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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.
a distant cousin of this idea
Perpetual_20Notion_20Machine
[pertinax, Mar 05 2008]
[stoaty]'s link
http://wffnproof.com
[angel, Mar 07 2008]
[link]
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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? |
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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. |
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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. |
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An example would be affirming the
consequent: |
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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. |
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This is a fairly lame example of a logical
fallacy of the form: |
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Would I want one of these?
I'm not so sure. |
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The problem with arguments is that most of the clauses are invisible and/or unspoken. |
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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!! |
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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. |
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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. |
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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. |
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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. |
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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. |
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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." |
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//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]. |
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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: |
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"A link consists of a URL, a short name, and a description." |
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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. |
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Think makes hurty. Snack now. |
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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? |
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// "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. |
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