Right, so the major premise needs the help of additional premises–observations, assumptions, axioms, whatever–but you can’t do anything with it alone (short of concluding “All men are black” as per Aristotle’s law of identity).
In formal logic, deduction refs to a pattern of reasoning whereby one starts with a set of premises and arrives at a set of conclusions with strict unwaivering logic–that is, without room for error or doubt. If the premises are true, the conclusions must be true. It’s not enough to just start with premises and stumble your way to a conclusion, the method has to be absolutely rigorous. It’s more than just a continuity of thought between premises and conclusions, it’s a continuity that thoroughly meets the criteria of logic.
Deduction is typically contrasted with induction, which is the method by which we draw conclusions from premises that requires a bit of a leap (or a generalization). For example, every morning I wake up, the sun rises. Therefore, the sun always rises in the morning. This is reasonable, but strictly speaking not logical. Logically speaking, it is possible that the sun won’t rise tomorrow (it might explode or something). Induction is essentially the tendency of thought to jump to conclusions when it feels like it has enough evidence or reasoning, but not necessarily all the evidence or reasoning it could possibly have.
Technically, this means if someone is doing deductive thinking in a sloppy way, they aren’t doing deduction at all.
I could believe that, but when we bring up the unconscious, we’re at the mercy of speculation. What seems like gaps in the logic of one’s thinking might really be unconscious steps in the thinking… but maybe not. Sometimes the unconscious forces that drive our thinking aren’t hidden logical steps, but motives other than being logical or seeking truth (for example, a clergyman arguing for the existence of God isn’t necessarily motivated by showing others the truth, but helping his religion to gain power). When it comes to the unconscious, anything can be proposed. Also, keep in mind that speculation on the unconscious content or motives of another’s mind might just as easily be unconscious content or motives of your own mind being projected onto the other.
A couple points:
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I’m not a logician, but what I gather is that an axiom is not just a baseless or underived assumption, but an assumption that can’t be doubted (or is very difficult to doubt). In Euclid’s geometry, two parallel lines will never meet. How could it be otherwise? ← That’s an example of an axiom. They are ungrounded because they don’t need to be. They are self-evidently self-sufficient. Compare that with the belief in God. Such a belief is questioned all the time and there is no reason to suppose it couldn’t be another way. (There is Einsteinian geometry which will tell you that two parallel lines can meet–just picture them on the surface of a sphere–but I question whether these really count as “lines”.)
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We’re on the same page when it comes to certain axioms being locked into the human brain as a result of natural selection, but then are they really “made up”? In a sense they are–the brain is “making them up”–but from our inner subjective point of view, we’re not making them up, we’re simply cognizant of them. We experience them as truths which we somehow know (like uniformity of nature, or the principle of sufficient reason). This experience can be contrasted with that of being creative with our imaginations, which we very consciously know we’re making up. Furthermore, there’s also a difference between axioms that seem self-evident only because our brains won’t let us think otherwise (or at least makes it very difficult), and axioms that are self-evident because they really are necessary. Uniformity in nature and the principle of sufficient reason are good examples of the former, and David Hume demonstrated this 300 years ago by sharply contrasting what we have a right to say based on strict logic and what we have a habit of saying simply because it seems intuitive to us. Euclid’s geometry, on the other hand, is, as far as I’m concerned, a good example of the latter (probably because geometry is purely an abstract conceptual construct).
What do you mean, they can’t be tested? I would think if anything can be tested, it’s empirical claims. But I suppose you mean that the test you would use to verify it is already the basis upon which you derived the belief, and there is no further test to verify the belief.
And should.