I’ll second the reccommendation for Jevons’ Elementary Lessons.
I have ten books, and I don’t have ten books / Therefore, I am Nietzsche.
I assume you understand the meaning of everyword in that argument, so is it deductively valid or not?
Logic extends far beyond what makes an argument deductively valid, it even rears its head in linguistics amongst various other disciplines. Studying it for those reasons is not as you say, ‘the exercises and examples and law force you to notice how tricky words can be’.
Also, it is only through the study of logic that we have made certain philosophical breakthroughs.
I suspect you are wrong about, ‘People have no trouble understanding what makes a valid deduction when words aren’t getting in the way.’
I fully agree with what I think your point is, but while there is no real authority to words, there is part of us that acts - even momentarily - as if they do mean what we first assume them to mean. That is the definitional stickiness. So it is not always dishonest when someone uses a different meaning. In fact, mostly it seems accidental. People just forget…because of the stickiness. Any preconceived notions or biases or ire will of course further delay their realization of what is going on - sometimes forever.
Even in the thread about bullying, it seems that one group of posters are using it to mean intimidation and teasing without violence, whereas another group is using the word to include violence. So they appear to hotly disagree for while, until they see what is going on. In that case, for example, it seems unintentional. Indeed, the word bullying is sometimes used to imply violence but other times it is used without referring to any actual violence, so it is ripe for this kind of problem.
It is not an meaningful statement. Or if it is, then I don’t understand at least one of the words in it, because there is no usual meaning I can assign to the word “have” (for example) that makes the statement “I have ten books, and I don’t have ten books” make sense. It is gibberish to me. Whoever utters it has not managed to communicate their thoughts to me, so there is no argument for me to evaluate.
Other disciplines may use the word “logic” but often it is in a different sense, e.g. circuit logic, but my comments in this thread are limited to the idea of learning logic in order to figure out how to argue better and reason better. For that, I suggest instead learning about the praxeology of communication, as that is where the action is.
AJ, I didn’t mean to imply that I disagreed with you about “definitional stickiness”. I certainly do agree that it happens to people. You’re right, too, that a person falling prey to it isn’t being intentionally dishonest. In such a case, though, he’s not consciously choosing to implicitly use a definition which he knows (or has strong reason to expect) is substantially different from that which other people use - which is what I was talking about.
I’m fond of pointing out differences in definitions to people during debates. You’d be surprised (or maybe you wouldn’t be) at how many people react with hostility. They often start to claim that their definitions are the “right” ones. In my opinion, they either lack sufficient self-awareness to realize otherwise, or they’re still trying to “win” the debate somehow. Neither of these sits well with me, of course.
Then you don’t understand the basics of propositional logic. I was asking if the argument was valid; it can be expressed in the following form, if turned into a conditional:
(B ∧ ¬ B → N)
It is a valid argument, but I’ll let you figure out why. So perhaps you better get back to studying some more logic, before you try to argue that if, ‘there is any value in studying “logic,” it is that the exercises and examples and law force you to notice how tricky words can be.’
I am well aware of the principle of explosion, but as I said I find the system in your textbook (and its terminology) superfluous. I never said it was not a “valid argument” in propositional logic; my point is that that terminology is un-elucidating, and it is more elucidating and cleaner to phrase things my way. Here is why:
Do you know why that is considered a logically valid argument in formal logic? Because if you have contradictory premises you can “prove” anything (principle of explosion), the practical application for becoming an effective reasoner being: don’t trust conclusions - no matter how wild - if there are any contradictions in your premises.
Notice that what I said, “the statement is meaningless,” results in the exact same conclusion, except that my way is cleaner and more efficient. Start with meaningless premises, and there is no argument at all. That is my way. Your textbook’s way is to say that it is an argument, but absolutely anything you put for the conclusion will still be “valid.” This results in a “wowee-zowee” result, but I see that as a weakness, because nothing too interesting is actually happening. Nonsense is being spoken, therefore no argument is being conveyed from the mind of the speaker to the mind of the listener. Your textbook considers statements as if they are free-floating, independent of expressing the content of any person’s thoughts.
My approach treats statements as attempts to convey thoughts or other experiences. Hence the different phrasing. My approach brings the focus to where the real action is, and where the real insidious errors are made (including all “logical errors”): the very nature of words and communication.
As far as learning how to reason, rules like the formal logical principle of explosion tell you nothing about the underlying communication situation, and therefore do nothing to shield the learner against reification and other quite illogical things. “Oooh wow, contradiction lets me prove anything, how mysterious” may be more fun, but “you’re not communicating anything to me, bro” is closer to what is actually happening, and I contend far less likely to lead to error in thinking - which is the whole point in the first place.
Yeah, this is a weird phenomenon, and I do that a lot, too (point out differences in definitions), and it irritates people sometimes. So most people refrain from pointing it out too much, like it’s taboo or something, but I don’t refrain, because it very often is the key to the whole debate. And even if it is not the big key, the debate certainly cannot even start until people agree on definitions. But it’s like deja vu, where the discussants at some point a few pages into the thread finally realize they had different definitions and resolve things, but then in the next thread it happens again with a different set of key words, and they go through the same process, thread after thread. It seems to take many exposures for most people to see the pattern, to the point where they finally learn to stay on the lookout for definitional differences from the very beginning.
The most insane thing is that if you point out semantic issues like this, people will often accuse you of “arguing semantics,” which is actually exactly what you’re trying to point out that they are doing! It’s yet another equivocation: “arguing semantics”=manipulating semantics to try to make a false argument look right (what they’re doing), vs. “arguing semantics”=making points about the semantics of the argument (what you’re doing). What a mess it becomes, when you point out an equivocation, they are blinded from seeing it by another equivocation.
Side thought: Someone said something like, “Label me, and you delete me.” It’s like people don’t want to part with their pet definitions, because by giving something a label they can put it in a box and feel like it’s a known quantity, not as scary, etc. Maybe people get irritated because you threaten to take that away from them when you remind them that definitions are arbitrary (OK, not quite totally arbitrary, but only non-arbitrary in the sense that a certain definition might be really common).
The reason it is deductively valid is because there is no case in which the conclusion can be false with the premises being true - because the set of premises can never be true; therefore, ‘if you have contradictory premises you can “prove” anything (principle of explosion)’
Meaning isn’t objective. And what an argument is, isn’t determined by its meaningfulness. Instead a set of sentences is an argument solely if it consists of a/some premise/s and a conclusion.
Logic isn’t restricted to the principle of explosion. You seem to be confusing validity and soundness. An argument taking the form of the principle of explosion can never be sound, because the set of premises will never be true - unless you include contradition into a new logic - but it is still a valid form. It is logical form that logic is concerned with, not soundness.
Yes, that’s it exactly. Meaning isn’t objective. Or better to avoid the word meaning and use the words intention and interpretation. By calling the string of words “meaningless” I mean I find no coherent way to interpret it into a thought in my mind. If one cannot interpret a string of words, one cannot even begin to evaluate it as an argument. (Yes, I know in propositional logic they let you do that; that is part and parcel of the whole system I find useless at best.)
Soundness, validity, etc. - it’s not useful terminology to me, so I may differ from your textbook from time to time.
In fact, all of propositional logic rests on a questionable foundation, for a reason you already seem to grasp: The meaning interpretation of a statement is not objective. Propositions (words) are not truth-apt until they are interpreted into thoughts. Propositional logic treats a sentence without considering the thought in the speaker that prompted it, and without considering how the listener interprets it - which are the only two things that matter for argumentation, conveying a theory, or any intellectual discourse.
It seems to me that what I am trying to do in intellectual discourse is this:
(1) I have a thought, and I would like to get other people to experience that same thought. Since we’re not telepathic, I am usually forced to (2) put the thought into words in hopes that other people will (3) interpret it into a thought that matches mine. It looks pretty simple: unless all three steps happen in order, it doesn’t seem useful to call it intellectual discourse, or an argument, or the conveying of a theory.
With that in mind, it might be easier to see why I say that if a proposition has a contradiction that prevents the listener from being able to interpret it, communication/discourse/argument simply has not happened yet. Steps 1 and 2 may have happened, but Step 3 hasn’t.
Now in the case of contradictions, there is question that comes even before that: What was the speaker thinking before he or she uttered the contradictory proposition? What was the initial thought (Step 1)? If it is truly impossible think a bona fide logical contradiction (not just the words, but the actual thought behind them), then the communication can’t even have started (Step 1 has been skipped), and the words hardly seem worth calling a “proposition” at all.
So when someone utters an apparent contradiction, the best idea would be ask the person to clarify. If they refuse, ask what they are even trying to do. Are they trying to get a thought from their mind into yours, or are they just making noises for some other reason?
This might seem mundane, but in fact there are many people who will try to espouse a theory while telling you flatly that they do not understand it, can’t visualize it, or that it has unthinkable elements in it. This means they are not communicating (they just told you Step 1 is impossible!), but rather they think the theory is sitting there in some kind of objective meaning in the words themselves. Those who speak of 4 or more spacial dimensions come to mind. Propositional logic can’t tell you how 11D space is a bogus idea, but the praxeology of communication can. I recommend it because it is both simpler and more broadly applicable than propositional logic. Plus it helps reveal word-based error, which propositional logic does not. Propositional logic won’t even catch equivocations or WTOs (in fact it renders them invisible), which are the real culprits in most fuzzy-headed thinking and so-called logical errors.
OMG. Though I probably agree with Selgin, he just did this!
Though I am not sure who is right, no he didn’t. He merely explained very clearly why the debate is not about semantics. And made a claim that his opponents are trying to win their argument by defining it into correctness.
If Selgin’s opponents are trying to define their position into correctness, the debate is (currently, at least) about semantics. Selgin’s equivocation seems to be keeping him from seeing that when your opponent makes a semantic argument as evasion, the solution is to point that out, and refuse to continue making points until definitions are agreed upon.