It was recommended to Pakka Desi and me to form "logic study group". Dunno about Pakka, but I am actually interested. Not sure if there are many people interested around this forum, but let's try... To start, here is a discussion on Kuro5hin site that I found interesting. In particular, I was surprised by the following comment, that shows how what I considered pure abstraction can find some practical applications. "What does it mean to say Bush is a Democrat is false not not necessarily false? If it's false, it's false. Well when logicians are thinking about the semantics of modal logic they often work with 'possible worlds'. Although it is true that Bush is a Republican we can imagine a world in which he is a Democrat (well I think I can anyway). Only when something is true in all possible worlds is it considered necessarily true, otherwise it's just plain true (this is not strictly the definition used but it's close enough for now)." I got interested in modal logic not because of logic per se but because of psychological measurement problems. In particular, I got interested in it because of issues with counterfactuals (issues surrounding the truth value of statements such as "If X were to be the case, Y would be the case.") It's relevant to psychological measurement because much of it makes assumptions about people that are counterfactual in nature--you never have even observed someone in some situation, but try to make statements about them to the effect of "this is the sort of person, that if you would put them in such-and-such situation, they would do Y." Eventually, this all led me to work on possible worlds, naming, and necessity, and by authors such as Kripke and Lewis. I'd highly recommend works of either Kripke or Lewis for those who are interested in modal logic or possible worlds. They both make incredibly convincing arguments for the utility of possible-world arguments (Lewis's position in Counterfactuals, about the reality of possible worlds, may ostensibly seem controversial, but is more compelling if you consider distinctions between reality and existence). Modal logic is fascinating to me because of its many connections with statistics and statistical reasoning, which is one of my main areas of interest. The problem of how to think about possible worlds, possible scenarios, is intimately related to statistical problems and provides a satisfying theoretical "base" for the latter. It's been fascinating to me to see how individuals in various realms of thought converge on each other in thinking about issues such as causality, counterfactuals, and stochastic reality." Well, to get more practical, here is The list of logical fallacies that I found useful. Going to do some lab now... If you have some interesting links to share, do not be shy, post them.

Like for example this joke from the same discussion: "There's a standard system of logic? I've always viewed it more like this: Microsoft Logic - Has convenient syntax for proving most common theorems, but is incapable of proving some more complicated theorems that we nevertheless believe to be true. *NIX logic - Allows proof of a much larger class of theorems, but with a more arcane syntax. Some very common theorems require a lot of practice to prove reliably. Klogic, Gnomelogic, etc - A lot of syntactic sugar for common theorems, while still allowing access to the underlying *NIX logic. And then there is Standard Logic (or the One True Logic), which is the ideal that they all strive towards.. none of the existing logics have made it IMHO (and I'm talking about logic here, not the software analogy)" http://www.kuro5hin.org/comments/2002/11/2/123247/073?pid=32#81

Originally posted by Mapraputa Is: It was recommended to Pakka Desi and me to form "logic study group". Dunno about Pakka, but I am actually interested. Not sure if there are many people interested around this forum, but let's try... In particular, I was surprised by the following comment, that shows how what I considered pure abstraction can find some practical applications. "What does it mean to say Bush is a Democrat is false not not necessarily false? If it's false, it's false. Eventually, this all led me to work on possible worlds, naming, and necessity, Well, to get more practical, here is The list of logical fallacies that I found useful.

I would find such a study group interesting. I had one class in Logic over 10 years ago and seem to remember very little although I remember being impressed with the concept of "truth tables" . In my mind I always visualized people (or their statements somehow) being strapped down on a table while the "truth" was extracted out of them... Regarding "necessarily" true or false; from my memory I had thought that something was necessarily true or false based on given assumptions or statements. For example, Herb is a great programmer and all great programmers know Java. Therefore, it is necessarily true that Herb knows Java. (maybe a bad example...) Great link to a handy list of logical fallacies. Whether this study group forms or not that list of fallacies certainly can be put to good use here in the forums....

Originally posted by herb slocomb: Regarding "necessarily" true or false; from my memory I had thought that something was necessarily true or false based on given assumptions or statements. For example, Herb is a great programmer and all great programmers know Java. Therefore, it is necessarily true that Herb knows Java. (maybe a bad example...)

Philosophy talks alot about necessary truths. Source

Distinction between kinds of truth. Necessary truth is a feature of any statement that it would be contradictory to deny. (Contradictions themselves are necessarily false.) Contingent truths (or falsehoods) happen to be true (or false), but might have been otherwise. Thus, for example: "Squares have four sides." is necessary. "Stop signs are hexagonal." is contingent. "Pentagons are round." is contradictory.

Truth tables... I was studying Boolean algebra as a part of "discrete mathematics" class in 1985 (whaaat? 18 years ago? I never realized I am so old . It was like yesterday!) I remember being perplexed that any arbitrarily complex logical statement can be express with only "NOT", AND, and OR functions. (so called "conjunctive normal form" or "disjunctive normal form"). But "statements being strapped down on a table" -- it's not so easy...

Originally posted by Jason Menard: Given your example: "Herb is a great programmer and all great programmers know Java. Therefore, it is necessarily true that Herb knows Java." Wouldn't that be a contingent truth?

Hm... I would call it a "valid" statement. Let's restate: 1. all great programmers know Java. 2. Herb is a great programmer Therefore Herb knows Java. "We may speak of deductive arguments as ones where the structure of the argument allows the premises to not only support but to guarantee the conclusion. Such arguments may be described as valid or as invalid. If they are invalid, the conclusion is not supported whether the premises are true or not. If they are valid, then if we accept the premises we must accept the conclusion." To put it simple, not all valid statements are true, but only those whose premises are true. In our example, both premises can be false (sorry, Herb ) So the statement above is valid, but not necessarily true. Another problem with logic, when we talk about it, we almost always talk about "deductive" logic. We have some premises and we can deduce something from them. But according to my knowledge (if I am wrong, somebody will correct me), there is only one deductive science - mathematics. All other sciences have to rely on induction. And "inductive logic" is problematic. "Many arguments do not pretend to "guarantee" the truth of their conclusions if their premisses are accepted. These arguments are inductive and we speak of their soundness as opposed to their validity." One popular example of inductive reasoning goes like this: "all swans we have seen so far are white. Therefore all swans are white". Which was a fine statement until black swans were seen in Australia. In our example "all great programmers know Java" is a result of some previous inductive reasoning and thus is questionable. With "Herb is a great programmer" we have to define what "great" means etc. And even with "deductive" science mathematics, its premises are premises not because they are "true", but only because deduction needs some base to start with. "The "existence" of f -- or of any mathematical object, even the number "3" -- is purely formal. It does not have the same kind of solidity as your table and your chair; it merely exists in the mental universe of mathematics. Many different mathematical universes are possible. When we accept or reject the Axiom of Choice, we are specifying which universe we shall work in. Both possibilities are feasible -- i.e., neither accepting nor rejecting AC yields a contradiction; that follows from models devised by G�del and Cohen." http://www.math.vanderbilt.edu/~schectex/ccc/choice.html Bertrand Russell: "Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing... It's essential not to discuss whether the proposition is really true, and not to mention what the anything is of which it is supposed to be true... If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." http://www.cut-the-knot.org/proofs/index.shtml [ January 29, 2003: Message edited by: Mapraputa Is ]

I remember being perplexed that any arbitrarily complex logical statement can be express with only "NOT", AND, and OR functions Or, for bonus points, using only NAND gates. Well, it's trivial to just replace AND/OR/NOT with equivalent NAND combinations - extra points are only merited if you bother to minimize the number of NANDs used. [ January 29, 2003: Message edited by: Jim Yingst ]

Originally posted by Jim Yingst: I remember being perplexed that any arbitrarily complex logical statement can be express with only "NOT", AND, and OR functions Or, for bonus points, using only NAND gates. Well, it's trivial to just replace AND/OR/NOT with equivalent NAND combinations - extra points are only merited if you bother to minimize the number of NANDs used. [ January 29, 2003: Message edited by: Jim Yingst ]

ANd then came fizzy logic.... nothing could be absolute discrete

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