Liar Last Conference
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NOTE ON THE LIAR PARADOX xxx
Abstract: In this short note, we try to de-mystify one more fantasy, or illusion, created by those proclaiming to be doing Science, statement which we reject, in order to calm down the instinct of those passionate about producing Science, so that they do not waste their time with things which are not real paradoxes in any possible sense. Key-words: paradox, liar, language, logic, classical, Sorites.
Introduction:
The Liar Paradox has appeared by at most the second century after Christ, according to note of the Stanford Encyclopedia (see [Paul Vincent Spade, 2005]), which brings a nice discussion on the history of the paradox. It is not a big deal when compared to the wealth contained in the Sorites paradox (see [xxx, 2006]), another paradox treated by us in scientific writing, but it does bring some allurement to the generous reader. Basically, the idea is that of the `external judge’ of someone else’s speech, who should be able to come up with an opinion that is going to be universal. The principle involved in the paradox is absolutely equivocated: Every person is entitled to say, or write, whatever they like about someone else’s statements and this could never be an object of any scientific discussion which is supposed to be of serious nature.
However, given the historical standing of the problem, one does feel obliged to write something about it. One possible description of the problem is:
1) Assume someone has stated p, p being: I always lie. 2) Assume you were listening to them, and you have been given only two choices (classical choices): a) writing their statement is true, or (exclusively) b) writing their statement is not true (false or anything else). 3) Assume a choice has been made by you in 2. 4) Would you then believe that the same subject uttering q: Would you believe me? deserves a a) `no’ Or (exclusively) a b) `yes’ (classical choices) as a response from you?
We now go item by item of the problem, written in the English language as it is, with no further complication, and absolutely no translation into symbols, given the level it reaches (already explained why a person cannot fit a bigger box into a smaller one, only
the other way around, that is, no point in playing stupid and trying to translate a problem well above the level of Mathematics into classical logic lingo (for this discussion, please refer to [xxx, 2008])). In the sections which follow, we analyze each one of the above steps, keeping the order of presentation above, to then reach a conclusion.
Step 1: The definite statement, as uttered by subject.
First of all, the oddity of manufacturing a non-existing situation is impressive: Someone comes, out of context, and utters either that they always lie or that they always tell the truth (exclusively), or even that they do both (or anything else which implies judgment of their honesty, in a universal way regarding their every statement in life), but all amounts to the same information content, that is, none. Basically, if a classical computer is listening (and that is the proposal of the problem, once the only accepted answers are `yes’ or `no`, so that the computer has to be classical, and we insert the element `machine’ here for whatever is logical is passive of programming), no input will be made. Why? A speech, of a person, judging themselves, has got absolutely no logical value. Basically, a system can never judge itself, on any grounds; this is not a valid process, which may lead to any universal inference, as the problem demands. It is obvious, even for a child, that the only person able to emit judgment is that out of the system… : If you are inside of the bubble, you cannot judge the nature of it because you do not hold enough information about all outside of it, and judgments may only be made by those dominating all available matters of the same nature, or level, of the `attrib’ element contained in the utterance
(considering a Maple element here), therefore judgment may only come from the people living outside of the bubble and with no contact with its surface, situation similar to that justifying the necessity to see the planet from the outer space, rather than from inside of it or from over it, in order to judge, in what is closest to a universal judgment, its shape. The first utterance is then empty in logical value. It is necessary that we have an external person, or thing, to make of that statement something logically useful (for any sort of logical system, which must, by default, mean something through which we are able to produce inferences). What may then be inserted is, for instance, the figure of the liar detector, which will then tell us the actual information content for that assertion. The human world is obviously not logical, only the machine world is… . Therefore, whatever cannot be dealt with via machine cannot be computational (Classical Logic is always computational), as for scientific purposes, for it does not deserve a universal decision, what means it cannot be suitable for either writing in scientific language or arguing about it. This way, it is ridiculous to even dare thinking of that as a statement for Logic, as a proposition. That is simply an incomplete logical proposition. It will become a logical entry, or proposition, that is, a unit that Philosophy (we have written what Philosophy should mean: scientific discussion of whatever is logical in the human actions on Earth which may be expressed, perfectly well, via language) can deal with, once we aggregate the judgment made by the liar detector to the already existing statement. The proposition will then be the revised p, now compounded: (I always lie, the machine has returned `x’), x replaces either `true’ or `false`, and exclusively one of the options. Of course there are only two allowed possibilities for a liar detector ( classical ones ), so
that there is also no room for any other speculation of delusional nature (both true and false, for instance).
Step 2: You were listening and must now make a choice.
Indeed, you were listening… . Now we must manufacture a situation in which you judge, in real life, wheter that is true or false, that is, a situation in which you bother, and dare, knowing more than the own person who has created the problem…( of course the simple thought that you can do it makes of you a megalomaniac person, for you cannot know more than the own utterer about themselves, but we keep on going… . Notice that the people thinking of it as a big deal really wish to manufacture a context that is almost impossible to be found in reality). All a normal person would do is stating, perhaps as Christ would: You said it, now you tell me ( and the worst of all, we still have content zero, for there was nothing useful to you, or added to your life, with those words). Here, we must also remind the reader that Science may only be called Science if whatever actions which lie inside of it lead to human progress, and it does not seem relevant, in those regards, to argue about the issues of the Liar Paradox. However, once more, suppose the problem is of use, that is, of scientific value. We then add the information from the liar detector, which is machine-useful, which is basically what a computer demands: The proposal (output of one, input of another) regarding the analysis. Now, it is us only repeating the information attained via another machine, what just puts
coherence in all (machines talk, same level, that is, the whole problem was put into a Classical Logic perspective and, therefore, made passive of judgment and presentation of solution there, as explained in our work from 2008). Step 3 is irrelevant.
Step 4: Would you believe them? Please write `yes’ or `no’.
Notice that the title for the section already implies information being added to the reader’s mind: logical entities must be passive of writing, never only thinking, that is, to deserve being considered as logical information, the thing must be passive of being told in writing, not only in discourse, to others… Now, of course, emitting your opinion is, once more, also logically useless action. You may, as well, lie or tell the truth… . Therefore, the question does not make any logical sense, and any logical speaker will say: 'Well, based on the liar detector test, `yes’ (or `no`)', so that they are being excluded from the environment the problem wishes to belong to (the logical environment), environment to which a being, if normal, cannot entirely belong, so that the exclusion is necessary. Basically, the Liar Paradox is not fun: There is no paradox once more, and the level it reaches is far lower than the level of the Sorites, in terms of human reasoning. It cannot be a paradox because there is obviously no conflict in life generated by it. A person would never waste their time, if ever depending on such judgments even if it were to save their own existence. Suppose, for instance, that a gun is pointed at their faces, and the utterer states that if they
solve the `Liar Paradox`, they will save their lives. What would a reasonable person do? They would throw another paradox over the utterer! Why bothering? If they cannot see it is not a paradox, why would you bother arguing with non-logical speakers? You do not waste your time, you do not try, you distract them from the fixed idea, and that has to be the only logical choice! Your life at stake, you will not go probability: Your only chance is making them as confused and busy as they try to make you be while you think of ways of getting out of the gun’s nose… Well, once more, as we did with the Sorites, if it were ever a paradox, point what word comes after paradox (paradox of language? Paradox of logic? ). Now we consider each one of those: a) Paradox of Language: in Language, there is allowance for anything to happen, even for the proposer (or presenter) to ask that and the `victim’ to leave the place with a `uh!’, that is, there is no duty of answering, so that there cannot, ever, be a single paradox in Language (Language is a tool, not a logical place, it is a tool for both entertainment and expression). b) Paradox of logic: apparently it is there they place it (in logic). If such is true, there must be at least two possible inferences, conflicting, which are passive of deduction from the same propositions and the same evaluations. However, both input and output of the problem are classical. That demands, once more, translation of a broader area into a smaller one. Such a translation can only be a forced move. What is required for that
forceful move to be plausible and acceptable is the use of logical tools, trivially. Basically, we have proposed the liar detector, which will change confused language speech (broad sector, involving emotions, logical decisions of any level, even impairment, for a person may not be able to say `lying`, or say `truth`, for instance…) into bivalent one (true, false), what is clearly possible in this case. To deserve being called a paradox in logic, it is necessary that the Classical Logic systems involved create confusion, that is, produce two possible results for each valid interpretation. However, once more, it also seems impossible to find paradox in this area if the right elements (or complete) of analysis are used. Notice that, for each valid interpretation, there is only one output, what means no confusion and, therefore, no paradox in Logic, or in the logic, at all. Who is confused? The person proposing the problem or the person reading it! Thus, it can only be a paradox of mind, what is not worth discussing, for the mind is not a logical place either! The mind is a messy place, where we really do not want to go when writing about Philosophy: We wish to work with what we may reach and the mind is obviously a place which we cannot reach through words or symbols, the only available tool for philosophical analysis. It is all well beyond that. Therefore, the Liar Paradox is a paradox of internal nature, thus it is no paradox at all for it will be for some, but not for others, not deserving a universal standing as a paradox.
Conclusion
The Liar Paradox is an allurement, as much as the Sorites paradox is. The Liar Problem exists to show the complexity of a human mind, while the Sorites Problem exists to show the complexity of the human verbal expression… Basically, it is an allurement, something to remind us on how our mind is complex, if anything ever deserving being told to belong to Philosophy at all… Place it belongs to (please refer to our 2008 work from the references, [xxx, 2008])? Philosophy of Mind. Adequate addressing then of these can only be made from inside of the Philosophy of Mind, but with the problem corrected, revised, according to our well-posedness theory for philosophical problems (see work from 2008, once more, [xxx, 2008]).
References:
[xxx, 2006] xxx (2006); A Solution to the Sorites, Semiotica, 160 (1/4).
[xxx, 2008] xxx (2008); Well-posedness problem in Philosophy, preprint, online repository at www.pdfcoke.com/illmrpinheiro2 (as accessed on the 17th of February of 2009). [Paul V. Spade, 2005] Spade, Paul V. (2005), Insolubles, The Stanford Encyclopedia of Philosophy
(Fall
2005
Edition),
Edward
N.
Zalta
(ed.),
URL
http://plato.stanford.edu/archives/fall2005/entries/insolubles/. Accessed in July of 2007.
=
Abstract: In this short note, we try to de-mystify one more fantasy, or illusion, created by those proclaiming to be doing Science, statement which we reject, in order to calm down the instinct of those passionate about producing Science, so that they do not waste their time with things which are not real paradoxes in any possible sense. Key-words: paradox, liar, language, logic, classical, Sorites.
Introduction:
The Liar Paradox has appeared by at most the second century after Christ, according to note of the Stanford Encyclopedia (see [Paul Vincent Spade, 2005]), which brings a nice discussion on the history of the paradox. It is not a big deal when compared to the wealth contained in the Sorites paradox (see [xxx, 2006]), another paradox treated by us in scientific writing, but it does bring some allurement to the generous reader. Basically, the idea is that of the `external judge’ of someone else’s speech, who should be able to come up with an opinion that is going to be universal. The principle involved in the paradox is absolutely equivocated: Every person is entitled to say, or write, whatever they like about someone else’s statements and this could never be an object of any scientific discussion which is supposed to be of serious nature.
However, given the historical standing of the problem, one does feel obliged to write something about it. One possible description of the problem is:
1) Assume someone has stated p, p being: I always lie. 2) Assume you were listening to them, and you have been given only two choices (classical choices): a) writing their statement is true, or (exclusively) b) writing their statement is not true (false or anything else). 3) Assume a choice has been made by you in 2. 4) Would you then believe that the same subject uttering q: Would you believe me? deserves a a) `no’ Or (exclusively) a b) `yes’ (classical choices) as a response from you?
We now go item by item of the problem, written in the English language as it is, with no further complication, and absolutely no translation into symbols, given the level it reaches (already explained why a person cannot fit a bigger box into a smaller one, only
the other way around, that is, no point in playing stupid and trying to translate a problem well above the level of Mathematics into classical logic lingo (for this discussion, please refer to [xxx, 2008])). In the sections which follow, we analyze each one of the above steps, keeping the order of presentation above, to then reach a conclusion.
Step 1: The definite statement, as uttered by subject.
First of all, the oddity of manufacturing a non-existing situation is impressive: Someone comes, out of context, and utters either that they always lie or that they always tell the truth (exclusively), or even that they do both (or anything else which implies judgment of their honesty, in a universal way regarding their every statement in life), but all amounts to the same information content, that is, none. Basically, if a classical computer is listening (and that is the proposal of the problem, once the only accepted answers are `yes’ or `no`, so that the computer has to be classical, and we insert the element `machine’ here for whatever is logical is passive of programming), no input will be made. Why? A speech, of a person, judging themselves, has got absolutely no logical value. Basically, a system can never judge itself, on any grounds; this is not a valid process, which may lead to any universal inference, as the problem demands. It is obvious, even for a child, that the only person able to emit judgment is that out of the system… : If you are inside of the bubble, you cannot judge the nature of it because you do not hold enough information about all outside of it, and judgments may only be made by those dominating all available matters of the same nature, or level, of the `attrib’ element contained in the utterance
(considering a Maple element here), therefore judgment may only come from the people living outside of the bubble and with no contact with its surface, situation similar to that justifying the necessity to see the planet from the outer space, rather than from inside of it or from over it, in order to judge, in what is closest to a universal judgment, its shape. The first utterance is then empty in logical value. It is necessary that we have an external person, or thing, to make of that statement something logically useful (for any sort of logical system, which must, by default, mean something through which we are able to produce inferences). What may then be inserted is, for instance, the figure of the liar detector, which will then tell us the actual information content for that assertion. The human world is obviously not logical, only the machine world is… . Therefore, whatever cannot be dealt with via machine cannot be computational (Classical Logic is always computational), as for scientific purposes, for it does not deserve a universal decision, what means it cannot be suitable for either writing in scientific language or arguing about it. This way, it is ridiculous to even dare thinking of that as a statement for Logic, as a proposition. That is simply an incomplete logical proposition. It will become a logical entry, or proposition, that is, a unit that Philosophy (we have written what Philosophy should mean: scientific discussion of whatever is logical in the human actions on Earth which may be expressed, perfectly well, via language) can deal with, once we aggregate the judgment made by the liar detector to the already existing statement. The proposition will then be the revised p, now compounded: (I always lie, the machine has returned `x’), x replaces either `true’ or `false`, and exclusively one of the options. Of course there are only two allowed possibilities for a liar detector ( classical ones ), so
that there is also no room for any other speculation of delusional nature (both true and false, for instance).
Step 2: You were listening and must now make a choice.
Indeed, you were listening… . Now we must manufacture a situation in which you judge, in real life, wheter that is true or false, that is, a situation in which you bother, and dare, knowing more than the own person who has created the problem…( of course the simple thought that you can do it makes of you a megalomaniac person, for you cannot know more than the own utterer about themselves, but we keep on going… . Notice that the people thinking of it as a big deal really wish to manufacture a context that is almost impossible to be found in reality). All a normal person would do is stating, perhaps as Christ would: You said it, now you tell me ( and the worst of all, we still have content zero, for there was nothing useful to you, or added to your life, with those words). Here, we must also remind the reader that Science may only be called Science if whatever actions which lie inside of it lead to human progress, and it does not seem relevant, in those regards, to argue about the issues of the Liar Paradox. However, once more, suppose the problem is of use, that is, of scientific value. We then add the information from the liar detector, which is machine-useful, which is basically what a computer demands: The proposal (output of one, input of another) regarding the analysis. Now, it is us only repeating the information attained via another machine, what just puts
coherence in all (machines talk, same level, that is, the whole problem was put into a Classical Logic perspective and, therefore, made passive of judgment and presentation of solution there, as explained in our work from 2008). Step 3 is irrelevant.
Step 4: Would you believe them? Please write `yes’ or `no’.
Notice that the title for the section already implies information being added to the reader’s mind: logical entities must be passive of writing, never only thinking, that is, to deserve being considered as logical information, the thing must be passive of being told in writing, not only in discourse, to others… Now, of course, emitting your opinion is, once more, also logically useless action. You may, as well, lie or tell the truth… . Therefore, the question does not make any logical sense, and any logical speaker will say: 'Well, based on the liar detector test, `yes’ (or `no`)', so that they are being excluded from the environment the problem wishes to belong to (the logical environment), environment to which a being, if normal, cannot entirely belong, so that the exclusion is necessary. Basically, the Liar Paradox is not fun: There is no paradox once more, and the level it reaches is far lower than the level of the Sorites, in terms of human reasoning. It cannot be a paradox because there is obviously no conflict in life generated by it. A person would never waste their time, if ever depending on such judgments even if it were to save their own existence. Suppose, for instance, that a gun is pointed at their faces, and the utterer states that if they
solve the `Liar Paradox`, they will save their lives. What would a reasonable person do? They would throw another paradox over the utterer! Why bothering? If they cannot see it is not a paradox, why would you bother arguing with non-logical speakers? You do not waste your time, you do not try, you distract them from the fixed idea, and that has to be the only logical choice! Your life at stake, you will not go probability: Your only chance is making them as confused and busy as they try to make you be while you think of ways of getting out of the gun’s nose… Well, once more, as we did with the Sorites, if it were ever a paradox, point what word comes after paradox (paradox of language? Paradox of logic? ). Now we consider each one of those: a) Paradox of Language: in Language, there is allowance for anything to happen, even for the proposer (or presenter) to ask that and the `victim’ to leave the place with a `uh!’, that is, there is no duty of answering, so that there cannot, ever, be a single paradox in Language (Language is a tool, not a logical place, it is a tool for both entertainment and expression). b) Paradox of logic: apparently it is there they place it (in logic). If such is true, there must be at least two possible inferences, conflicting, which are passive of deduction from the same propositions and the same evaluations. However, both input and output of the problem are classical. That demands, once more, translation of a broader area into a smaller one. Such a translation can only be a forced move. What is required for that
forceful move to be plausible and acceptable is the use of logical tools, trivially. Basically, we have proposed the liar detector, which will change confused language speech (broad sector, involving emotions, logical decisions of any level, even impairment, for a person may not be able to say `lying`, or say `truth`, for instance…) into bivalent one (true, false), what is clearly possible in this case. To deserve being called a paradox in logic, it is necessary that the Classical Logic systems involved create confusion, that is, produce two possible results for each valid interpretation. However, once more, it also seems impossible to find paradox in this area if the right elements (or complete) of analysis are used. Notice that, for each valid interpretation, there is only one output, what means no confusion and, therefore, no paradox in Logic, or in the logic, at all. Who is confused? The person proposing the problem or the person reading it! Thus, it can only be a paradox of mind, what is not worth discussing, for the mind is not a logical place either! The mind is a messy place, where we really do not want to go when writing about Philosophy: We wish to work with what we may reach and the mind is obviously a place which we cannot reach through words or symbols, the only available tool for philosophical analysis. It is all well beyond that. Therefore, the Liar Paradox is a paradox of internal nature, thus it is no paradox at all for it will be for some, but not for others, not deserving a universal standing as a paradox.
Conclusion
The Liar Paradox is an allurement, as much as the Sorites paradox is. The Liar Problem exists to show the complexity of a human mind, while the Sorites Problem exists to show the complexity of the human verbal expression… Basically, it is an allurement, something to remind us on how our mind is complex, if anything ever deserving being told to belong to Philosophy at all… Place it belongs to (please refer to our 2008 work from the references, [xxx, 2008])? Philosophy of Mind. Adequate addressing then of these can only be made from inside of the Philosophy of Mind, but with the problem corrected, revised, according to our well-posedness theory for philosophical problems (see work from 2008, once more, [xxx, 2008]).
References:
[xxx, 2006] xxx (2006); A Solution to the Sorites, Semiotica, 160 (1/4).
[xxx, 2008] xxx (2008); Well-posedness problem in Philosophy, preprint, online repository at www.pdfcoke.com/illmrpinheiro2 (as accessed on the 17th of February of 2009). [Paul V. Spade, 2005] Spade, Paul V. (2005), Insolubles, The Stanford Encyclopedia of Philosophy
(Fall
2005
Edition),
Edward
N.
Zalta
(ed.),
URL
http://plato.stanford.edu/archives/fall2005/entries/insolubles/. Accessed in July of 2007.
=
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