Does the expression "does not describe itself" describe itself or not? Whether we answer this question in the affirmative or in the negative, we will receive a contradiction
Marius Cohen, "Galileo" magazine
Many of the terms we use describe concepts themselves (or, if you will, apply to concepts). For example, the concept of "well defined" is a concept that applies to any concept whose definition allows us to unequivocally determine its field of application (that is, the group of items to which it applies).
The concept of "big", for example, is not a well-defined concept, because not everything can be determined unequivocally whether it is big or not. On the other hand, the term "three-syllable" is a well-defined concept, since its field of application is the group of all words that have exactly three syllables. Another example of a concept that applies to concepts is the concept of "common in the language" (which itself is not well defined). The concept of "interesting", for example, is a common concept in the language, and the concept of "dim" is not.
We will define below two concepts, "autological" and "heterological", which themselves are used to describe concepts: we will call any concept that describes itself (or, if you wish, that applies to itself) autological. For example, the following concepts are autologous:
* "Multisyllabic" - if we define a multisyllabic phrase as a phrase of at least 3 syllables, then "Rav-e-b-r-ti" is also like that.
* "In Hebrew" - this concept applies to any expression in the Hebrew language, including itself.
* "Word" - this concept also applies to himself, because "word" is also "word".
Conversely, any concept that does not describe itself is called heterologous. For example, the concepts below are heterologous:
* "Monosyllabic" - since "Had-e-b-r-ti" is not monosyllabic, this concept does not apply to itself.
* "In English" - this concept applies to expressions in the English language only, and therefore, due to being in Hebrew,
* He does not describe himself.
* "Unintelligible" - this concept is understandable to us, and therefore it does not describe itself.
In light of these definitions, it is possible to ask whether the term "heterological" is itself heterological, that is, one that does not describe itself, or not. Well, if we assume that the concept "heterological" is indeed heterological, then it describes itself (in the same way that the concept "in Hebrew" describes itself because it is itself in Hebrew). But if he describes himself, then according to the definition of the concept he is not heterologous (but autologous).
On the other hand, if we assume that the concept "heterological" is not heterological, then by definition it does not have the property "does not describe itself", that is, it does describe itself. But if he describes himself, he must be heterological, because heterology is exactly the characteristic that this concept attributes to the concepts it describes. It follows from this that the term "heterological" is itself heterological if and only if it is not heterological!
This paradox was presented in 1908 by the logician Kurt Grelling and the mathematician Leonard Nelson, who were also well-known philosophers, and among other things also dealt extensively with Russell's paradox (see "Galileo" 105).
points for thinking
The Garling-Nelson paradox has characteristics reminiscent of Berry's paradox ("Galileo" 103), which discusses the concept of "the first natural number that cannot be described in less than ten words", and Russell's paradox ("Galileo" 105), which discusses the concept of "the set of all sets that do not contain themselves as an organ". Identifying the similarities between the different paradoxes may lead to possible solutions.
Note that an implicit assumption (that is, not explicitly stated) that we made in presenting the paradox is that every concept is either autologous, that is, one that describes itself, or heterologous, that is, one that does not describe itself. Is this assumption reasonable in your opinion, or may there be concepts that do not belong to either of these two categories?
And another point for thought: does the attempt to determine whether the term "autologous" is autologous or non-autologous (that is, heterologous) lead to a contradiction? If not - is "autologous" autologous or not?
Solving the paradox
Below are two suggestions that have been put forward to resolve the paradox. As is also true regarding many other paradoxes, including those discussed previously in this section, these solutions are also controversial, but they certainly provide interesting insights into the use of language in general, and regarding the Garling-Nelson paradox in particular.
Limiting the conceptual category of "heterological" - this proposal rejects the implicit assumption that every concept is either autologous or heterologous. The reason for this is that each concept has a group of items (which will be called below its conceptual category), the determination of whether the concept applies to them or not is significant, while any attempt to make such a determination regarding items that are not in this category is meaningless.
For example, the concept "prime" (a number divisible by itself and 1 only) is a concept that can be determined whether or not it applies to natural numbers only, and therefore these numbers constitute its conceptual category. Thus, for example, it is possible to determine (according to the definition of the concept) that the numbers 2, 7 and 13 are prime, while the numbers 12, 35 and 100 are not prime.
In fact, all natural numbers can be divided into two groups: one of prime numbers and the other of non-prime numbers (and they all belong to the conceptual category of "prime"). However, it would be meaningless to determine with regard to anything else, such as a person, a book or an idea, whether it is primary or not, and therefore these things do not belong to the conceptual category of "primary" (that is, we do not say about the claim "Daniel is primary" which is false, except that it is meaningless).
If so, there are things that are primary, there are things that are not primary, and there are things that it would be meaningless to say that they are primary or not primary. So is the concept of "blue": there are things that are blue, there are things that are not blue, and there are things that it would be meaningless to say that they are blue or not blue (such as an idea, love, a number, a concept), because they do not belong to the conceptual category of "blue" at all. ".
Therefore, the claim "the sky is blue" is true, the claim "the grass is blue" is false, while the claim "the number 7 is not blue" is a meaningless claim (and therefore neither true nor false). We can apply this insight to the Garling-Nelson paradox if we say that not every concept belongs to the conceptual category of "heterological".
In contrast to concepts such as "unintelligible" or "in Hebrew", which are in this group (the first is heterological and the second is not), there are concepts, among them the concept of "heterological" itself, which do not belong to this conceptual category, and therefore it would be meaningless to determine whether they are heterologous or not. The problem that this solution raises is that, unlike concepts such as "primordial" and "blue", it is relatively easy to reason why something does or does not belong to their conceptual category, it is not easy to reason why the conceptual category of "heterological" does not include this concept itself.
Interdependence that leads to contradiction - the second proposed solution also rejects the implicit assumption that every concept is either autologous or heterologous. In fact, it can be shown that the problem stems from the definition of the term "heterological".
Suppose that all concepts can be divided into two groups: Group A, which is the group of autologous concepts, and Group B, which is the group of heterologous concepts (such a division should be possible based on the implicit assumption above).
It is clear that the assignment of any concept to one of the two groups is conditioned by the answer to the question: "Does it describe itself, or not?". However, the term "heterological" is equivalent to the expression "belongs to group B", then the answer to the question "does the concept describe itself or not" depends on how it belongs to one of the groups, so that in this case there is a mutual dependence between the answer to the question "does it describe itself" ” and associating the concept with the appropriate group.
Mutual dependence does not always lead to a contradiction, but it does lead to a contradiction in the case in question, since associating the term "heterological" with group A requires its association with group B and vice versa, and therefore it is impossible to associate it with either group. In other words: it is impossible to divide all concepts into two groups as required in this case, and the concept of "heterological" is neither autologous nor heterologous.
For dessert 1
A relationship is a relationship that can exist between two or more things. For example: "I love you" or "higher than", which are both relations, express a connection between, for example, two people: "Yonathan loves Ruth" and "Naomi is high from Ronan".
These connections can of course exist or not exist, that is, it is possible that Jonathan does love Ruth, and it is possible that this is not the case (and it is also possible to use the negative relation, such as "he does not love you", or "he is not taller than"). In a similar way, it is also possible to define relationships that express connections between two relationships.
For example: "describes better than" is a relation that may be useful in a sentence like: "'loving you' describes better than 'likes you'" (what Jonathan feels about Ruth, for example). Let's now look at the relation "more common in the language than", which can be applied to two relations (for example: "love you" is more common in the language than "hate you").
If we try to apply this relation to itself and to another relation, we will get a sentence of the type: "'More common in the language than' is more common in the language than 'I love you.'" This is obviously a false claim, and therefore it is said that the relation "more common in the language than" does not exist between itself and the relation "I love you". But "does not exist between itself and a relation" is in itself a relation, and therefore it can also be applied to itself and receive a claim of the type: "'does not exist between itself and a relation' does not exist between itself and any relation R". Is this claim true or false?
Marius Cohen is currently completing his doctoral studies in philosophy at Ben-Gurion University. Originally published in "Galileo" magazine
15 תגובות
The expression "does not describe itself" does not not describe itself, and does not describe itself at the same time. Sounds like a bunch of nonsense to you? Well, the question itself is phrased in an equally sloppy way. It is impossible to come to an unequivocal conclusion in such cases, saying the phrase "does not describe itself" is just like saying "the number defined in this sentence + 1" - both are paradoxes, meaningless, and embarrassing to say publicly! why? Because everything is a pile of nonsense! Regardless of the stacking paradox! And now seriously, does the phrase "5" describe itself? Does the phrase " " describe itself? The answer - it's not an expression at all! And about something that is not an expression, it is impossible to ask that!
The mind is an electro-quantum-mechanical mechanism.
The laws of physics apply to it.
to Moses It is good that you understood that the mind is not part of the physical world. The laws of physics are not relevant to her..
To Moshe.. indeed a point for thought!!
to the point
Now I must admit your righteousness. From your correct comments regarding the definition of paradoxes that exist only in language, I can conclude that you are indeed a philosopher. However, as you say, the language does not exist in the world, so apparently you also cannot exist here in the world, and of course, as you point out, you cannot develop either.
Therefore, everything is now in its place in peace.
to burst If you thought a little more and talked less about the things you personally dealt with, you should demand that philosophy solve the problem of death in general. A car accident or cancer…
Every second sentence you've written reveals that you should urgently start studying some philosophy. Examples:
"If they only deal with what is interesting and not what is important and vital like car accidents" and who decides what is important?
"Guilty is one who admits guilt"... you will understand.
for a rookie
The car that I wanted to burn was rudely parked on the sidewalk on the Haifa (or Namir) road and forced the pedestrians to cross the street to the busy road and thus endanger them.
Burning the car would send a message to the government that the citizens are very, very bothered by the situation, otherwise it won't move anything!
I actually tried to elevate the importance of philosophy.. It's interesting that it seems the opposite to you! Maybe because of the burnt car!
There is no point in me taking a breath because it will only make my comments worse.
And I hope you didn't miss the sarcasm at the end of my response!
to the point
If this is the approach in philosophy and I believe you did represent it in your response...then philosophy has nothing to look for in this world! If they deal only with what is interesting and not with what is important and vital like car accidents (this is of course only a small example out of hundreds of problems that man faces every day alone)!
The philosophy you presented (probably the accepted one) floats above reality and is very careful to touch the material world...which is ridiculous or they are afraid that they will find out that the king is naked! , what's to blame?..why haven't they dealt with it yet?
Guilty is someone who admits guilt or blames himself for anything (it's not Olmert..that's for sure) the one who sold him the car is guilty ..the road is to blame..the garbage driver who woke him up is to blame..the neighbor who raped his wife is to blame ..the one who dumped his son The one who gave a license.. (according to the song by Zac Berel Amsterdam) and... a mediocre philosopher will easily fill several volumes that no one will read
What is an accident?..really what? It would be great if there was a list of questions and answers that would not exceed more than one page (for each question of course) that could be used!
A traffic accident is: a situation in which vehicles of any type are involved in an accident on the road or close to it with or without casualties and the driver was drunk or talking on the phone (similar) or just fell asleep... these actually belong to the causes of the accident!
I didn't understand what a philosophical meaning is and why is it important? For me, philosophy is a tool for investigating and testing reality like any laboratory, and the more sophisticated it is (complex forms of thinking that include as many different aspects of reality as possible), the faster and deeper the philosopher's ability to analyze and offer solutions!
One of the unique advantages of philosophy is its ability to analyze every situation and thing and learn from everything about everything else from its essence.. I once thought that a society that wants to advance another step must have a philosophical infrastructure that includes the most analyzes that will serve as a connecting network for presenting solutions and examining different solutions whether they fit reality or conflict with it and where ! But I dealt with it for three years until 96 and left it completely!
I haven't read a lot of philosophy and only recently I read Plato who tells about Socrates (the banquet) and Xenophon who tells about the same banquet in a different way and other things... the books are very interesting and understandable (requires concentration), but I never understood the paradox of Achilles and the tortoise (maybe I'm limited) I didn't understand why Achilles or any healthy person wouldn't get the tortoise in the second or third step!
The previous "rookie" - to hack of course!
And philosophy as a whole - and not as a whole...
got much, got nothing.
You started with a mission of attacking the rear of philosophy as a whole (which, of course, I disagree with you) and continued with pieces of truth to establish a theory of the causes of car accidents and ended up with a predatory dictatorship: sorry I didn't burn... I wouldn't dare!..I'll show them!!!
I suggest you take a break after every ten typed words - read - and only then continue.
And by the way - I'm glad it wasn't my fault when I finally stopped at the tambon of the car I was driving two weeks ago...
Where are the authorities???
For Jubilee:
Is the language of mathematics not part of the language? All basic concepts in mathematics are basic concepts, they have no meaning for those who do not understand the language.
For example, the concept of "group", a collection of details will try to explain to us. And what is a "collection"? And what is "details"? Isn't it about the details of the collection of hallucinations that our brain emits? The answer is no, so this is a fundamental concept.
to hack:
Everything that can be considered is related to philosophy.
And regarding the traffic accidents, you can analyze the whole progression of the matter. For example: You can start by asking what is "at fault", what is an "accident", and what is "movement" in general... and only after we have clarified all these concepts will it be possible to try to understand whether the question you asked has any philosophical significance at all (meaning, is it interesting. For example: counting how many toothpicks are in a box is an uninteresting philosophical matter), because if it has no philosophical meaning there is no point in bothering with it.
Moshe:
The paradoxes are in language and only in language. And things in language are not in the world. Therefore, they cannot be an engine for any development in the world. Only in language.
Without paradoxes there would be no existence for the world. Because they are an engine for all development processes. Applicability or relation or interaction of a factor upon itself appears in nature and thought in endless ways. Some of them in the immediate form discussed and most of them as interactions between the elements and their histories. After all, these are the ones that drive the development processes and cause the creation of the many arrangements that emerge as a result of these repetitive interactions.
As a proper example discussed here: without the paradox the author of the article would not be trying to sharpen his mind and the minds of the readers. And of course this is how the development of thinking comes about. It is worth remembering that until recently, for hundreds and thousands of years, philosophy was almost the only source of the development of thinking. In recent years it has declined from its greatness for one simple reason. that the processes discussed in philosophical thinking have moved from the metaphysical lines to technological physical lines. And today we see copies of paradoxes etc. in quantum theory and the like and computational theories in computer science and the like.
What is the question ?
Trying hard to push philosophy into the world of science and what comes out is one big nonsense chasing its own tail!!
What does this have to do with reality? To some inclusive scientific reality?
Is the sky blue a true claim? Really! And are they only blue? And not red, gray, blue, white, and more? Does it matter when the sentence is said? Is the sky blue at night too?
And the grass can't be blue? As above "the number 7 is not blue" can be true or false depending on what it is about!
As long as the sentences are not related to a certain reality they are meaningless including the sky is blue and the water is abundant!
I am now reminded of the disdain and contempt that scientists felt in the past for "philosophers" (and maybe even today) in their memoirs, including the story about Bohr who wrote on his door "philosophers are not allowed to work here". And they say.. where are they and where is the Greek philosophy!!
Why, for example, don't the philosophers use their tools to address an essential and contemporary issue such as car accidents? Or philosophers are only interested in vague things that cannot be examined in reality!
For example, I analyzed the issue of accidents about ten years ago and came to an unequivocal conclusion "the Israeli driver is not at fault" or only 5% at fault! And this at a time when all the commentators and experts did not stop talking about the fault of the Israeli driver and did not focus the claims on the main culprit which is the government!!
And how did I come to this conclusion? I just checked the condition of the road signs near the house (in Tel Aviv)..the condition of the intersections (angles of vision, blinding sun from an unclear traffic light, etc.) ..confusing signs on main roads, crooked signs ..I thought this was only the case in an urban area? And I multiplied by 6 for the whole country And that's how you get very quickly to the main culprit "the government" in accidents, including the lawlessness on the trains, etc.. Isn't this the "work" of philosophy? Like a vanguard marching ahead of the camp in this case ahead of the traffic!
At least as far as accidents are concerned, numbers of all colors (mainly red) are not lacking, nor are there quite a few paradoxes such as...why does a car stop at a crosswalk at a red light when it gains only a meter?? When if he stands as marked his profit will be greater (if everyone drives properly the roads will be freer) how many times!!
And who is to blame for the drivers standing at the crosswalk? the drivers? Absolutely not..it's the government that doesn't find a way (because it didn't search) to clarify this point just like vehicles parked in critical locations as if nothing is happening and there's a whistle here and there..I'm sorry I didn't burn one of them!
Give me the Tel Aviv area and within six months no car will dare to stand at a crosswalk as above, will not dare to park in blocking places while expressing disdain for others without an "overwhelming" response!! And if it happens (a car will be parked for more than an hour) all the blame will be on me as the representative of the government!
Are there philosophers who can explain why in such a case the blame would be mine??
anti-point
Russell's paradox can be described in mathematical language, in set theory.
In fact Russell's paradox is so mathematical that for some time it stopped the development of group theory.
All paradoxes and non-paradoxes stem from one basic false assumption, and that is, that language has a logical meaning beyond the combinations of words.
When the truth is that in language there are only substantive claims and non-substantial claims. And what is my business? It's a matter of personal taste that changes over time and with the mood and with many other known and unknown factors, for example, in a psychotic state (in a dream) claims like "7 has the color blue" can be matter-of-fact and have a deep meaning, while at the same time there can be nonsense words in others. And so exactly with every sentence in the language (and one can generalize, in thought).