if it is true that inductive arguments are less likely to convey truth than deductive arguments, wouldn't a deductive argument stating a premise based off inductive arguments be weakened? Thanks for all of your help in advance.

Answer 1

You have rediscovered an argument made by John Stuart Mill in the 19th century. He was highly critical of syllogistic logic on the basis that in practice we can never know the truth of universal premises, except as inductive generalisations, and therefore we have nothing better than inductive support for the conclusions of such arguments. Like you, he particularly singled out the syllogism you discuss, though his example was, "All men are mortal; Socrates is a man; therefore, Socrates is mortal".

His point is, roughly speaking, that we could never know the truth of the first premise unless we already knew the truth of the conclusion. So either the first premise is an inductive generalisation, and hence uncertain, and so the conclusion is uncertain also, or the argument is question-begging, since we would need to know the truth of the conclusion before accepting the truth of the premises.

Mill's criticism is that all we are entitled to believe is that we have strong inductive support for men being mortal and this in turn means we have nothing more than strong inductive support for the claim that Socrates is mortal. This would make the claim, "all men are mortal" not strictly something we know to be true, and would make the syllogism itself redundant, since we are then reasoning from the observation that lots of men have been observed to be mortal directly to the conclusion that Socrates is probably one of these.

But Mill is really missing a few tricks here. There are at least three classes of case where I would say we can go beyond the claim that a universal proposition is nothing more than an inductive generalisation.

1. Some universals are nomological in character. That is to say, they state something that we might consider to be a law of nature, and our confidence in them is much greater than with a mere generalisation. There are good reasons to believe that all men are mortal: it is baked into our genetics.

2. Some universals are well-attested facts that we can accept on authority. I have it on good authority that Ben Nevis is the tallest mountain in Scotland. So, for any Scottish mountain that is not Ben Nevis, e.g. An Teallach, we can form the syllogism, "all Scottish mountains that are not Ben Nevis are less tall than Ben Nevis; An Teallach is a Scottish mountain that is not Ben Nevis; therefore, An Teallach is less tall than Ben Nevis." The first premise here is known to be true; it is not an uncertain generalisation. And the argument is not question-begging. It would have been question-begging at some earlier time before all the Scottish peaks had been surveyed, but now they have been, we can rely on the first premise without having to know the conclusion.

3. Some universals are true by fiat. Some universals are simply made true by an appropriate authority declaring that they are. If someone shows me a pound coin and asks whether it is legal tender in the UK, I can confidently reply, "all pound coins are legal tender in the UK; that is a pound coin; therefore, that is legal tender in the UK". This is not question-begging. I don't have to inductively examine individual pound coins to know that they all legal tender. The Bank of England says they are legal tender, and it is the appropriate authority on the subject, so that is sufficient to make the first premise true.

Answer 2

There's always a difference in terms of strict soundness between real life or scientific arguments and ideal math/logic-like deductive systems' (theories). In math your above P1 is called axiom, not premise or theorem or inductive reasoned result of the theory. So axiom is utmost important at the beginning for any theory and there's a branch in math called Reverse Mathematics to seek to determine which axioms are required to prove certain theorems of mathematics. Finally although your example premise may not be true, but the form of the fundamental modus ponens logic as a meta inference rule is still perfectly valid, though your argument may not be perfectly sound in reality due to imperfect premise and possibly false conclusion.

The weakness of inductive inference is the so called Hume's problem of induction:

In inductive reasoning, one makes a series of observations and infers a new claim based on them. For instance, from a series of observations that a woman walks her dog by the market at 8 am on Monday, it seems valid to infer that next Monday she will do the same, or that, in general, the woman walks her dog by the market every Monday. That next Monday the woman walks by the market merely adds to the series of observations, but it does not prove she will walk by the market every Monday. First of all, it is not certain, regardless of the number of observations, that the woman always walks by the market at 8 am on Monday. In fact, David Hume would even argue that we cannot claim it is "more probable", since this still requires the assumption that the past predicts the future.