The Presentation, Critical Elements and Structure of a Deductive Argument

A deductive argument is one which uses a series of premises to attempt to structurally guarantee a conclusion. For example, if we say that all A are B, and that all B are C, we can conclude that all A are C with complete certainty, assuming that the first two premises are true. An argument can be said to be deductively valid if it is impossible to have all of the premises be true while the conclusion is false. Deductive arguments are structural because, as in the given example, we do not need to know what "A," "B," and "C" actually are to be able to accurately draw a conclusion. If you so desired, you could even draw out the argument structurally. Imagine a circle labeled "A." This circle is completely enclosed in a larger circle labeled "B." This illustrates "all A are B," as the entirety of the A circle is within the B. If we now draw an even larger Circle C around Circle B, we add the premise "all B are C." Looking at the structure of the three circles, you can see that there is no way for an A to be outside of Circle C given the premises on which the argument is built.

An inductive argument, on the other hand, cannot be presented in such a rigidly structural way, and cannot be made (at least not validly) without actually knowing what "A," "B," and "C" actually are. An enumerative inductive argument offers a series of premises in an attempt to make a conclusion seem more probable. Inductive arguments make no structural guarantee of a true conclusion. If we say that A, is a B, and that A2 is a B, and that A, is a B, we can attempt to conclude that all As are Bs, or simply that the next A will be a B. For a specific example, you can say "I saw 50 geese and all 50 were white, therefore, all geese are white."

Of course, your observation of 50 white geese does not guarantee that no goose of any other color exists, but it does offer some evidence that seems to make the case for all geese being white at least somewhat more believable. If you were to say "I observed 100,000 geese, and all 100,000 were white," you might be able to convince more people, but your conclusion would still not be guaranteed. This is where philosopher and ever-the-skeptic David Hume raises an objection. What, exactly, makes an inductive argument good?

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Since no inductive argument guarantees a conclusion, it seems as if it is difficult to make a case for what makes an inductive argument valid, or even useful. If I were to say "I saw one white goose, therefore, all geese are white," it seems unlikely I would be able to convince you, or anyone with even the slightest ability to think critically, that all geese are indeed white. But what is the number of observations required for me to convince you? The correct number for my inductive argument to be considered a good one? Certainly ten would be better than one, but it still feels like it leaves something to be desired. Is it 100 then? 1,000? There simply isn't an answer to this question, and this, according to Hume, shows that inductive arguments can never be good, or at the very least, that we can't know when they are good.

Even if we hold up hundreds of thousands of inductive arguments that seem to be valid with a set number of premises, we still can't argue that this makes inductive arguments in general, valid. Why is that? Well, if I hold up 100,000 examples of inductive arguments with, say, 100,000 premises each, all of which seem to lead to valid conclusions, and say "this shows that inductive arguments are valid," the very thing I'm doing is making an inductive argument. I'm laying out premises (the 100,000 examples of seemingly valid inductive arguments) and drawing a conclusion from them. Hume says, and many would agree, that you can't use an inductive argument to argue for the validity of inductive arguments.

To answer this problem of induction, Hume says that while there are no valid inductive arguments, we do develop "habits of expectation." What this means is that, over time, our experiences teach us what sort of inductive arguments tend to hold, and what sort tend to turn out false. From this we develop a habit of trusting inductive arguments which seem to match up with the type that tends to be valid, and a habit of distrusting arguments which match up with the type that tends to be invalid. That is why you are probably not convinced with my "I saw one white goose" example. You have formed a habit of expecting inductive arguments with only one premise to be faulty at best.

René Descartes argued for a demarcation (or a defined line between) science and non-science based on his premise of Cartesian Dualism (the idea that the world is made up of matter, or extended substance, and mind, or thinking substance) and a desire for mechanical explanations for the world over explanations involving teleology and entelechies (explanations involving objects having agency, desire, and/or a potential to fulfill). Isaac Newton, on the other hand, developed a system of demarcation between science and non-science based on one thing: testability. Newton simply says that if something is testable, then it is science, and if it's not testable, then it's not science.

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