Isn't that exactly the question that informal logical fallacies seek to address?
I don't think you can just throw away the word "logic" like that. We try to make arguments using deduction and inference, so there is a logical structure behind them. It's just that it isn't as well-defined and doesn't have the mathematical rigor of formal logic.
I did link to a book on informal fallacies. And I do not agree with your classification. It's narrow and doesn't reflect the history of the field. Logic is a tool for mathematicians, philosophers, and computer scientists. Like any versatile tool, it can be adapted for different — but related — tasks.
Deductive logical systems cannot reliably find truth. That is the lesson of the scientific revolution and the revolution in mathematics that is most closely associated with Godel.
Yet when people invoke "logical fallacies" they are almost always fallacies in deductive logic. Hey Internet--how about catching up to the 19th century and employing some inductive reasoning in your arguments?
The problem with that, though, is that the starting point is facts. The arguer actually needs to possess domain knowledge/experience. It's so much more convenient to mock an inferred deductive structure...no real facts required!
Given that logics (of all sorts) are subsets of mathematics, I'm not sure one can convincingly hoist (any) logic above all other mathematics to make arguments.
I didn't mean to imply that the fallacies have anything in particular to contribute to symbolic logic. It's just that, when one takes a logic course, one expects to leave the class with better logical skills, both formal and informal. Gracefully, most logic teachers and books take the time to briefly cover some additional topics such as the fallacies.
But how do you know that "informal logic" has anything to do with formal logic? Outside of math, formal logic seems actively misleading. For example, the "principle of explosion" (from a contradiction follows anything) is definitely not how people think.
Philosophically, I prefer the reasonable / rational / meta-rational framework explained by David Chapman. [1] But if you want to know how people ordinarily think, better to study how they think.
(And in practical everyday use on the Internet, I find logic mostly useful for for shooting down attempts at inappropriately applying logic to conclude things that you can't safely conclude.)
Thank you very much - and to 'foldr and 'TeMPOraL as well. Yes, I was referring to the logic/reasoning education/experience that one tends to gain in "STEM" - as an example of study outside of the humanities, which I had mentioned in point 3. Not direct/explicit study.
>Your point (4) appears to implicitly making the claim that learning formal logic (or rather, "informal formal logic") doesn't help much with informal logic.
No. My point is that formal logic isn't sufficient, not that it isn't valuable or necessary. It is indeed very valuable and necessary.
>Doing any sort of serious math, you will learn how an argument really works, how to take it apart.
Your "really" there is presuming the thing in dispute, which is what is a "real" or paradigm case of argument/logic. Is it artificial formal language/symbols, or how people actually talk? In the vast majority of circumstances in which we are called upon to reason, the materials we must work with are natural language arguments. At the very least, study in informal logic is useful for understanding what's different about natural language argument; what can go wrong when converting it into formal expression; etc. As you noted, a good mathematician makes even natural language arguments precise "when possible". That requires knowing when is it "possible"; what can and can't be expressed in formal terms; whether some concepts (like democracy, art, etc.) are essentially contestable, which I presume presents difficulties for formalized expression; when is inconsistent nomenclature worth stopping and resetting over; how does one do interpretation; what can go wrong with interpretation; etc. And here's an important one: When are we better off without precision? (For example, would we be better off as a society if the meaning of "cruel and unusual punishment" could be expressed w/ mathematical precision? Some norms are valuable because they facilitate debate rather than settle debate.) If a good mathematician has a sense for all of these things, that sense is no doubt strongly aided by foundation in formal logic. It would also be aided in different ways by foundation in informal logic, but my sense is informal logic is relatively neglected.
Obviously I'm speaking in the vernacular and as I stated I used the terms as they meant to me.
Besides logically sound and sound argument aren't the same thing in my mind. One refers to soundness of logic and the other to soundness of the argument. And that was the essence of my point. There's a difference in talking about an argument and talking about the logic used. Logical fallacies are only useful in determining if the reasoning was flawed.
I didn't disagree with anything you wrote and even clarified my meaning so as to be clear. There is also the fact that, linguistically speaking, every person has a unique language. The meaning of words can vary slightly between people who nominally speak the same language. That's why I mentioned to me in my previous post.
Clearly I was not writing in a mathematically precise way. I took mathematical logic in graduate school many years ago but am not qualified to use all of the terminology in a mathematically precise way. But this is an internet forum and not a course in mathematical logic. The standards of rigor are not so strict. Hence my phrase to me ought to have sufficed as far as clarification.
Logic a fundamentally different process of intellectual productivity, which is why mathematicians don’t see proving and reasoning as the same thing. Formal methods weren't even widespread until late in mathematical history, yet somehow we had mathematical productivity.
Mathematicians can scarcely describe their own thinking process, and proving is often the last step to mathematical reasoning.
Talking about logical fallacy in ordinary conversation is backward.
"this book is aimed at newcomers to the field of logical reasoning"
What I find in practice with these (quite popular) lists of logical fallacies, is that they are usually written with the assumption that the reader is already familiar with the fundaments of logic and is able to correctly apply them.
This work is no different. While I do enjoy the style of the illustrations, we already have a glut of these things skipping to the juicy parts. What we don't have is approachable, accessible works, free of unexplained jargon, that explain for instance, what exactly a "premise" is. How to decide whether a piece of writing or speech contains an argument. How to correctly identify the conclusion of an argument, and connect it with its premises. And so on, for all the list of things that are usually misunderstood about these lists of "fallacies" by people who are… reallly.. genuinely new to logic.
But us logical people cannot resist fixing lack of logic. It's in our bones. By "logic" I mean that our arguments are based on an explicit line of reasoning that we can articulate. When people ignore logic and trust their own or someone else's vague intuition instead, us logical people get a mental rash.
I think your point (4) has substantial problems. I mean, as other commenters have already noted, hardly anyone in STEM studies formal logic. But OK. Let's suppose you mean "informal formal logic" -- not actual formal logic, but that sort of essential sense of how predicate logic works, that it becomes a backbone of much of your thinking. Math teaches that, as do subjects which are essentially math; but does the rest of "STEM" teach that? I'm not sure that's even true. Many quantitative disciplines look terribly sloppy from my point of view.
But let's get to something more interesting. Your point (4) appears to implicitly making the claim that learning formal logic (or rather, "informal formal logic") doesn't help much with informal logic. I don't think that's right at all. Learning that sort of formal logic is a great way to learn informal logic, and I think this works much better than the other way around. Doing any sort of serious math, you will learn how an argument really works, how to take it apart. Largely you will learn this from the numerous errors you and other people will make. ("Oops! I swapped the quantifiers!") You will see contradictions presented to you and have to find the mistake. I think it's easier to learn to spot errors in this setting, where you can say certainly what's right and what's not, and then move to the fuzzier setting.
Like, the arguments I see most people making most of the time are so bad, and they'd be better if they had experience with actually finding holes in arguments, and learned to apply this to their own. Well, that's what a mathematician does. In an informal setting, of course, almost everything is potentially a hole -- and so of course you learn to explicitly lay out your assumptions, ask the reader to bear with you or spot you an inference, and otherwise explicitly acknowledge where you're making a jump.
Because really, the worst errors in informal reasoning also pop up in formal reasoning. The biggest problem I typically see with people's arguments is equivocation. That's something you learn to spot doing math! And because terms in math are overloaded, you learn to break things down, to say, "OK, we've got 'continuous' in this sense, and 'continuous' in that sense...". Learning to spot equivocations and break down concepts would help people a lot.
My experience is that mathematicians, being familiar with this sort of thing, are in fact better at informal logic than most people, by a substantial amount.
I mean, I know there's the idea of the engineer who attempts to perform (informal) formal logic on e.g. politics, taking various statements as axioms and writing down the conclusions, without noticing that the terms used in the axioms aren't used in a consistent manner, or that the axioms are ill-specified, or that the terms don't connect to anything we actually care about, etc., and coming to ridiculous conclusions. And it's possible some forms of STEM teach that, this taking of imprecise things and treating them as if they were precise, because such people certainly exist (they're easy enough to find on the internet). But my experience is that a mathematician instead learns to notice equivocations, notices imprecision, and to actually do the work of taking things that are ill-specified and making them well-specified (when possible).
Basically, pretty much all the advantages people talk about for learning philosophy, to me seem to come up in math as well. The one big exception, I think, is learning not to take texts at face value, to wonder what the author is trying to accomplish by writing this. A math paper may contain errors, but you can typically assume it's a good-faith effort at truthseeking. Whereas that is something that's definitely necssary in other fields.
Of course, though my point was about the term "logic" in general rather than "formal logic". I am happy to say that Hegel's logic isn't a formal logic, but it's not exactly what we know to be "informal logic" either (i.e arguments and fallacies). Funnily enough, a Boolean opposition between formal and informal logic doesn't seem to include the full range of possible values...
I don't think you can just throw away the word "logic" like that. We try to make arguments using deduction and inference, so there is a logical structure behind them. It's just that it isn't as well-defined and doesn't have the mathematical rigor of formal logic.
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