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Defining concepts used in an argument is the most important step of that argument as it determines our question and makes it objective.

However, what is the definition of this act of definition? Can we ever define this act? Maybe there is a fallacy of equivocation here, but it is clear that if someone wants to define something, he should know what he is doing (in this case defining something), and so one cannot define definition because definition has not been defined yet! For instance, imagine someone has defined the act of defining to be "to give meaning"; then could he give this definition to the act of definition without knowing that he wanted to give a meaning to it? Didn't he define the act of definition by itself?

If we can never define something, we are just speaking subjectively at all time and we can never have an ideal objective platform for arguments. This is why I think there is a fallacy somewhere as scientists and philosophers are already defining concepts in their articles. However, this might be due to a common sense of the definition of the act of definition, which means there is no objective platform as common sense is subjective.

Would you please inform me of any fallacy or develop/justify this argument?

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    See Definition : "the action or process of stating the meaning of a word or word group". – Mauro ALLEGRANZA Dec 13 '19 at 11:58
  • You trouble is with the "obvious" circularity of language; we cannot define all. The issue is that we do not learn language through definitions. – Mauro ALLEGRANZA Dec 13 '19 at 12:00
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    The Aristotelian idea of definition you have in mind is of limited applicability. Concepts used are rarely defined in arguments this way, and most interesting concepts do not have useful definitions in terms of other concepts. The arguers must already have a shared repertoire of concepts, and most of those are mastered not through such definitions but through use in examples and practical application. When necessary, this use can be made more precise in mathematical formalisms, see SEP Definitions. – Conifold Dec 13 '19 at 12:28
  • @Conifold, so you mean that a concept X can be defined by its function (like examples and practices) not by other concepts. But what defines those practices? Is it something else than the X itself? Can you define X by its uses when they are already defined by X? (when you say: practices of X, you are assigning those uses to X so you need X as part of their definition) – seyed sepehr mousavi Dec 13 '19 at 12:49
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    Nothing defines them because there is no sense to "defining" them, they pre-exist. In the end, the use of concepts is embedded into practice, both linguistic and not, and is only possible within it. So, in the end, one has to exit the sea of concepts transcribed into more concepts to find their meaning. Life comes before arguments, and one has to master ways of life before they can even understand definitions, let alone use them. To paraphrase Wittgenstein, "there is a way of grasping a concept which is not a definition". Definitions are just a transcription device, not a conduit of meaning. – Conifold Dec 13 '19 at 13:20
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but it is clear that if someone wants to define something, he should know what he is doing (in this case defining something)

It is not clear to me that this part of the argument works. We do things correctly all the time without deeply and explicitly understanding them. Some examples:

  • Interpreting visual scenes: we look at the world and automatically infer (usually correctly) what objects there are and where they are located without understanding how hard the problem is that our brains are solving to get to that point.

  • Judging whether sentences are grammatical. Here's one of my favorite examples: Is the following question ambiguous? "Which horse do you want to win?" (Yes -- the horse could be a contestant or a prize.) How about the following? "Which horse do you wanna win?" (Most people will say it is not ambiguous; only the -- somewhat strange -- interpretation that the horse is a prize seems reasonable. But if asked to explain why, generally people don't have a clue why the question is no longer ambiguous.)

As has already been pointed out in the comments, we cannot get started on formal reasoning without having already somehow bootstrapped ourselves into some basic shared concepts (through evolution and reinforcement learning, presumably). Whether and when these concepts can serve as a sound basis for formal reasoning beyond that is of course a deep and challenging question.

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    Thanks for your answer. Let me grab your attention to a point: it is enough for me to implicitly define things without really caring about what I am doing. However, in an argument, it will not be necessarily enough for other people and I. Why? Because we can potentially have different definitions in our minds. If we do, then we must bring our definitions on paper to make them visible by the others, and so object to judgement. This means that we need explicit definitions. You are right that we are not necessarily in need of explicit definitions, but we might be at some point. – seyed sepehr mousavi Dec 13 '19 at 16:44
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    Therefore, you would potentially need to know what you are doing when you define things, so that we can make an objective, non-emotional platform. Of course, "common" sense is a sense and of course all sense are subjective. – seyed sepehr mousavi Dec 13 '19 at 16:56
  • This all makes sense. However, I can also imagine an argument between two people who very carefully define their terms, except they never carefully thought about the nature of definition itself. Nevertheless (by sheer luck? or by absorbing the habits of more careful thinkers?) they do so in the same way that someone who did carefully think about the nature of definition would have. Is their argument any less valid as a result? – present Dec 13 '19 at 22:13
  • Their argument is less valid BUT the results of the argument is true. It is why usually high Mathematically filled articles are published in physics journal. It means that it's probability to be wrong is low. (here validity means the probability of being true.) – seyed sepehr mousavi Dec 14 '19 at 7:10
  • But is the definition of definition (or theory of definition) a part of the argument itself? Usually, we would not consider it to be. Consider a computer that has been programmed to do automated theorem proving (in a relatively straightforward, non-general-intelligence way). It produces a proof of a theorem. But it has no real understanding of what it is doing, what the meaning of the symbols it is manipulating is, what a definition or a proof even really is, etc. Does this make the produced proof less valid? – present Dec 14 '19 at 11:53
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Wittgenstein would see 'defining' as a system (set of rules) for establishing family resemblances: in his parlance, definition would be a language game in which we use piece-wise similarity to construct an abstract class. For instance, we could look at a collection of objects of various sizes, shapes, colors and materials and declare them all 'boxes' by establishing a chain of similarities from Object A through other Objects to Object Z, even though Objects A and Z themselves seem to have little directly in common. Rules in such language games are sometimes overt and explicit, but as often as not are implicit and fluid, and we often know how to proceed with applying rules even though we cannot always explicitly say what the rule is or why we should follow it.

As often as not, we will not bother analyzing the rules of a language game unless they are explicitly challenged. For example, if I say to you:

Give the next number in this sequence: 1, 2, 3...

You will almost certainly sat '4,' assuming habitually that we are following the rule of counting (1, 2, 3, 4...). But if I were to say instead:

Give the next number in this non-linear sequence: 1, 2, 3...

Then you would discard the pre-given assumption and cast around for another sequence that fits the bill (e.g., the Fibonacci sequence: 1, 1, 2, 3, 5...). As a community we have many, many implicit rules that set up family resemblances we tout as definitions. We don't question them except where they start to cause us headaches, because definitions are not important in terms of their exactness, but instead in terms of our ability to move forward in whatever we are doing.

  • Thanks for the answer. However, your answer is not quite correct in my opinion. In this comment I will try to write why do I think so. I agree with you that if a definition works for a specific purpose, then we can continue to use this. But notice that there is still a problem even when definitions exist but are not explicit: not all people have the same definitions in their minds. This makes many arguments obsolete as the two sides cannot get to any conclusion. Notice that both people have some implicit definitions, but they are not the same. Now, how to solve this problem? – seyed sepehr mousavi Dec 13 '19 at 15:54
  • The only way to solve this problem is by formalising the definitions, or in other words, to make them explicit so that the other people can see what the others are seeing. This means that having definitions is not enough: having explicit definition is enough. Using your own words, having implicit definitions can potentially bring headaches and so there would be sometimes that we have to explicitly define something. Now, consider my original question: how can we ever write an explicit definition to resolve this issue if we don't explicitly know what we are doing (that is defining that thing). – seyed sepehr mousavi Dec 13 '19 at 16:01
  • This explicitly knowing of what we are doing (which is defining) is the definition of the act of defining. As you see, my question is reproduced. In the case of your mathematical example, if you ask the first question from someone, you must IDEALLY say exactly what you want by mentioning "linear sequence". You put the assumption that the other person has also this in his mind, but are you 100% sure about it? It is not impossible for someone to tell you that your question has infinite answers, and then you would have to tell him that you want a linear sequence. Thus, you need to formalise it. – seyed sepehr mousavi Dec 13 '19 at 16:08
  • This act of formalisation, which is in this case mentioning the type of the sequence, is impossible without knowing how to formalise it, like not knowing what types of sequences exist. If you don't know what shall you do to formalise, for example if are not aware of different types of sequences, then you can never build that formal platform. So, as conclusion, we really have to be able to explicitly define things to ensure that we can develop a common language and to achieve this, we have to explicitly define the word definition. But why shall I know the definition of defining if I can define? – seyed sepehr mousavi Dec 13 '19 at 16:29
  • That is because everything can be object to this subjectivity. Ideally, a logical argument does not include any subjective element, and all are explicitly defined. So even if you don't like to write a 100% objective article because you think the reader (probably) knows what you mean, you might need to define the concepts being used. One of these concepts is defining. So, can you prove that we will never have headache because of not having a common definition of the act of defining? If you can't, then it's better to have a definition of this act of defining in your pocket, just in case. – seyed sepehr mousavi Dec 13 '19 at 16:34
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This is a suggested answer by myself to the question I have proposed:

In a question, every single word used must be defined, so that the question can potentially have a well defined answer. This is not the case for any question that asks for the definition of a concept that is already used in the question. Why? Because this question needs its own answer to be a defined question. My question is one of these sort of questions which is not defined, as it uses a concept it is asking for, which is defining. By showing that my question is not defined, we can just ignore it and think of it as it never existed. Why? Because only definable things exist and non-definable phenomena are like paradoxes which are not viable. By this definition of existence of a question or proposition, we can say that my question does not exist, and so it has no definable, existing answer.

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    Only definable things exist? Rocks predate definitions according to science. Long before there were people throwing them at each other, they were here on earth. According to the tradition of analtyical philosophy definitions describe reality, they do not create it. Of course, some philosophers reject the tradition. – J D Dec 13 '19 at 18:36
  • Your argument does not dispute the statement that only definable things can exist. Being definable is a property of rock not of the people throwing them. So, one doesn't need to consider the existence of humans to show if something is definable or not. If something can be defined by a super intelligent species evolving in the next 1000 billion years, then it must exist. If it cannot be defined by those infinitely intelligent creatures, it cannot exist! (In other words, they can define everything that exists so everything is definable and so a non-definable thing cannot exist.) – seyed sepehr mousavi Dec 13 '19 at 18:54
  • In the analytical tradition, being definable is NOT the property of a rock, it's the disposition of the philosopher. Rocks have mass and energy, but not definitions. Ask any geologist. You confuse the territory for the map. Definitions are representations of real things. Real things exist independent of definitions as sure as rocks existed before people were around to define them. You can maintain your position or accept science; you can't have both. – J D Dec 13 '19 at 20:24
  • You are true with respect to your definition of definable and I am true with respect to mine. We both are right but our language is different. – seyed sepehr mousavi Dec 13 '19 at 20:29
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    You purport to come seeking answers. A glass that is already full cannot have anything added. By your definition unicorns are real because they can be defined. Am I supposed to accept that unicorns are real? Of course not, becuase by definition some things are not real. And there is the contradiction of your position. You define real by that which can be defined. But some definitions define things as unreal. Hence, somethings are both real and not real when defined. The rejection of this absurdity is why science works. – J D Dec 13 '19 at 20:33
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The Nature of Definitions

Can we define the act of defining?

Yes, and in a multiplicity of ways. Definition is essentially an association between a term and other terms, and is related to the intension and extension of terms.

Definitions might be stipulative, lexical, precising, theoretical, or persuasive if classified by function.

You seem to be concerned that lexical definitions are inherently and ultimately circular in a dictionary like the OED. Words in a soft dictionary indeed are defined in terms of one another, and that might create the illusion that there's no real meaning. Yet, meaning can be conveyed in a variety of ways in language alone. For instance, language has phonological, syntactic, and semantic structure at a minimum, and words convey meaning at the morphological level. Semantics is a complicated affair, and the philosophy of language has shown that it's not as simple as words are containers of meaning.

If you have an interest in definitions and meaning, start with an introductory logic book which covers definitions such as Hurley's _A Concise Introduction to Logic... as you get more advanced, dip into linguistics such as Jackendoff's _Foundations of Language. Become familiar with the basics such as the genus-differentia method before looking towards more philosophically complicated versions such as recursive definition and explication.

Defining Doesn't Require a Definition of Defining

one cannot define definition because definition has not been defined yet!

There are some definition methods that don't require definition. Consider the ostensive definition. If you want to teach an ape sign language, you could get it to associate a gesticulation in sign language by pointing. Note, the chimp requires no definition of definition to associate the meaning of the symbol with the referent. This is how a child learns the meanings of word: context within experience.

Object and Metalanguages

This is why I think there is a fallacy somewhere as scientists and philosophers are already defining concepts in their articles. However, this might be due to a common sense of the definition of the act of definition which means there is no objective platform as common sense is subjective. Would you please inform me of any fallacy or develop/justify this argument?

Your error in reasoning confuses the ability to use language with metalanguage. Let's take a phone system, for instance. When you talk to an automated voice system, it can understand 'yes' and 'no' when it asks you questions, and act appropriately. However, what it cannot do is define 'yes' and 'no'. Human beings often show the same signs of a lack of reflection when acquiring language. Ask a young child what is a banana, and they might reply 'A banana is a yellow piece of fruit'. But, then ask them, 'by what way did you define banana, by genus-differentia?' You might not get a response. That is because using an object language and using a metalanguage are two DISTINCT uses of language, with the latter being more sophisticated than the former. For more information, read the article on use-mention distinction.

The Turing Test is an example of an operational definition that defines human-level intelligence by using the ability of a system to convince a human being that it understands language like a human does. These systems inevitably perform poorly because computers, while able to use definitions, seldom are able to respond to definitions ABOUT definitions or show other signs of metalinguistic awareness. By using a series of probing questions, most systems can be shown to lack comprehension of a metalanguage that comes naturally to even children.

  • Thanks for the answer. About the meta language, would you please mention which define is a meta language (and what type) and which one is its object language? – seyed sepehr mousavi Dec 13 '19 at 19:13
  • And about otensive language analogy, this does not dispute my statement. Why? Because two different people can link two similar symbols to two different referents, which means they don't have a common definition. Notice that the purpose is to logically - and so objectively - define concepts and symbols, not just making a subjective association. This means that the act of defining needs a conscious knowledge of it to make it explicit. For the chimps case, they can never arrive at a consensus about the definition of something if they don't make their referent common, that they must be aware of. – seyed sepehr mousavi Dec 13 '19 at 19:20
  • Honestly, by your post it's not entirely clear what you are attempting to say. However, all definitions are arbitrary to some degree, which is why philosophers in general spend all of their time arguing. There is not "objective" way to define things. The sounds and words and terms we associate are at best conventions, not "logically irrefutable acts". Chimps can arrive at a consensus about definition, because they can teach each other signs. When a community of chimps use the same sign, they have a common symbol and a common referrent. They can't debate it bc there's no shared metalanguage. – J D Dec 14 '19 at 0:12
  • Some categories of referents do seem to be near universal, and are recognized as natural kinds. There is controversy over natural kinds, but the gist of it is that some classes of things tend to be identified across languages and cultures consistently. Deer are deer and fish are fish, and different cultures define each in similar ways. Why this happens is open to philosophical and scientific debate. – J D Dec 14 '19 at 0:14

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