21 Apr 05
1 edit
Let us define 2 words, heterological and homological. A heterological word is one that does not apply to itself, a homological word applies to itself. So as examples ...
Heterological :
Big, White (unless you have messed with the colours of this page), French, square, curly
Homological :
Black, English, supercalifragilisticexpialidious, homological
Question: Is the word "heterological", a heterological word, or a homological word?
I tried figuring out but my synapses shorted.... 🙄
Before you get on my case, this is taken from http://www.dbsugden.clara.net/paradox.htm
22 Apr 05
Originally posted by PawnCurryWell, if 'heterological' is a heterological word, it is not a heterological word. This is a paradox.
Let us define 2 words, heterological and homological. A heterological word is one that does not apply to itself, a homological word applies to itself. So as examples ...
Heterological :
Big, White (unless you have messed with the colours of this page), French, square, curly
Homological :
Black, English, supercalifragilisticexpialidious, homolo ...[text shortened]...
[b]Before you get on my case, this is taken from http://www.dbsugden.clara.net/paradox.htm[/b]
If 'heterological' is a homological word, it is a heterological word. In this case the word both describes itself and does not describe itself. Another paradox.
Paradoxes are impossible; therefore 'heterological' is neither heterological nor homological. Yet aren't all words either one or the other? So it must be heterological or homological. Another paradox.
I'm not sure how you'd describe this situation properly.
22 Apr 05
Originally posted by PawnCurryWhy is Black a homological word and white hetero? I don't understand. Is it because it is written in Black? If so, then you are wrong. The colour which we use to write a word isn't the word itself, so it doesn't have influence on a word being hetero or homological.
Let us define 2 words, heterological and homological. A heterological word is one that does not apply to itself, a homological word applies to itself. So as examples ...
Heterological :
Big, White (unless you have messed with the colours of this page), French, square, curly
Homological :
Black, English, supercalifragilisticexpialidious, homolo ...[text shortened]...
[b]Before you get on my case, this is taken from http://www.dbsugden.clara.net/paradox.htm[/b]
For example a word can be curved out of ice then it doesn't have a colour at all. Or even easier,...a word can be thought or spoken.
22 Apr 05
Originally posted by orfeo
You see, I don't know why you describe HOMOLOGICAL as being a homological word either. How does it describe itself?
Why do all words have to fit in one category or the other?
Why do all words have to fit in one category or the other?[/b]
I agree with this point.
Heterological isn't a heterological word and also isn't a homological word. So the statement that it has to be homoligical or heterological is false.
If I don't close a door it doesn't meen I'm opening it either.
To go even further If a door is not closed it doesn't state that the door is open.
22 Apr 05
Originally posted by SiebrenHence the proviso that you haven't tampered with the font colour on this page.
Why is Black a homological word and white hetero? I don't understand. Is it because it is written in Black? If so, then you are wrong. The colour which we use to write a word isn't the word itself, so it doesn't have influence on a word being hetero or homological.
For example a word can be curved out of ice then it doesn't have a colour at all. Or even easier,...a word can be thought or spoken.
"Black" is only a homological word if written in black ink, or seen in a black typeface. So I guess we have to add further provisos, that the "state" of a word can change depending on it's medium. Carved in ice, it is a heterological word (unless it's in a completely darkened room...)
I still think that a word must fall into either category: either it describes itself, or it doesn't. ATY's explanation of the paradox was very succinct.
Is it because it is written in Black? If so, then you are wrong. The colour which we use to write a word isn't the word itself, so it doesn't have influence on a word being hetero or homological.
The way to think of a homologicla word is this (I think!):- If you can say the phrase, "X is X", where X is your chosen word, and the logical result is truthful, then it's homological. If the logical result is false, then it is heterological.
e.g. Black is black - black is therefore homological as the word black on this page IS black (see proviso above).
Big is big - big is therefore heterological as the word big ISN'T big (OK we need a definition of how many letters a word need to be "big", or what the fontsize needs to be, etc.
So, "heterological is heterological" - if this is true, then it's a homological word. Which is clearly a paradox. If it's FALSE, then it's heterological - another paradox.
Either there's a fault with my reasoning, or it is a genuine paradox.
😕
22 Apr 05
1 edit
Originally posted by Siebren"The colour which we use to write a word isn't the word itself, so it doesn't have influence on a word being hetero or homological. "
Why is Black a homological word and white hetero? I don't understand. Is it because it is written in Black? If so, then you are wrong. The colour which we use to write a word isn't the word itself, so it doesn't have influence on a word ...[text shortened]... colour at all. Or even easier,...a word can be thought or spoken.
Agreed. "Ceci n'est pas une pipe".
There have been threads before on Russel's paradox. But I can't find them easily.
22 Apr 05
1 edit
Originally posted by PawnCurryThe words heterological and homological are descriptive terms. They
Let us define 2 words, heterological and homological. A heterological word is one that does not apply to itself, a homological word applies to itself. So as examples ...
Heterological :
Big, White (unless you have messed with the c ...[text shortened]... case, this is taken from http://www.dbsugden.clara.net/paradox.htm
aim to explain how a word is acting.
Let's use two other descriptive terms: black and red (referring to the
ink used to write a word).
Now, consider the two following words:
Black
Red
Let's describe them. The word black is black. The word red
is black. Would you describe this as a paradox? Of course not.
You've simply described the words. Just because the word 'red' is
written in black ink doesn't mean that the word 'red' loses any of its
significance.
Similarly, if you describe the words 'homological' and 'heterological'
as both being homological, no paradox ensues (just like saying the
word 'red' is black).
Nemesio
22 Apr 05
Originally posted by NemesioPerhaps I haven't explained clearly enough (or I've misunderstood the thrust of the problem myself).
The words heterological and homological are descriptive terms. They
aim to explain how a word is acting.
Let's use two other descriptive terms: black and red (referring to the
ink used to write a word).
Now, consider the two following words:
[b]Black
Red
Let's describe them. The word black is black. The word red ...[text shortened]... h being homological, no paradox ensues (just like saying the
word 'red' is black).
Nemesio[/b]
I think your example re black and red doesn't really fit: to say the word red is black is clearly NOT a paradox: using the terminology, it simply means that the word "red" is a heterological word (whereas, the word "black", in this case, is homological).
The paradox comes when trying to determine which set the word "heterological" belongs: the set of heterological words, or the set o homological words.
You've stated that the word "heterological" is a homological word, i.e. it applies to itself. But for it to apply to itself, it must be heterological. Can a word be both homological AND heterological at the same time? I think not: surely boths "sets" are mutually exclusive?
23 Apr 05
if "heterological" does not apply to itself, then it must be homological, as it falls into the set of words it describes.
if "heterological" is homological, then it applies to itself, and thus it must not apply to itself.
if "homological" does not apply to itself, then it must be heterological, as it does not fall under its own catogory. no paradox, all works out fine.
if "homological" applies to itself, then it must be homological, as it fits its own criteria. no paradox, all works out.
thus: "homological" can be either. "heterological" cant eb eiter.
the mathmatical counterparts are 0/0 and n/0, on which there has been much blather on this fourm. we never found anything more than what i have stated here.
23 Apr 05
3 edits
Originally posted by Pawnokeyhole"yields a paradox when appended to its own quotation" is either not a noun, inwhich case it can not be the subject of "yields", and the statement is not qramaticaly sound, or it is a quotation, in which case it is just a clump of words about which some comment is being made.
Here's the most brain-twisting verbal paradox of all!
"Yields a paradox when appended to its own quotation" yields a paradox when appended to its own quotation.
True or False?
if we try to determin if that comment is in fact true, we take the quoted phrase, and subject it to the specified situation, in which case we get the original statement. if order to find wether the original statement is true, we must find wether the following can be said of the new (identical) statement:
"it is not possible for it to be either true of faulse."
so we consider each possibility.
if the statment is faulse, then this statment must be ture:
"Does not yield a paradox when appended to its own quotation" does not yield a paradox when appended to its own quotation.
in which case ............................................................................................
the truth or faulsness of the statment can not be determined. intuitivly we can say it is neither, but we can not show anything logicaly, because any attempt to anilise the statement results in a loop. its paradoxal status is just as undertermiable as its turthfull status.
although this matter may seem out of place on this thread, the situations are a bit similer. it may be true, it may be faulse, if may be a paradox, but none of these posibilities can be determined as actual.
24 Apr 05
1 edit
Originally posted by Pawnokeyholei got it:
Here's the most brain-twisting verbal paradox of all!
"Yields a paradox when appended to its own quotation" yields a paradox when appended to its own quotation.
True or False?
Statment A:["Yields a paradox when appended to its own quotation" yields a paradox when appended to its own quotation.]
i think i is apparent that this is equivilant to
Statment A:[Statment A is a paradox]
if statment A is a paradox, then statmetn a is true.
if statment A is true, then statment A is not a paradox, and thus statment A is faulse
if statmetn A is faulse, then statment A is not a paradox, and thus statment A is faulse.
thus statment A, although it can never be fully anilised, cannot be true, and it cannont be a paradox, and it can be faulse. as those are the only options, statment A must be faulse.