A question about axioms

[dream_weaver]

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.

[Leonid]

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.

[dream_weaver]

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.

[Plasmatic]

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

[Leonid]

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.

Edited February 2, 2012 by Leonid

[Plasmatic]

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.

[Leonid]

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.

Edited February 2, 2012 by Leonid

[dream_weaver]

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?

Edited February 2, 2012 by dream_weaver

[Plasmatic]

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

[Grames]

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.

[Leonid]

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.

[Leonid]

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.

[Leonid]

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.

[dream_weaver]

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.

[Grames]

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.

[Plasmatic]

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

Leaving your construction aside for the moment, existence does not itself have a genus of which it is a species.

[Leonid]

Leaving your construction aside for the moment, existence does not itself have a genus of which it is a species.

Not according to Ayn Rand.

"A definition is a statement that identifies the nature of the units subsumed under a concept...Just as a concept becomes a unit when integrated with others into a wider concept, so a genus becomes a single unit, a species, when integrated with others into a wider genus. For instance, “table” is a species of the genus “furniture,” which is a species of the genus “household goods,” which is a species of the genus “man-made objects.” “Man” is a species of the genus “animal,” which is a species of the genus “organism,” which is a species of the genus “entity.”"

(“Definitions,” Introduction to Objectivist Epistemology, 42)

Definition of existence is "every entity, attribute, action, event or phenomenon (including consciousness) that exists, has ever existed or will ever exist." ( ITOE 56)

Existence therefore is a widest abstraction, a genus which designates as its species every single entity and concept The nature of the units which this genus identifies is that they all existents.

[Leonid]

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.

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.

Basically I agree with your position. However there is a difference between concept of "existent" and " existence". "Existent" designates a certain unit of existence- one may refer to dog or to mother-in law as " existent" Existence, however designates all these units.

[Plasmatic]

Not according to Ayn Rand.

"A definition is a statement that identifies the nature of the units subsumed under a concept...Just as a concept becomes a unit when integrated with others into a wider concept, so a genus becomes a single unit, a species, when integrated with others into a wider genus. For instance, “table” is a species of the genus “furniture,” which is a species of the genus “household goods,” which is a species of the genus “man-made objects.” “Man” is a species of the genus “animal,” which is a species of the genus “organism,” which is a species of the genus “entity.”"

(“Definitions,” Introduction to Objectivist Epistemology, 42)

Definition of existence is "every entity, attribute, action, event or phenomenon (including consciousness) that exists, has ever existed or will ever exist." ( ITOE 56)

Existence therefore is a widest abstraction, a genus which designates as its species every single entity and concept The nature of the units which this genus identifies is that they all existents.

Do you realize you just restated that existence has species? I'm saying existence is NOT a species of any genus because it is the widest abstraction. And the above in your post is not a definition as such as you can only ostensivley define it .

[Steve D'Ippolito]

Actually the last line of his quote asserts that existence is a genus. The implication is that it cannot be a species of some higher-order genus, which is what you have been saying all along. In other words, his quote undermines his argument.

In any sort of hierarchy, be it conceptual or not, there is an uppermost element, with other elements below it branching out, like an upside down tree. (That uppermost element is sometimes called the "root" of the tree even though it's drawn at the top, because the hierarchy looks like an upside-down tree.) Talking about genus and species is simply a specific way (specific to the hierarchy of concepts) of stating that every element in the tree has an element immediately higher than it. Which isn't actually true; unless the tree is of infinite extent there will be at least one exception, the root or topmost element.

So what? Is this really a problem? I don't think so.

Ayn Rand realized that "existence" is a special case because it is at the top of the tree, that's why existence is an axiomatic concept; you can't define it as being a species of some higher genus. She was far more interested in making the point about every single OTHER concept that they were a species of a genus, and were oftentimes (but not always) a genus to some other concepts' species.

[Plasmatic]

Steve said:

"So what? Is this really a problem? I don't think so."

Neither do I. I was pointing at the similarity of earlier postings with the criticism that it is a problem.

[Leonid]

Do you realize you just restated that existence has species? I'm saying existence is NOT a species of any genus because it is the widest abstraction. And the above in your post is not a definition as such as you can only ostensivley define it .

You said "existence does not itself have a genus of which it is a species." and it is true. Existence itself is a final genus which species are all possible existents. Existence is a genus-stopper preventing infinite regress of existences which would be contradiction in terms. But that doesn't mean existence is undefinable. It could be defined in terms of its existents, but it couldn't be reduced to them.Since Existence is a broadest concept, it also couldn't be defined ostensibly because it includes all other concepts. What I quoted is the only possible definition of existence.

[dream_weaver]

it also couldn't be defined ostensibly because it includes all other concepts. .

Are you suggesting that a proper definition (ostensibly or otherwise) must be exhaustive?

[Grames]

Basically I agree with your position. However there is a difference between concept of "existent" and " existence". "Existent" designates a certain unit of existence- one may refer to dog or to mother-in law as " existent" Existence, however designates all these units.

I agree with that.

I wondered why it is that Rand used the collective noun existence as the axiomatic concept instead of the singular existent. At my first thought it was mere stylistic flourish, the semi-poetic form of "Existence exists" and "A is A" being justification enough for Rand as a writer with style but this is not correct. Concept formation according to her theory requires at least two units, so the existence of multiple units is a prerequisite for conceptual consciousness to exist. So we have both "a consciousness conscious of nothing is not consciousness" and "a consciousness conscious of only one thing is not a conceptual consciousness". The fact of existence as a state or condition is axiomatic, but so equally is the plurality of existents.

[Plasmatic]

Multiplicity is ontologically necessary to me.