A question about axioms

Metaphysics and Epistemology
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Dream_weaver “Doesn’t the conceptual level operate from the perceptual level?” Not necessary. Think about “dog”-if you are a dog -owner you’d think about your own dog. If not, you may imagine some animal which has essential features of dog, but doesn’t represent any specific perceptual dog. You can even imagine non-existent animal-like unicorn or flying dragon, or an animal you never saw before, only read its description. Think about higher concepts like capitalism, altruism etc… You don’t have any equivalents of such a concepts on perceptual level. Although it is true that concepts are implied in perception, we usually operate with explicit concepts,that is-words."With the exception of proper names, every word we use is a concept that stands for an unlimited number of concretes of a certain kind". The proper function of concepts is an expanding grasp of existence because concept includes all entities which belong to the same species (all dogs) or genus ( all animals) or existence ( all existents).

In Ayn Rand words:

"A concept is a mental integration of two or more units which are isolated by a process of abstraction and united by a specific definition. By organizing his perceptual material into concepts, and his concepts into wider and still wider concepts, man is able to grasp and retain, to identify and integrate an unlimited amount of knowledge, a knowledge extending beyond the immediate concretes of any given, immediate moment. In any given moment, concepts enable man to hold in the focus of his conscious awareness much more than his purely perceptual capacity would permit. The range of man’s perceptual awareness—the number of percepts he can deal with at any one time—is limited…He cannot visualize a hundred trees or a distance of ten light-years. It is only his conceptual faculty that makes it possible for him to deal with knowledge of that kind."

“The Psycho-Epistemology of Art,”

The Romantic Manifesto, 17

Since we cannot operate on perceptual level, the situation is quite opposite to that which you’ve described. Even by referring to concretes we use concepts. Suppose you see a birch tree and this is a percept. But when you refer to it you refer to birch tree, not to this particular birch tree you saw. It will take hours and maybe days to describe the particular birch tree in all details which distinguish it from all other birch trees and even so you won’t be able to do so without using concepts. Even if you describe it ostensibly-just point out on it and say-that what I mean, you are using at least 4 concepts.

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Dream_weaver “Doesn’t the conceptual level operate from the perceptual level?” Not necessary. Think about “dog”-if you are a dog -owner you’d think about your own dog. If not, you may imagine some animal which has essential features of dog, but doesn’t represent any specific perceptual dog.

Yes, this is what measurement omission is about. The concept integrates the perceptually given similarities. In this way, when I encounter another instance of a dog, I recognize it as such, and the new instance gets “added” to the concept as another confirmation as sort of a “This, too, is a dog.” It is in this way I can consciously maintain the correlation between the conceptual grasp of “dog” with the perceptually given dogs.

You can even imagine non-existent animal-like unicorn or flying dragon, or an animal you never saw before, only read its description. Think about higher concepts like capitalism, altruism etc… You don’t have any equivalents of such a concepts on perceptual level. Although it is true that concepts are implied in perception, we usually operate with explicit concepts,that is-words."With the exception of proper names, every word we use is a concept that stands for an unlimited number of concretes of a certain kind". The proper function of concepts is an expanding grasp of existence because concept includes all entities which belong to the same species (all dogs) or genus ( all animals) or existence ( all existents).

Rather than tackle capitalism and altruism, can I try “creator”. We can form the concept of a “creator” by observing someone create a cake from ingredients, mixing them up, putting them in a cake pan and sticking it in the oven for a period of time. We can observe someone using a brush, dabbing it in paint and applying it to a canvass, becoming a “creator” of a painting. When we abstract from our observations to create our concept of creator, we too, become a “creator” in a sense. We take the material provided by our senses, and “create” a concept from those materials. Understanding this can help understand why the application of “creator” to our metaphysical understanding of “existence” is a stolen concept. Capitalism and altruism have longer, more complex, conceptual chains anchoring them back to the perceptually given, still it is the material from the data of sense which they are validly formed,

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"Existence and identity are _ not attributes _ of existents, they _ are _ the existents. . . . The units of the concepts “existence” and “identity” are every entity, attribute, action, event or phenomenon (including consciousness) that exists, has ever existed or will ever exist." (ITOE 56)

This quote directly supports the conclusion that Rand held that existence is a first level concept because some of “… every entity, attribute, action, event or phenomenon (including consciousness) that exists, has ever existed or will ever exist” are possible percepts.

No one ever says “I see dog”. They say “I see a dog” or “I see the dog” which simultaneously picks out a particular dog and identifies it as a referent of the concept ‘dog’. Someone might say “I see deer” when referring to multiple animals that are each a deer (the definite articles ‘a’ and ‘the’ are singular and so do not agree with plural sense and usage of ‘deer’), but the referent is still to the particular animals perceived in the line of sight not to all deer that exist, have ever existed or will ever exist.

As a proposition “I see a dog” is a perceptual judgement which David Kelley defined as “a conceptual identification of what is perceived.” It is recognizing a percept as belonging to a certain type. Perceptual judgment is analyzed in terms of the two parts of the act: reference and predication. The linguistic expression of a perceptual judgment is a statement of the form “x is P”. The questions that can be asked are: Why do we believe (predicate) “x is P” but not “x is R”? and Why do we believe (reference) “x is P” and not “y is P”? In the proposition “I see a dog” the reference is the object of “I see” and the predicate is “a dog”. The predicate can be a word representing a concept and this never creates the claim or implication that the concept is perceived directly. What is perceived directly is only the object implied by “I see”, the focus of one’s perceptual faculty.

Systematically comparing terms in pairs will help combat the confusion.

“I see an existent” and “I see existents” differ in that the first predicate is singular and the second predicate is plural, and the number of referents differs.

“I see existents” and “I see existence” again differ in that the first predicate is plural and the second predicate is singular, but both have plural referents.

“I see an existent” and “I see existence” are both singular predicates, but the first referent is singular while the second referent is plural.

The grammatical singularity of ‘existence’ is because it is a collective noun not because it asserts only one thing exists to be a referent. This is Rand’s reduction of the concept of existence to multiple units.

Existence is perceived is exactly the same manner in which an existent is perceived. The only way this could not be true is if it were only possible to perceive one existent at a time.

1 Like
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Dream_weaver.

Yes, that what I mean when I said that concepts are working in both directions: from percept to concept and from concept to percept. However, since adult humans operate on conceptual level, when the most of concepts already formed or learned via language, the direction is mainly from concept to percept. You mind is constantly running sort of simulation program and compares it with the perceptual input. So you can recognize a dog even if you never saw one, if by that or other way you managed to form a concept of it. And even if interstellar traveler will find some completely alien animal, his mind will try to fit the new percept to the one of already existent concepts (it looks maybe like a cross between dog and crocodile). It is a well known legend that Mezzo-Americans couldn’t see Columbus’ ships because they hadn’t had a concept of ship. They tried to fit the new percept into already existing concepts ( a cloud, giant fish etc…). The bottom line is-as adults we have constant perceptual input which immediately translated into existent concepts, since the conceptual level is the only level we can operate on.

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Grames:"This quote directly supports the conclusion that Rand held that existence is a first level concept "

I don’t think so. It simply indicates that concept of “existence” is the second level integration of the concepts of “existent” (A, B, C exist) by omission of A,B, C. The concept designates that whatever exists exists, or in Ayn Rand words " Existence exists".

Even a first level concept has to be formed as " a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.” ( ITOE 97-98) . What such a unit could be? Every entity which has a characteristic of existence when all other characteristics are omitted. Integration of such units by the common denominator would create the concept of “existent” Ayn Rand clearly differentiated between concepts of “existent” and “existence”. While " existence "is an axiomatic concept, “existent " is not. This concept simply designates that A, B, C…exist. Although such a concept is implicit in every percept ( like all primary concepts), explicitly such a concept could be grasped only on conceptual level. Existence, however, is much more complicated concept since it includes not only observable existents but everything at all including all other concepts, memories, feeling etc…and not only at present but also in future and past. Evidently such a concept cannot be a first level concept, to form it one has to integrate the fact that all other things, concepts, time, mental content exist. Such an integration could be done only via concept of " existent”.

"As a proposition “I see a dog” is a perceptual judgement which David Kelley defined as “a conceptual identification of what is perceived.”

Once you invoke conceptual identification you operate on conceptual level, on which that or this particular dog doesn’t exist. When you say " I was bitten by a dog" the particular characteristic of a dog is not relevant. When you use a word " dog" you use a concept which designates all dogs in existence. So strictly speaking you cannot see a dog, since concept is a mental content. Properly, one should say I have a perceptual input which I conceptually identify as a dog .For the same reason one cannot say " I see existence" since such a concept designates everything- physical and mental, past, present and future which are outside of the scope of perception. The very function of concept is to take you out of very limited scope of perception. As Ayn Rand observed-one cannot directly perceive a distance of ten light years, but by creating a concept of distance one can easily deal with it and measure it.

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Leonod.

I would have thought that the bottom line is,- as adults we have constant perceptual input. How we choose to process that perceptual input determines the progress or stagnation of our conceptual faculty.

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Leonod.

I would have thought that the bottom line is,- as adults we have constant perceptual input. How we choose to process that perceptual input determines the progress or stagnation of our conceptual faculty.

Yes, but I’m not sure that we even able to operate on perceptual level. A man with destroyed cognitive faculty is not a healthy animal who operates on perceptual level, he’s a cripple human who cannot operate at all.

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Yes, but I’m not sure that we even able to operate on perceptual level. A man with destroyed cognitive faculty is not a healthy animal who operates on perceptual level, he’s a cripple human who cannot operate at all.

I do not think I am trying to state we can operate purely on the perceptual level.

When we see a new instance of a dog, the brain uses the perceptual data and summons the concept of dog we have and we integrate that particular dog into our concept of dog, although I don’t think it is done as consciously as when we first formed “dog”. Perhaps it is done sub-consciously.

When we form the concept of ‘exists’ we have grasped the criteria necessary to say that something exists. To state that something exists, is to acknowledge that it meets the criteria necessary to be an existent. At the perceptual level, this is pretty simple. We can only perceive what exists. If we perceive something, it meets the criteria of existing. In a broader sense, existence is simply what we perceive.

Axioms, on the other hand provide nothing for us to gaze at and state that axioms exist. To do this, we have to develop the process of validating what we mean by the existent “axiom”.

We see a ball roll. We see a tire roll. We see a pencil or a log roll. When we abstract the “rolling” from the entities which performed the action, we understand that “rolling” too, exists. Watching a race, we can see that the cars move at different rates of speed. We can ascertain that velocity, speed, acceleration, etc., exist. We add these to our understanding of existence. We add anything we may have discovered about validating the existence of these more abstract existents, to our understanding of what it means to exist. The fact that every existent exists though, is inescapable. The fact that every existent is what it is, is inescapable. The fact that we are aware of it is also inescapable.

Using a dictionary definition of axiom yields: an established rule or principle or a self-evident truth. To exist, considered independently as an existent, or collectively as existence, is derived from the self-evident, and extended via abstraction to every existent we are able to validate. By further extension, it is to also encompass or include what we have not yet discovered, providing it meets the criteria of what it means to be an existent.

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Leonid you are butting up against Kelly and Peikoffs particular idea of what a first level concept is.

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dream_weaver_ :“We see a ball roll. We see a tire roll. We see a pencil or a log roll. When we abstract the “rolling” from the entities which performed the action, we understand that “rolling” too, exists” _

That’s right, that how we form the concept of" existent" . But this is first level concept, an entity or unit of existence. Integration of two or more of such units forms concept of existence which designates much more,than observable “existents”. It includes entities which we never observed and perhaps never will, everything which is beyond known Universe and imagination, regardless of our ability to validate it at present, past or future. It includes every dream which anybody can dream millions years from now. How it could be first level concept? Primary concept is result of " integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted” What are the units from which we form concept of " existence?" I claim that this is a concept of “existent”. ( ball exists, rolling, speed, acceleration exists, etc..) There are the first level concepts, existence is abstraction from these abstractions. Self-evident truth is not an axiom, it’s our perceptual data. _ "An axiom is a proposition that defeats its opponents by the fact that they have to accept it and use it in the process of any attempt to deny it. _" (GS)-in other words it is a logical tool, a concept, like exclusion of the middle,

Plasmatic: _ “Leonid you are butting up against Kelly and Peikoffs particular idea of what a first level concept is.” _

Not at all.“Axioms are usually considered to be propositions identifying a fundamental, self-evident truth. But explicit propositions as such are not primaries: they are made of concepts.” ( ITOE 55). Axiom of existence is primary concept in the sense that it cannot be validated by means of logical analysis, it itself foundation of such an analysis. But since it is highest abstraction which designates everything which exists, it cannot be a first level concept like entity.

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No ,you aren’t getting what I was referring to and I don’t have the time just now to explain. I wasn’t criticizing you.

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No ,you aren’t getting what I was referring to and I don’t have the time just now to explain. I wasn’t criticizing you.

Please explain when you do have time. This discussion is fascinating. Let me give a bit of background about how this topic started. Here is a claim that since a concept is a mental integration of two or more units, but there is only one existence, the concept of existence which designates everything which exists cannot be formed. I decided to refute this claim.

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Self-evident truth is not an axiom, it’s our perceptual data. _ "An axiom is a proposition that defeats its opponents by the fact that they have to accept it and use it in the process of any attempt to deny it. _" (GS)-in other words it is a logical tool, a concept, like exclusion of the middle,

You do not think you are relying on (accepting and using) your perceptual data here?

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Leonid, the same argument happens when people criticize existence for not being definable as it doesn’t have a genus.

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That’s right, that how we form the concept of" existent" . But this is first level concept, an entity or unit of existence. Integration of two or more of such units forms concept of existence which designates much more,than observable “existents”. It includes entities which we never observed and perhaps never will, everything which is beyond known Universe and imagination, regardless of our ability to validate it at present, past or future. It includes every dream which anybody can dream millions years from now. How it could be first level concept?

The concept “existent” also refers to "which we never observed and perhaps never will, everything which is beyond known Universe and imagination, regardless of our ability to validate it at present, past or future. It includes every dream which anybody can dream millions years from now. " The same objection you raised to “existence” being first level can also be raised against “existent”. Therefore “existent” cannot be first level. In fact, if this objection was valid there could not be such a thing as a first level concept at all, ever.

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You do not think you are relying on (accepting and using) your perceptual data here?

Implicitly-yes, but not when you are using axiom explicitly, on conceptual level. For example one may say- I see trees, dogs, stars etc…but he cannot claim that he sees existence because the concept includes other concepts, mental contents in present, past and future.

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Leonid, the same argument happens when people criticize existence for not being definable as it doesn’t have a genus.

But it does. Existence is genus, existents are species.

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Grames: "The concept “existent” also refers to “which we never observed and perhaps never will,”

Ayn Rand doesn’t define " existent" in this way.

"The building-block of man’s knowledge is the concept of an “existent”—of something that exists, be it a thing, an attribute or an action. Since it is a concept, man cannot grasp it explicitly until he has reached the conceptual stage. But it is implicit in every percept (to perceive a thing is to perceive that it exists) and man grasps it implicitly on the perceptual level—i.e., he grasps the constituents of the concept “existent,” (“Cognition and Measurement,” Introduction to Objectivist Epistemology, 5–6).

Therefore “existent” is primary concept.

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Implicitly-yes, but not when you are using axiom explicitly, on conceptual level. For example one may say- I see trees, dogs, stars etc…but he cannot claim that he sees existence because the concept includes other concepts, mental contents in present, past and future.

Your claim “but he cannot claim that he sees existence because the concept includes other concepts, mental contents in present, past and future.” just informed me that you perceived these things too.

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Grames: "The concept “existent” also refers to “which we never observed and perhaps never will,”

Ayn Rand doesn’t define " existent" in this way.

"The building-block of man’s knowledge is the concept of an “existent”—of something that exists, be it a thing, an attribute or an action. Since it is a concept, man cannot grasp it explicitly until he has reached the conceptual stage. But it is implicit in every percept (to perceive a thing is to perceive that it exists) and man grasps it implicitly on the perceptual level—i.e., he grasps the constituents of the concept “existent,” (“Cognition and Measurement,” Introduction to Objectivist Epistemology, 5–6).

Therefore “existent” is primary concept.

Every concept has an open ended number of referents, including “existent”. Every concept refers to the known and the unknown, the present, past and future instances, the perceived and the not-yet-perceived and never-to-be-perceived. That open-endedness is part of what it means to be a concept. “Existent” is not formed by a method that differs from the method used in forming first level concepts such as “table” or “dog”. That some of the referents of “table” are remote in distance or time and so never-to-be-perceived does not make “table” a high level concept. Furthermore, the way in which the concept “existent” refers to other concepts as mental existents is not the same logical relationship that obtains between a concept and a lower level concept it abstracts from such as “furniture” and “table”.

There is some ambiguity in interpreting the meaning of “highly abstract” concepts. The same two percepts can be the basis for forming the first level concept of “dog” or “existent” but “existent” is the more abstract concept because more is omitted in the measurement-omission process. It is also the case that an abstraction from an abstraction such as “justice” or “mother-in-law” is necessarily more abstract than its constituents, or in other words higher level concepts are more abstract than the lower level concepts and percepts that constitute their referents. These two senses of the word abstract are distinct so the danger of committing equivocation exists. “Existence” is highly abstract, yet it remains first level and not abstract at all.

I add that existent is an axiomatic concept.

Ostensive definitions are usually regarded as applicable only to conceptualized sensations. But they are applicable to axioms as well. Since axiomatic concepts are identifications of irreducible primaries, the only way to define one is by means of an ostensive definition e.g., to define “existence,” one would have to sweep one’s arm around and say: “I mean this.”

Existence and existent are both irreducible primaries, both necessarily implicit in any attempt to deny them, and both ostensively defined. Rand is very insistent that “existence” is an axiomatic concept, and if existence collectively exists then it must be true that at least one existent exists.