OK, so if I ignore the assumed premises (assuming there is any), and stick to the syntax, and assume we are talking about Aristotelian, or classical first order predicate logic, then they are both invalid.
OK, so if I ignore the assumed premises (assuming there is any), and stick to the syntax, and assume we are talking about Aristotelian, or classical first order predicate logic, then they are both invalid.
The usual definition of validity is "it's impossible for the premise(s) to be true and the conclusion false". Thus the second would be invalid (because the conclusion is false when it exists even though it seems to follow from the premise) and the first valid (if the premise exists, then it is a negative proposition, therefore the conclusion is true).Originally Posted by Mangafranga
But with such self-referential statements, this definition of validity is inadequate, because in both those cases the they are contrary to other arguments with these forms (No Xs are Y therefore some X is Y, All As are B therefore no A is non-B).
Buridan defined a valid argument as "it's impossible for the fact to be as the premise says and not as the conclusion says". So the second is valid and the first invalid, as per the normal arguments of the same form.
The statement "no proposition is negative" is an example of what Buridan calls "not possibly true". It is not a logical impossibility like square circle, because it is logically possible to obtain the state of affairs it descibes, i.e. the non-existence of negative propositions. But while the proposition exists, it is itself a negative proposition, so it cannot be true while it exists.
“The history of the 20th century is full of examples of countries that set out to redistribute wealth and ended up redistributing poverty.”
“There’s no point blaming the tragedies of socialism on the flaws or corruption of particular leaders. Any system which allows some people to exercise unbridled power over others is an open invitation to abuse, whether that system is called slavery or socialism or something else.”—Thomas Sowell
years ago i had enough problems getting my mind around this conjunction:
READ MY LIPS (AND) NO NEW TAXES
_ ghw bush
carry on
_ g duggan
.
But without the unstated premises, they are still formally invalid. And my intuition is that with the unstated premises, they lose their bite (since affirmative and positive are rather arbitrary properties for a proposition to have). It is also rather odd to talk of propositions existing. Nonetheless, it is interesting.Originally Posted by JonoIt is rather picky, but to make it formally valid you need to import a premise that states that if something is a negative proposition it is not an affirmative proposition.Originally Posted by JonoThe simply reply is to say that this isn't really different from the first definition given (so for "the fact to be as the premises says" just means that the premises is true, and "the premises is true" just means that the facts are as the premises says). And that the confusion has come from ascribing propositions properties that they don't have, and existence.Originally Posted by JonoAgain, it is rather odd to talk of propositions existing. What would it be for a proposition to exist, or to not-exist?Originally Posted by Jono
I don't dismiss all this. It is, as I say, interesting. So these are really my first thoughts on the matter. Also it might be possible to strengthen the argument (e.g. switch from propositions to sentences).
They are fairly standard definitions though.Originally Posted by Mangafranga
I don't think so, because this is true by definition.Originally Posted by Mangafranga
Buridan treated propositions as real utterances or inscriptions, truly or falsely describing a state of affairs. That is why he could differentiate between a possible situation in which no negative propositions existed (e.g. Buridan proposed that God could eliminate all existing ones*), and an actual negative proposition describing this possible state of affairs. But if this proposition existed, then the state of affairs it describes would no longer be true.Originally Posted by Mangafranga
So if all propositions are affirmative, then by definition, this implies a state of affairs lacking any negative propositions, i.e. the facts are as the conclusion says, so the argument is valid according to Buridan's definition. But according to the normal definition, ""the conclusion is true", this argument is invalid, because the conclusion can't be true if it, a negative proposition, exists.
Fair enough. Buridan's solution was noting that any proposition P virtually entails another proposition about its truth, (P is true). So to solve the simple one person liar paradox:Originally Posted by Mangafranga
P is the proposition "This statement is false".
This implies the proposition (P is true).
Also, a proposition implies itself (identity)
So "This statement is false" implies ("this statement is false" and "this statement is true")
Since the consequent is a contradiction, it is necessarily false. A premise implying a false conclusion must be false by the standard modus tollens. Thus its truth entails its falsity.
But not vice verse, as he showed, because the sentence can't meet the other condition for truth, the virtual entailment of (P is true). So the statement of the liar paradox is false according to Buridan's analysis, not in limbo, and not dialetheistic as your answers in the poll suggest.
I haven't really looked at this for over a decade, sorry. Next time I go to Wellington I'll try to revisit Buridan's book.
* Prof. Hughes, also a strong Christian theist, advised that Buridan's strong Christian theistic views in his book should not be taken as necessary to the force of his arguments. Prof. Hughes supervised my logic tutor's MA thesis on Buridan. My tutor applied this to quantum measurement paradoxes, replacing Burídan's virtually entailed proposition with an analogous on: that any measurement proposition has a virtually entailed proposition: "this is a good measurement".
Last edited by Capablanca-Fan; 15-10-2007 at 05:42 PM.
“The history of the 20th century is full of examples of countries that set out to redistribute wealth and ended up redistributing poverty.”
“There’s no point blaming the tragedies of socialism on the flaws or corruption of particular leaders. Any system which allows some people to exercise unbridled power over others is an open invitation to abuse, whether that system is called slavery or socialism or something else.”—Thomas Sowell
But if they are arbitrary, they can be dispensed with (maybe not the right way to put it). On the other hand if the paradox revolves around truth, it is harder to accept dispensing with that!Originally Posted by JonoI thought that you might be able to do conversions (change a negative into a logically equivalent affirmative, and I was operating under a different definition of proposition), but I don't think you can now, so I'll accept that reply.Originally Posted by JonoI am used to the word "sentence" being used in this case. This does make things more interesting.Originally Posted by JonoCheers for the rundown of the argument.Originally Posted by JonoI don't really have a firm position on this question. Like lots of philosophical issues I find myself pulled in conflicting directions, and don't want to commit until I have undertaken a rigorous study of the issues. I picked the inconsistent answer because I like the attitude, and because I am impressed by the fact that the dialetheists manage to put up coherent arguments (and that they are able to do a lot with paraconsistent logic).Originally Posted by JonoI am just a begginer in these liar paradox problems. I considered, for a moment, doing it for an honours thesis, but decdided against it. So I'll still be a begginner for at least another year. But I do expect to encounter it quite a bit (it seems to be a popular issue in Australasia, and the rest of the world too), so I will keep this approach in mind in case I ever take it on seriously.Originally Posted by Jono
i can't wait for axiom's entire chesschat oeuvre to be subjected to a propositional calculus audit
.
With all the "what ifs", a modal logic audit would also be warranted.Originally Posted by eclectic
“The history of the 20th century is full of examples of countries that set out to redistribute wealth and ended up redistributing poverty.”
“There’s no point blaming the tragedies of socialism on the flaws or corruption of particular leaders. Any system which allows some people to exercise unbridled power over others is an open invitation to abuse, whether that system is called slavery or socialism or something else.”—Thomas Sowell
Possibly p, Possibly q, Possibly r, Possibly s, Therefore z!Originally Posted by Jono
The false solution seems to be popular amongst NZers, Prior supported it-
"Prior, following the informal suggestions of Buridan and Peirce, takes this way out and concludes that the Liar Sentence is simply false."
http://www.iep.utm.edu/p/par-liar.htm
Heh. Maybe even necessarily zOriginally Posted by Mangafranga
I'm not sure why Buridan's Sophisms ch. 8 all about liar paradoxes should be called "informal".Originally Posted by Mangafranga
“The history of the 20th century is full of examples of countries that set out to redistribute wealth and ended up redistributing poverty.”
“There’s no point blaming the tragedies of socialism on the flaws or corruption of particular leaders. Any system which allows some people to exercise unbridled power over others is an open invitation to abuse, whether that system is called slavery or socialism or something else.”—Thomas Sowell
Where are you getting the information that Prior got his ideas from ch. 8? Prior died before the translation which you referenced was published. Also, informal might just mean non-symbolic.Originally Posted by Jono
I'm now fairly confident the answer to this is yes. See e.g. "The Liar Paradox from John Buridan back to Thomas Bradwardine" by Read, who argues that Buridan's solution is a mucked up version of Bradwardine's. At a conference coming up I may get to see a paper on Bradwardine's solution. (I say may because they seem have 2 talks going at a time, hence I will have to choose between it and something else.)Originally Posted by Jono
Last edited by Aaron Guthrie; 01-07-2008 at 02:35 PM.
Reminds me of a joke:
If God is all knowing, what is the one question he cannot answer?
I think for the problem to be defined the conjunction (in this particular statement) has to be defined.
For private coaching (IM, four times VIC champion) call or SMS 0417519733
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This one is simple - "none"Originally Posted by Zwischenzug
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