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Logic

As a student of law with a vivid interest in logic (in a broad sense), I find myself intrigued by the possibility of combining these two subjects. From what I so far have found, the implementation of the latter field of thought to legal discipline is mostly only done with regard to informal logic, with fairly simple overviews of the rules of inference etc.; the scope is mostly one aimed to serve the practical law-man in, say, procedural contexts. The ones that serve the academic community, seem not to be quite technical. Yet, the legal system seems highly infested with what logic is concerned. The relation between propositions of facts and norms, the norms being constructed with the help of sentential connectives, say, material conditionals or bi-conditionals to name just a few. Yet other phenomena could be named: judgments and other propositional attitudes, the normative "it is the case that", whose descriptive accuracy depends on what legal institution one is in(e.g. penal-law demands higher...

I would hope that my askphilosophers.org colleagues might be able to answer your question better than I can with respect to the law and logic in philosophy , but I can try to give you some pointers to the literature on the law and logic in artificial intelligence . The first pointer is not so far removed from philosophy. My former colleague in the School of Law at the University at Buffalo, L. Thorne McCarty, applied deontic logic to legal issues, often citing the work of the philosopher Hector-Neri Castañeda. See, e.g., McCarty, L. Thorne (1983), "Permissions and Obligations", Proceedings of the 8th International Joint Conference on Artificial Intelligence (IJCAI-83; Karlsruhe, W. Germany) (Los Altos, CA: Morgan Kaufmann): 287-294. There is also a journal, Artificial Intelligence and Law , which occasionally has papers that you might find relevant.
Logic

Do false statements imply contradictions? Consider the truth table for logical implication. P...........Q.............P-> Q T...........T.............. T T...........F...............F F...........T...............T F...........F...............T Notice that for a false statement P, the last two rows of the truth table, both Q and ~Q follow. No matter what Q is, it's truth follows from false statement P, as the third row shows. We can therefore take Q to be "P is true." From here it follows that a false statement P implies it's own truth, as the third row shows. Do false statements really imply their own truth? Do they really imply contradictions? Are false statements also true?

One branch of logic that deals with an alternative to material implication, and that has applications in artificial intelligence, is called "relevance logic". For more information on it, take a look at: Anderson, Alan Ross, & Belnap, Nuel D., Jr. (1975), Entailment: The Logic of Relevance and Necessity (Princeton, NJ: Princeton University Press) -- especially the introductory chapters that present arguments as to why relevance logic is "better" than classical logic. Lepore,Ernest (2000), Meaningand Argument:An Introduction to Logic through Language (Malden, MA: Blackwell),§A3 ("Conditionals"), esp. §A3.1.1 ("Paradox ofImplication), p. 317, and §A3.1.3 ("Paradox of ImplicationRevisited"), pp. 319-320. For a literary discussion of what happens when a computer or robot usesclassical logic, see: Asimov, Isaac (1941),"Liar!", Astounding Science Fiction ;reprinted inIsaac Asimov, I, Robot (Garden City, NY: Doubleday),Ch. 5, pp. 99–117. And for applications to AI,...
Logic

Hi I understand how to apply derivation rules like the rules of inference etc. My question is do we have a method of proving the rules themselves? Is there a way to prove that If P then Q; P; therefore Q? Or do we accept these rules out of intuition?

Rules of inference are "primitive" (i.e., basic) argument forms; all other arguments are (syntactically) proved using them. So you could either say that the rules of inference are taken as primitive and not (syntactically) provable, or you could say that they are their own (syntactic) proofs. However, the way that they are usually justified is not syntactically, but semantically: For propositional rules of inference, this would mean that they are (semantically) proved by means of truth tables. A rule such as Modus Ponens (your example) is semantically proved (i.e., shown to be semantically valid) by showing that any assignment of truth values to the atomic propositions (P, Q in your example) that makes all of the premises true also makes the conclusion true.
Logic

Sometimes my students want to argue that "my opinion is as good as anyone else's opinion." How do I counter this view with a reasonable philosophical argument? Thanks! Richard in New York

The opinion that all opinions are equally good is one that is usually held by people whose attitude toward knowledge is what some psychologists call "Multiplism" or "Subjective Knowledge". This is the view that, because there are often conflicting answers to questions (or conflicting solutions to problems), people must trust their "inner voices", rather than external authorities (like teachers or professional philosophers:-). In particular, many "Multiplists" believe that most questions (or problems) are such that we don't yet know what their solutions are, and that this is why everyone has a right to their own opinion. Although I like Allen Stairs's counterargument--if all opinions are equally good, then so is the opinion that all opinions are not equally good--I'm not convinced that a Multiplist would find it convincing! In general, Multiplists are unfamiliar or uncomfortable with logical argumentation. A better way to get Multiplists to see that proposed solutions to problems (call them ...
Logic

This question has been given to my year 7 son and he has permission from his teacher to seek help from the web! Any assistance gratefully received. "A wicked year 7 pupil, the self-styled "Logician", was up before the year head on a serious charge of misleading the rest of the year into avoiding homework through clever argument. The head of year promised expulsion from the school, but added the following strange condition that, if on the day of expulsion the Logician signed a statement making one true declaration about his punishment, the expulsion would be reduced to confinement in the Head's study for 10 days. If on the other hand the statement is false, then the sentence will be carried out immediately. The day of expulsion arrives and the Logician, beaming, signs a declaration which is handed to the head of year who reads it in bewilderment. Tearing the document to shreds in his anger he orders that the Logician suffers no punishment whatsoever." What could the Logician have said which resulted in...

I won't give you an answer, but I'll give you a hint: Read Don Quixote :-)
Logic

I always assumed that there could be no contradictions -- that the principle of non-contradiction was absolute, so to say. Recently, however, I read about dialetheism and paraconsistent logic and realized that some philosophers disagreed. It seems all of logic falls apart if contradictions are permitted. I fail to understand how their position makes any sense (which could admittedly be just a failure on my part). So is it possible someone could better explain their viewpoint? Surely none of them believe that, say, one could simultaneously open and close a book, right?

It's not so much that some logicians believe that there are no contradictions as it is that there are different ways of dealing with them. There are different kinds of paraconsistent logics. Many (e.g., "relevance logics") got their start by trying to handle the so-called paradoxes of the material conditional (e.g., that from a contradiction, anything can be derived). There are also situations in which it makes sense to allow for propositions that can be both true and false as well as propositions that are neither true nor false, in addition to ones that are either true or else false (see Belnap's paper, cited below). (Just for a quick example: "This sentence is false" might be both true and false, whereas "Colorless green ideas sleep furiously" might be neither true nor false.) In artificial intelligence, there have been applications of relevance logics to deductive knowledge bases (see the Martins & Shapiro paper, cited below): Suppose you have a deductive knowledge base and that person A...
Logic

Is there a specific name for the study of good reasoning or good thinking? I guess that some people call this "logic", but definitions of logic that I find on the internet are a bit different (narrower?). In some areas, "methodology" seems an appropriate word. Has epistemology a significant relation to this?

Some terms that are used for what I think you have in mind are "informal logic" and "critical thinking". To see if those are, indeed, what you have in mind, you might check out the article on Informal Logic in the Stanford Encyclopedia of Philosophy. And there's some discussion of "critical thinking" in SEP in its article on Philosophy for Children (but the topic of critical thinking is by no means limited to children!).
Logic

How does one _prove_ that an informal fallacy is a fallacy (instead of just waving a Latin name?)

Peter's quite right, of course, but I think there's a bit more we can say. What makes a good pattern of reasoning good ( logically good, that is) is whether it preserves truth, that is, whether it only leads from true premises to true conclusions and never from true premises to false conclusions. (If it starts with false premises, that's another matter altogether.) And the best way to tell whether an argument pattern will be truth-preserving is to do a truth-table analysis of it: Assume (that is, make believe) that the premises are true, then figure out what the truth values of the atomic propositions are, and, finally, figure out what the truth value of the conclusion is. If, whenever you assume that the premises are true, it turns out that the conclusion has to be true, then you know the argument is a logically good one; otherwise, it is a "fallacy", i.e., a logically bad argument. See any introductory logic text for the details (I understand that Peter has a very nice one :-) There are a...
Logic

Are so-called "slippery slope" arguments effectively appeals to modus tollens?

I'm not sure that there's any single standard form for a slippery slopeargument, so let's look at just one, a "sorites" or "heap": If I havea heap of stones and remove just one of them, I still have a heap. Repeating that, I will always be left with a heap. But, obviously, atleast when I remove the last stone, I no longer have a heap. Therefore... Well, therefore, what? A heap of stones is equivalentto having no stones at all? Suppose so. That's "obviously" incorrect,so (a) the original premise or (b) some step in the argument must havebeen wrong. Suppose (a). Then a heap of stones with one stone removedis not a heap. This does indeed seem to be an application of modustollens, which is the inference rule that says: From "p implies q" and"not q", you may infer "not p". Here, p is our original premise, q isthe conclusion of the slippery slope. But (b) it could be that there'snothing wrong with either p or with q, but that what's wrong isrepeated application of stone-removal. In...
Logic

What grounds the truth of logical inferences such as modus ponens or hypothetical syllogism? Are these logical truths grounded in "intuition" similar to Foundationalism?

I hate to sound like, well, like a philosopher, but I think we need to get some terms straight before we begin: Logical inferences such as modus ponens (more properly, rules of inference) are neither true nor false. Truth and falsity are properties of things like sentences, statements, or propositions (depending on your ontology). The analogue of truth values for rules of inference are "validity" and "invalidity". Very roughly, a rule of inference is valid if and only if it is truth- preserving . That is, it is valid if it will only allow you to infer truths from truths--if you input true propositions and apply a valid rule of inference to them, you will output only true propositions. (If you input a false proposition, anything can happen; "garbage in/garbage out" as they say.) So, a slightly more accurate way to phrase your question is this: "What grounds the validity of a rule of inference?" And now, I think, the answer is clear: Just as something like "correspondence to reality...

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