Nope. This is a typical induction, it does follow (non-sequitur=does not follow), it is logically correct (although empirically faulty).

I would have thought that it would be correct if stated as "Therefore anything may be possible", or is that incorrect?

Precisely, it was stated that it is empirically false.

I'm confused. What was stated that what was empirically false? Does the fact that we think something is possible or impossible have any bearing on whether or not a thing is possible? If we define 'possible' as a purely human construct, then maybe, but if we define it as an abstract quality with a kind of truth value independent of human thought, surely the non-sequitur holds.

It is logically correct to induce something from an arbitrary number of observations, although it might be empirically wrong. One or a hundred observations of black crows are enough to assume they all are black (logic does not guarantee the correct use of logic). Although, empirically such logic could be wrong. The only way to know with absolute certainty that all crows are black is observing them ALL. And that's evidently impossible.

Are you confident enough in that for me to delete my response? I don't want to confuse things.

Just think that the only number of observations necessary for an induction to be empirically valid is ALL, but for it to be logically valid is just ONE. Less than ALL observations are not a false induction. Induction is the logical mechanism that leads to a conclusion from a previous and related fact, even if it's a single observation. "Induction is the glory of science and the scandal of philosophy" (C.D. Broad)

I think my biggest hurdle is your point that logic 'does not guarantee the correct use of logic'. I assumed that incorrect use of logic is not logic. In other words, to assume that all swans are black because of one observation can never be logically correct; that a non-sequitur has in fact occurred. I'm curious as to what others think. I have no formal training in this area.

Consider this misuse of mathematics (it is real: this was written by a real kid): A dog has: tail: 1; legs: 4; ears: 2, eyes: 2, snout: 1, teeth: 32. Total = 42. This is an example of how logic and mathematics can be correct, although its application in real life is wrong (a martian scientist would accept this logic without hesitation). More formally, Kant says that logic is pure (independent from experience) knowledge, so, it has no relation whatsoever with its use. Induction is part of logic, but its empiric application (how to use the tool in the real world) is not always correct.

Basically your answer is wrong because you have confused concepts. You have confused deductive reasoning with inductive reasoning. The main distinction between the two is only deductive reasoning leads to certainty. It is guaranteed if all the premises are true. There is no failure if done correctly. Inductive reasoning is what we knsow as the sciences. This requires sense verification where deductive reasoning does not require the senses. Inductive reasoning can only lead to probability above zero and under 100 percent. This is no argument that leads to certainty.

@Logikal. Okay. Thanks. So, just to be clear, you are stating that the fact that 1: 'Flight used to be thought impossible but is now possible', logically leads to a conclusion, that 2: 'Therefore anything we think of as impossible is possible?'. That feels so wrong. What about logical impossibilities? Can they also be deemed possible by this logic?

You seem still to be using the terminology wrong. Inductive reasoning is the type of reasoning that can never lead to certainty. No science can offer certainty. There are no exceptions. Deductive reasoning CAN lead to certainty & is the highest form of reasoning human beings have. The reasoning you are evaluating is impossible to lead to certainty. We must use percentages to determine how accurate the claims are. We know it can't be 100 percent because we know there are false instances.

You seem still to be using the terminology wrong. Inductive reasoning is the type of reasoning that can never lead to certainty. No science can offer certainty. There are no exceptions. Deductive reasoning CAN lead to certainty & is the highest form of reasoning human beings have. The reasoning you are evaluating is impossible to lead to certainty. We must use percentages to determine how accurate the claims are. We know it can't be 100 percent because we know there are false instances.

@Logikal. This might need to go to chat, but I haven't expressed any certainty at all, except for my claim that statement 1 (see previous comment) cannot lead to the certainty of statement 2. It seems to me that if you accept the 2 stage argument of my previous comment, you are accepting as possible all things, even though we know that there are things that are simply not possible. So again, to be clear, are you stating that 2 follows from 1? It is my position that it cannot.

Your answer is correct but your reasoning about the correct answer is bad. There is no conclusion because the reasoning is faulty. You are using terminology that only applies to a deductive argument still. You can't say the conclusion does not follow with inductive reasoning period. There is no guarantee of anything with inductive reasoning. Because the reasoning is inductive we know there are false instances. Also there may be cases where the statement the person used holds true. This means today it can be false & tomorrow it can be true and so on. You can't use FOLLOWS FROM with induction.

@Logikal. Oh. Okay. I'll have to read more about it. Thank-you. I would appreciate a corrective edit of my answer if you can be bothered. It would help me understand where I've gone wrong. Cheers.

Your answer would work if the argument was deductive reasoning. The issue is the language of the reasoning such as THOUGHT or BELIEF or THINKING typically spell out the reasoning is subjective. There is no reliability in any of the statements. It was once believed the Earth was flat is another example of the same kind. People can be wrong about there beliefs!! So nothing logically follows. Correct reasoning should either lead to certainty or a high percentage of truth. When science gets things correct there is a high percentage of truth not a low percentage of truth. We either deal with ce

We either deal with certainty or percentages. There is no third option to choose from. I don't know how to best edit your answer without misrepresenting your thoughts. You could state if the reasoning were deductive reasoning it would be. . . . But this is not deductive reasoning. Or you could state this is inductive reasoning & this is not a COGENT argument. The argument as is could be improved . . . This is what comes to mind now. You can use the ideas but in your own words.

@Logikal. From IEP: "If the arguer believes that the truth of the premises definitely establishes the truth of the conclusion, then the argument is deductive. If the arguer believes that the truth of the premises provides only good reasons to believe the conclusion is probably true, then the argument is inductive". What is it about the way I framed the argument that makes it inductive? I would have thought it was deductive. It comes to a definite conclusion, not a likelihood. This is why the non-sequitur seems to apply.

Let us continue this discussion in chat.

You must find other sources than that one. There are a ton of textbooks that stayed otherwise. An argument is NOT determined by what a person BELIEVES. There are exact criteria what makes an argument deductive or inductive. I stayed deductive reasoning leads to certainty. Inductive reasoning leads to probability at best. Probability indicates the claim has true instances & false instances in reality. Certainty means the result has to be this & could not have been another way. It is neccessary if Sally is a woman then Sally must be a human being. There is no probability there.

I am unable to use the chat now. But there are many sources you can view to see what I am saying is standard. Deductive reasoning should not have the phrases they believed, I believe, I think, etc. Thise are indicator words for inductive reasoning or what people call subjective. Deductive reasoning is the highest form of reasoning known to man because it is certain & constant. A proposition doesn't go from true to false or vice versa EVER.