08 Jan 08
2 edits
Antinomy: An apparent contradiction between valid principles or
conclusions that seem equally necessary and reasonable. Built-in
contradiction, conflict or opposition of one law to another. Not to be
confused with 'antimony', one of the metallic elements.
#1 The only well remembered line of the Cretan poet Epimenides
is one of the oldest examples, "All Cretans are liars."
#2 Another contemporary version of the same 'antinomy' is more
succinct and more troublesome. It reads, "This sentence is false."
#3 ________________________________________________________
08 Jan 08
Originally posted by Grampy BobbyErr......... what??
Antinomy: An apparent contradiction between valid principles or
conclusions that seem equally necessary and reasonable. Built-in
contradiction, conflict or opposition of one law to another. Not to be
confused with 'antimony', one of the metallic elements.
#1 The only well remembered line of the Cretan poet Epimenides
is one of the oldest exampl ...[text shortened]... his sentence is false."
#3 ________________________________________________________
09 Jan 08
Originally posted by Grampy Bobby#3 Black is White
Antinomy: An apparent contradiction between valid principles or
conclusions that seem equally necessary and reasonable. Built-in
contradiction, conflict or opposition of one law to another. Not to be
confused with 'antimony', one of the metallic elements.
#1 The only well remembered line of the Cretan poet Epimenides
is one of the oldest exampl ...[text shortened]... his sentence is false."
#3 ________________________________________________________
?
09 Jan 08
Originally posted by Grampy Bobby#1 is only troublesome if uttered by a Cretan.
Antinomy: An apparent contradiction between valid principles or
conclusions that seem equally necessary and reasonable. Built-in
contradiction, conflict or opposition of one law to another. Not to be
confused with 'antimony', one of the metallic elements.
#1 The only well remembered line of the Cretan poet Epimenides
is one of the oldest exampl ...[text shortened]... his sentence is false."
#3 ________________________________________________________
aren't these examples of paradoxes, rather than antimonies?
09 Jan 08
Originally posted by Iron MonkeyW.V. Quine (1962) established several classes of paradoxes:
#1 is only troublesome if uttered by a Cretan.
aren't these examples of paradoxes, rather than antimonies?
1. Veridical- Result that appears absurd but is true.
2. Falsidical- Appears false and is false.
3. Antinomy- in neither class but reaches a self-contradictory
result by accepted ways of reasoning.
4. Dialetheia- (identified after Quine) Paradox is both true
and false at the same time... "John is in the room." In fact
John is standing precisely halfway through the doorway
-Wikipedia
09 Jan 08
1 edit
Originally posted by Grampy BobbyYes, but the Epimenides paradox is classed as a 'self-refuting idea'. See http://en.wikipedia.org/wiki/Self_refuting_ideas section 2.4. I'll check Quine to see what he says about it - sometimes the Wikipedia can be a bit dodgy, especially on philosophical matters.
W.V. Quine (1962) established several classes of paradoxes:
1. Veridical- Result that appears absurd but is true.
2. Falsidical- Appears false and is false.
3. Antinomy- in neither class but reaches a self-contradictory
result by accepted ways of reasoning.
4. Dialetheia- (identified after Quine) Paradox is both true
and false at the sam in the room." In fact
John is standing precisely halfway through the doorway
-Wikipedia
09 Jan 08
2 edits
Originally posted by Grampy BobbyCe n'est pas une réponse.
Antinomy: An apparent contradiction between valid principles or
conclusions that seem equally necessary and reasonable. Built-in
contradiction, conflict or opposition of one law to another. Not to be
confused with 'antimony', one of the metallic elements.
#1 The only well remembered line of the Cretan poet Epimenides
is one of the oldest exampl his sentence is false."
#3 ________________________________________________________
(Nor is it a pipe, for that matter.)
09 Jan 08
Originally posted by Iron MonkeyHe says that the interest of the Epimenides paradox is captured by 'This sentence is false', and that this is the "essence of antinomy" (Quine, "The Ways of Paradox", 1961, pg. 7).
Yes, but the Epimenides paradox is classed as a 'self-refuting idea'. See http://en.wikipedia.org/wiki/Self_refuting_ideas section 2.4. I'll check Quine to see what he says about it - sometimes the Wikipedia can be a bit dodgy, especially on philosophical matters.
09 Jan 08
Originally posted by bbarrfair enough - is he using 'antimony' in the same way that Kant translations use the term, do you think?
He says that the interest of the Epimenides paradox is captured by 'This sentence is false', and that this is the "essence of antinomy" (Quine, "The Ways of Paradox", 1961, pg. 7).
09 Jan 08
1 edit
Originally posted by Iron MonkeyI don't think so, but that is because I can't see the relevance of self-refuting propositions to Kantian antimonies. The way out of the paradox apparently foisted on us by 'This sentence is false' is to deny that this series of marks actually expresses a proposition (which I believe was Tarski's solution, pace his disquotational theory of truth). The way out of the Kantian antimonies (those relating to space and time, at least) is to deny that apparently exclusive and exhaustive disjunctions like 'The world is either finitely or infinitely divisible' are actually exhaustive, since we can reform our concept of 'world'.
fair enough - is he using 'antimony' in the same way that Kant translations use the term, do you think?