24 Mar 04
1 edit
Originally posted by qwiksylveri've always heard that, in logic, a paradox cannot be resolved and simply remains a paradox.
In communication a statement is considered false if it contains a paradox, for example:
the sentence below is false
the sentence above is true.
would be false as it is a paradox.
two other constructs which are defined but have little place in logical arguments are the tautology and the absurdity.
the assertion "x is equal to 1 or x is not equal to 1" is a tautology because it is always true regardless of what the value of x is.
the assertion "x is equal to 1 and x is not equal to 1" is an absurdity because it is always false.
obviously, these are not what we are looking for here.
25 Mar 04
Originally posted by iamatigerthat's the one i wanted!
"I am lying"?
anyone who has seen the original star trek series can remember this in the episode "i, mudd" where the humans defeat a huge collection of very logical androids with illogic, and this was one of the final tactics used--and the androids went into infinite loops trying to figure it out!
ti went something like this:
kirk (to norman the chief android): note this, norman. everything harry mudd ever told you is a lie. remember that!
mudd: norman, listen closely. i am lying.
norman: you say you are lying. but if you lie that you lie, you must be telling the truth. but you cannot be telling the truth because everything you say is a lie. if you lie that you lie... illogical! illogical! only humans can explain their behavior. please explain. please explain!
kirk: i am not programmed to respond in that area.
norman, with smoke rising from his head, shuts off, the humans win, and mccoy gloats.
29 Mar 04
1 edit
Originally posted by DumDum81no, "i am lying" is not a statement.
This would be a true statement. If he says that he is lying he is telling the truth about lying😏
it is not because it is both true and false simultaneously.
if you say you are lying, then you are speaking the truth that you lie, but lying in and of itself is the absence of truth.
people simply reject such an assertion as being nonsensical. note, however, that, "i was lying" is a perfectly valid statement since either you did or didn't lie in the particular time ago to which you are referring.
once again, timing (in this case, verb tense) makes all the difference.
29 Mar 04
2 edits
Originally posted by Acolyte"reducing to the point of sbsurdity" is a valuable logical tool, in which you reach a level of what would be absurd, but arguing an absurdity to start with is not a valid way to prove something.
I disagree: what about reductio ad absurdum?
in a similar vein, consider "proof by contradiction" in which you assume the opposite of what you are trying to prove and show that this is impossible so your original assertion must be true. it goes without saying, of course, that the original assertion must be a statement or the "proof" is not valid.
here is an example of attempting to prove an absurdity in geometry:
assertion: all triangles are isosceles.
"proof": in triangle abc, draw the perpendicular bisector to side bc (calling the intersection point with that side d) to vertex a. triangles adb and adc contain a common side (ad), congruent sides (bd and dc), and the angle between is a right angle since ad is a perpendicular bisector. therefore, those two "sub-triangles" are congruent by side-angle-side, and so sides ab and ac are congruent by corresponding parts.
the flaw? you can't draw a perpendicular bisector to side bc from vertex a unless you have an isosceles triangle to begin with! otherwise, the bisector to a is not perpendicular and is called the median. the perpendicular bisector will hit side ab or ac but not the vertex--unless the triangle is isosceles from the start.
so, sometimes, what seems to be perfectly logical turns into an absurdity.
30 Mar 04
Originally posted by BarefootChessPlayer😵
"reducing to the point of sbsurdity" is a valuable logical tool, in which you reach a level of what would be absurd, but arguing an absurdity to start with is not a valid way to prove something.
in a similar vein, consider "proof by contradiction" in which you assume the opposite of what you are trying to prove and show that this is i ...[text shortened]... eles from the start.
so, sometimes, what seems to be perfectly logical turns into an absurdity.
31 Mar 04
Originally posted by BarefootChessPlayerThis reminds me of a common way to criticise someone else's arrogance: "You always think you're right, don't you?" To which the only sensible response is along the lines of "Well how often do you think you're mistaken?" 😀
no, "i am lying" is not a statement.
it is not because it is both true and false simultaneously.
if you say you are lying, then you are speaking the truth that you lie, but lying in and of itself is the absence of truth.
people simply reject such an assertion as being nonsensical. note, however, that, "i was lying" is a perfectly va ...[text shortened]... hich you are referring.
once again, timing (in this case, verb tense) makes all the difference.
