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Propositional calculator

(or any other kind of formal logic)
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Mathematical calculators can be used for resolving arguments about the likes of finance or how many football fields long a dermally expanded whale is. However, not all arguments are solely about numerical issues, and in fact are usually either emotional or logical in form. There are other situations where one might want to plan a logically structured speech or article to persuade others or show comprehension of a problem in an educational context, and a calculator would be of limited use here.

Something of greater use might be a propositional calculator: a hand held device into which formal logical arguments could be entered and evaluated for validity, parsed for well-formedness or tested for truth values. Whereas this would not resolve arguments at all, it would serve as an annoying gambit if, in the middle of a row, one were to whip out one's propositional calculator and show the other person why you are right and they are wrong. It would also be useful in such circumstances as planning logic circuits and designing algorithms.

nineteenthly, Mar 05 2008

a distant cousin of this idea Perpetual_20Notion_20Machine
[pertinax, Mar 05 2008]

[stoaty]'s link http://wffnproof.com
[angel, Mar 07 2008]


       1. Would an implementation of the Prolog language for a palm-top cover this?
2. Can you think of any example of an argument that people actually care about which would not, if tackled with this machine, decay into a frustrating meta-argument about how the original argument should be formalised?
pertinax, Mar 05 2008

       1. No. As far as i know, it doesn't cover modal operators, deontic logic and the like. Also, it uses textual reserved words so it's a bit like COBOL in that respect - long-winded and pointlessly laborious to type in.   

       2. Sometimes. There are arguments which take place between people which would indeed turn into meta- arguments, but that might distract from the original argument sufficiently to calm people down or lead to abandonment of the idea that led to the original disagreement. There are also situations where the user would be trying to construct a line of argument for a presentation, talk, article or paper, which doesn't depend at that point on possible future disputes.   

       An example would be affirming the consequent:   

       If the house is cluttered because you haven't tidied up, i may fall over and hurt my leg. I fell over and hurt my leg. Therefore, you must tidy up.   

       This is a fairly lame example of a logical fallacy of the form:   

       P=>Q Q Therefore P.
nineteenthly, Mar 05 2008

       Would I want one of these?
I'm not so sure.
coprocephalous, Mar 05 2008

       The problem with arguments is that most of the clauses are invisible and/or unspoken.   

       If the house is cluttered because you haven't tidied up, I may fall over and hurt my leg. I fell over and hurt my leg, and am particularly annoyed about it. I am also annoyed at the clutter in my house. You are here. I am annoyed. Grrraaaaahhhh!!   

       The other fallacy is that arguments should in any way be logical. They are not, and never will be - adopting a calculator approach may cause the other party to adopt a big stick approach.
zen_tom, Mar 05 2008

       Arguments of the emotional variety are indeed illogical, but looking at how each person is arguing in a logical way could expose both differences and similarities between the people. The unspoken clauses could become explicit.   

       It could be a bit like the I Ching. You try to come up with a question which expresses your predicament, and in doing so you clarify its nature, maybe dispensing with your original desire to consult the oracle in the first place.   

       There is annoyance and there is disagreement where both parties are uncomfortable with the fact that they disagree and would welcome a chance to negotiate agreement. Alternatively, the machine could be made hefty enough to beat someone over the head with it if the other approach failed.
nineteenthly, Mar 05 2008

       I would think you could easily codify such a thing after fiddling with the WFF 'n' Proof games (wffnproof.com, since I am new and uncertain how to make links). It's been...a whole lot of years since I played them, but I remember colored dice with letters printed on them to represent kinds of logical statements. In one variation of the game, you shook a bunch of these tiles onto the table and arranged the result in the longest possible Well Formed Formula.   

       As I remember it, when we applied these methods to real-life conversations, we received many offers of "such a wedgie" and "a poke in the snoot."
stoaty, Mar 07 2008

       //I am new and uncertain how to make links//

You look up there --^ under "meta" and go to [help], then to [linking to other pages].
angel, Mar 07 2008

       Ahhhhh...the help file is the reason I had a crisis of confidence. Had I not RTFM, I would've cheerfully typed angle-bracket a href= and so on in the body of my message and assumed the best. What it says under linking to other pages is:   

       "A link consists of a URL, a short name, and a description."   

       A dog consists of four legs, a tail and a bark, but I don't know how to make one. Then I noticed that links appear directly under the main post and assumed something other than sticking them in my message was called for.   

       Think makes hurty. Snack now.
stoaty, Mar 07 2008

       Thanks, [stoaty]. Back in the mid- 'eighties, i used a program on a Vax- eleven/seven eight five which parsed propositional and predicate calculi, though it couldn't do modal logic, and could recognise the likes of modus tollens, De Morgan and reductio ad absurdam. I know it can be done; the question is, how useful is it?
nineteenthly, Mar 07 2008

       // "A link consists of a URL, a short name, and a description."
Heh, that really is spectacularly unhelpful if you don't already know to click on the word [link], and why would you read it if you did! I've edited the text to be a little more specific.
jutta, Mar 07 2008


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