I will occasionally hear an argument for some position and find that it sounds logical, but on later reflection realize that it really doesn't follow the rules of logic and therefore might lead to a false conclusion. For example, if we are told that "Someone must plug the leak or the boat will sink," and then are told "The leak has been plugged, so the boat won't sink,", we might feel that is a logical conclusion. It turns out that this is not logically valid. Even if the original statement is true, it is possible that both the leak could be plugged and the boat could sink anyway for some other reason.
For us to survive as well as we do, the human mind has to be very good at coming to correct conclusions and making good judgments (despite the occasional blunder) and so it is reasonable to say that it has the ability to perform logically. However to the extent that we are logical, I do not believe it is because we take sequences of statements expressed in words and correctly perform logical deductions on them. If we did, we would not make or accept flawed logical arguments as often as we do. Instead I think the arguments we hear conjure up images or impressions of what is going on, and if our impression is consistent with the conclusion of the argument, we are likely to accept the argument as valid. In the case of the boat, we imagine a situation in which a boat is in danger of sinking because of a leak, and if the leak is fixed the problem will not get any worse and the boat will continue to float. If the statement had been made in the context of a boat in a terrible storm or engaged in a naval battle, our image would be different and we would not be so quick to assume that the leak was the only threat to the boat's sinking.
Suppose someone made the statement: "You must buy a lottery ticket or you will not win the lottery," and later concluded "Since you bought a ticket, you will win the lottery." It is very obvious that this is not a valid argument even though the logic is essentially the same as in the leaking boat case. The situation makes it obvious that the conclusion isn't true, since most people can instantly recognize that having a ticket doesn't guarantee winning a lottery.
The visualization strategy is fairly logical in its own way and seems to be quite adequate for helping us to survive. However it also can lead us to accept a verbal statement that is not correct for situations that are different from what we visualized. It is very different from reasoning using syllogisms and logical proofs that we may learn about in philosophy or mathematics classes.
An article in Science News (Jan. 22, 2000, p56) tells of a psychologist talking to a nomad in central Asia. The psychologist told the nomad that all bears in the North are white, and that a friend living in the North had seen a bear. The psychologist then asked the man what color the bear was. The nomad responded "How should I know? Ask your friend who saw the bear." Apparently western education teaches us how to deal with this sort of question, but people from some other cultures can get along fine without skill at this kind of reasoning.
I think it is important to learn about formal logic and deduction; it is a very useful tool if we are to make good judgments about what is true. But I think it is also important to recognize that it is not a tool we use automatically or even very often. It requires stopping, concentrating, and carefully analyzing what is said.
Is there a way to detect faulty arguments without a great deal of study and practice in formal logical rules? Fortunately I think this can be done fairly well with a simple principle, although it still requires us to stop an reflect for a time. When I hear reasoning I'm not sure is valid, what I usually do is look for a counter-example. Is there a way the conditions in the argument could be true but the conclusion would still be false? In the case of the sinking boat it was not hard to think of ways the boat could sink even if a particular leak was fixed.
I expect that most people look for counterexamples when faced with an argument that leads to a conclusions they disagree with. We are usually pretty good at finding flaws in arguments we don't like. The problem comes if we like the conclusion, or if we are so impressed by the speaker that we assume the person wouldn't make the argument unless it was valid. If we care about not adopting false beliefs, we need to examine not only the logic we don't like, but also things we agree with. It is particularly important to look for the holes in our own reasoning. Of course if we make our points to others who disagree with us, they will probably be eager to "help us out" by pointing out where we are wrong. This is why free inquiry and opening up our ideas for criticism is valuable. Still, most of us usually prefer to find our own mistakes rather than having someone else point them out to us.