In my logic class we are discussing induction/deduction, but the professor makes it seem like deduction is the only sound way to arrive at a conclusion.
You have to look deeper into the word “sound” – it’s a technical concept. It’s a little odd to use the word “sound” rather than “valid”, since soundness introduces something about the premises and not the method of inferring (which is what deduction is about), but maybe something was lost in translation. Inferences that have certain properties are called “valid”, for example:
Premise: P->Q
Premise: ~Q
___
Conclusion: ~P
is a “valid inference”, meaning that it is a sequence of symbols satisfying certain formal requirements. There are various versions of those requirements, such as using rules of inference (sometimes names in Latin – “modus ponens” etc), sometimes using T-tables, or trees, or the dreaded axiomatic / substitution method (a la Kleene). There are also different logics (hence different rules), for example the biconditional is not necessary.
The usual explanation is that a deductive argument is valid iff its conclusion “necessarily follows” from its premises. You need to just take the concept of “necessarily” as a primitive – explanations usually invoke paraphrases such as “could not be otherwise”. The problem with that is that a contingently true statement cannot be false (since it is true), so it could not be otherwise. What they mean is “a rational, logically-trained person could not imagine it being otherwise”. The underlying point is to avoid any concrete ontological commitments, and only focus on the “form” of the argument.
So my question is, if that is true, then how did we come about the knowledge to deduct if not through induction? (the professor said induction wasn’t capable of certainty)
That’s outside the scope of deductive logic. In the classic “All men are mortals” claim, this is just assumed as not requiring proof, or at least what you’re saying is the mortal-Socrates conclusion is not itself certain, but rather it is certain that as long as you assume that all men are mortals and provided you assume that Socrates is a man, then you can say with certainty that Socrates is a mortal. The same holds for the argument “All goats give milk; Socrates is a goat; therefore Socrates gives milk”, the difference being that we would not ordinarily agree that the premises are true.
Maybe I am misinterpreting what induction/deduction is. Are there any books specifically on logic that have an Objectivist’s perspective?
Not specifically that I know of. Peikoff has lectures, and there is a classic (and challenging) book by HWB Joseph An Introduction to Logic, and also Lionel Ruby’s Logic: an Introduction, both available from Paper Tiger.
OH, and also, according to the author of the book we are using for logic, he claims that for deduction, once the logical form is known, the subject matter no longer is relevant in terms of finding out if the premises lead to the conclusion. At face value that seems pretty odd–thoughts?
It’s accurate, in the sense that the concern of contemporary deductive logic is over abstract symbolic relations, so as to avoid the problem of relating epistemology to reality. The purpose is to try to reduce all arguments to steps such as the “P->Q” type step above, where it doesn’t matter what “P” means or what “Q” means.