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A Definitive Criticism of Objectivist Epistemology

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DW, I was talking about neutrality as in "absence of decided views", as in without assuming Rand is right. As if we're recreating what Rand may have thought about - absent of a decided view on if she is right. This is what SK seems to mean. Did you read the paper? She's not trying to -develop- an "impartial" theory of concepts.

You should already know from reading part of a paper I wrote about that you commented on, that I think partiality about one's evidence is needed to be rational.

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Just now, StrictlyLogical said:

Can you provide a concrete example of a single referent for which a concept is required and which cannot be referred to simply with a proper noun?

 

Depending on the sense of that question, no and yes. If by it you mean a concept with a single referent which cannot be merely named, then no, because given a concept represented by a predicate "a thing which has the property X and is the only thing with that property" could simply be named "The Thing Which Has The Property X And Is The Only Thing With That Property". If, however, you mean, now, in this nontrivial sense, a thing that satisfies a given property, is the only thing with that property, but which cannot be explicitly exemplified (given one's current state of knowledge), then yes.

For example, the only real solution of the equation: x^5 - 3x^4 + 5x^3 - 15x^2 + 4x - 12 = 0.

Quote

Can you succinctly state a reason why any abstraction would be required in the case of a truly single referent?

 

Because some things are defined only abstractly at first, and only later an example (possibly unique) is discovered. An interesting historical example is the discovery of the planet Neptune.

Edited by SpookyKitty

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Just now, dream_weaver said:

It would be nice to see something on justification as it relates to conceptualization here rather than resorting to an ad hominem attack.

 

That wasn't an ad hominem attack. That was an insult. The only appropriate response to refusing to engage with an argument on the basis of dismissing something one knows absolutely nothing about.

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37 minutes ago, SpookyKitty said:

 

That wasn't an ad hominem attack. That was an insult. The only appropriate response to refusing to engage with an argument on the basis of dismissing something one knows absolutely nothing about.

When you used the term Hyperspace, were you referring to String Theory?

 

Edited by New Buddha

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Just now, New Buddha said:

When you used the term Hyperspace, were you referring to String Theory?

 

 

No, I was referring to higher-dimensional spaces in general, but so what if I was?

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1 hour ago, SpookyKitty said:

 

No, I was referring to higher-dimensional spaces in general, but so what if I was?

What observations exist that cannot be explained by the 4 dimensions of spacetime?

Edited by New Buddha

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Claim 29. For every concept, there are at least two subjects subsumed by the concept.

Claim 29 still does not represent Rand's theory. In Objectivism the subjects (or units) can be lower-level concepts. This contradicts your dichotomy of subjects as things, and predicates as concepts, which would not allow for subjects/units to be lower-level concepts.

Quote

Someone who accepts the definition of 'concept' provided here should be able to also accept Rand's theory of concept formation without contradiction. If there is a direct contradiction between the definition provided here and Rand's theory of concept formation, then the critique is biased, and therefore, of little worth.

There is a direct contradiction between your definition of concept and Rand's theory. I therefore find your critique to be biased and of little worth.

Should we expect another revision soon?

 

Edited by MisterSwig
Formatting issues.

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Just now, MisterSwig said:

Claim 29 still does not represent Rand's theory. In Objectivism the subjects (or units) can be lower-level concepts. This contradicts your dichotomy of subjects as things, and predicates as concepts, which would not allow for subjects/units to be lower-level concepts.

There is a direct contradiction between your definition of concept and Rand's theory. I therefore find your critique to be biased and of little worth.

Should we expect another revision soon?

 

 

There is no contradiction. That concepts can themselves be subjects of predicates has already been explained earlier in the thread. Please read it before commenting again.

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13 minutes ago, SpookyKitty said:

That concepts can themselves be subjects of predicates has already been explained earlier in the thread.

So in addition to being a mental phenomenon which outputs statements, a concept can also be both the subject and the predicate of an outputted statement?

Is the idea here that some concepts output concepts?

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Just now, MisterSwig said:

So in addition to being a mental phenomenon which outputs statements, a concept can also be both the subject and the predicate of an outputted statement?

Is the idea here that some concepts output concepts?

 

Concepts output statements, and statements do not represent concepts. Some concepts are about other concepts.

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2 hours ago, Eiuol said:

Sure, they are at least things said of some other thing. This is a fine starting notion for a discussion. But there is no reason I see to say a concept must only consist of statements. The problem of universals as I understand is and to connect particulars to something wide as a universal. Such a universal to Rand is a concept, and speaks of things in addition to statements, such as percepts. Rand didn't attempt to prove herself right by the premises you started with - she had more. You already arrived at the idea "more is needed".

 

Concepts are represented by predicates (if by statements you really meant to say predicates), but that does not automatically mean that they "consist" of them. What concepts consist of is a question about the ontology of concepts, and I don't have an answer for that.

Quote

Thus we arrive at discussing concepts being invalid and valid, rather than only true and false. Definition 2 already presents us with erroneous representations, as is sensible to do. You said, essentially, "not all concepts are any good".

 

I said, at most, not all statements are true. I never explicitly stated that "not all concepts are any good". I do agree with it, however, but only in the sense that not all concepts are particularly useful, and definitely not in the sense that some concepts are "invalid" or "unjustified" or "false".

Quote

Validity is a way to introduce human error into epistemology. That is, validity is about justification. I may be justified in saying dolphins are fish if I were Aristotle, but from what I know about dolphins now, there is no justification to say dolphins are fish. An invalid concept would be an unjustified concept entirely, not just a few unjustified predicates from a set of predicates that make up my concept "dolphin". Notice I didn't say "the" concept there. If concepts are representations, they may be different in other minds. The intension may not be identical between us, even if the extension is identical. So, we need to slow down and get to things like a) what makes a concept justified, and b ) do concepts contain things in addition to statements or predicates?

Propositions that contain invalid concepts are no issue. Perhaps there's a better word besides "invalid". I'd still like to call a mermaid  a concept, one that I also know in fact is not justified.  Rand is at least claiming that two or more referents are required for a concept to be proper/valid/justified. Once you answer a and b, and see if the "at least two" idea fits, your paper could be considered finished.

Your edit makes sense, and I agree.

 

You switch from talking about statements to talking about concepts. Statements can be justified or unjustified, predicates and concepts cannot be.

You still have not explained why it would be at all problematic to make use of an "unjustified" or "invalid" concept.

 

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9 hours ago, SpookyKitty said:

If, however, you mean, now, in this nontrivial sense, a thing that satisfies a given property, is the only thing with that property, but which cannot be explicitly exemplified (given one's current state of knowledge), then yes.

For example, the only real solution of the equation: x^5 - 3x^4 + 5x^3 - 15x^2 + 4x - 12 = 0.

Why does this referent require a concept? 

Assuming you are taking this to be truly unique, i.e a solution to an equation, the referent itself is an abstraction, it is a mathematical referent defined conceptually, but a proper noun refers to that single referent perfectly well.  In other words we do not need to form a new abstraction - a whole new concept - in order to understand/identify what we are talking about - which is only a single specific unique thing, even when the thing referred to is an abstraction.

Why would you need to abstract away from the single unique thing?  What reason does one have to form a concept here?

 

If you are submitting AS the referent, a multiplicity of things, i.e. had you worded this "ALL real solutionS of the equation", then we have a group of concrete referents, and are no longer referring to a single referent and hence simply does form an example of a single referent requiring a concept.

 

9 hours ago, SpookyKitty said:

Because some things are defined only abstractly at first, and only later an example (possibly unique) is discovered. An interesting historical example is the discovery of the planet Neptune.

 

The fact that a referent is defined abstractly (or is itself an abstraction) or is as of yet undiscovered is not in and of itself any reason for forming a whole new concept for it.

The referent can be defined and referred to with a proper noun.

Neptune is an example of a unique cause of observations, and was detected and identified before it was observed with light and named.  This does not change whether or not a concept is required to refer to it.  A proper noun was sufficient at all stages of its discovery and is sufficient now.

 

Do you have an example where a unique single referent actually requires a concept, requires abstraction from the referents (over and above them) rather than a proper noun simply pointing at it?

 

Edited by StrictlyLogical

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7 hours ago, SpookyKitty said:

What concepts consist of is a question about the ontology of concepts, and I don't have an answer for that.

Fair enough, but recognize that you are at least saying concepts are mental, so are distinguishing them from predicates that are not necessarily mental. I mean, that is some claim about the ontology of concepts. You're right that what concepts consist of is a different issue.

To be more precise, a predicate or a set of predicates does not completely represent a concept. Does a set of predicates ever totally represent a concept? I think you've already recognized that predicates at best partially represent concepts. Or, you are restraining concepts to only be represented by predicates at the outset - a hidden premise - before saying what the conditions are for a fully represented concept. So, amend b to say "are concepts represented by things in addition to predicates?"

7 hours ago, SpookyKitty said:

You still have not explained why it would be at all problematic to make use of an "unjustified" or "invalid" concept.

Hmm, I see how I was skipping ahead to -normative- evaluations of one's concepts. But do you see that "at least two entities" is a normative claim and how a normative claim implies a notion of validity with regards to concept's relation to a referent or reality? To be sure, I was skipping ahead when we didn't even get to explaining what concepts are good -for- anyway. We're not there yet. At the end of the paper, you seem to cede that some concepts have a peculiar relation to reality in terms of their referents, with some lacking referents entirely. Rand offers a way to see if one's concepts are "normal", i.e. have an objective relation with reality.

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17 hours ago, SpookyKitty said:

I understand everything except your overall point.

My point is that often when we form a concept we do not know how many subjects are subsumed by that concept. When the concept of complete ordered field was created, it was unclear that there were any. Then two distinct constructions were made: Dedekind cuts and equivalence classes of Cauchy Sequences. It was not clear that these weren't distinct initially. It appeared that there were two subjects in this concept until it was proved that these two are isomorphic representations of the same thing. Finally, it was proved that all complete ordered fields are isomorphic to the so-called real numbers. Was "complete ordered field" never a concept, even when it appeared that there were two distinct constructions? Did this label not function in every respect as a concept despite the fact that there exists only one? While "real numbers" is the name of a subject, isn't "complete ordered field" still a concept for which there is only one applicable subject, the real numbers? This, I believe, is a fair point to make in discussing what we mean by "concept".
 

I have another point to make. Consider the following definition:

Definition: A dragon is a flying reptile that breathes fire.

Everyone knows that a flying reptile that breathes fire is a dragon. However, this concept is invalid because there are no subjects/units to which it applies. We do not have two or more units isolated by these characteristics. We don't even have one! However, it is hard to say that dragons are not concepts. They just happen to be invalid concepts.

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22 minutes ago, aleph_1 said:

However, it is hard to say that dragons are not concepts. They just happen to be invalid concepts.

Dragon is not an invalid concept. Your definition of it is incorrect. A dragon is a mythological creature often depicted as a large, lizard-like monster that can fly and breathe fire. This concept does have representative units in reality, in fictional books and movies.

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8 hours ago, SpookyKitty said:

What concepts consist of is a question about the ontology of concepts, and I don't have an answer for that.

Sure you do. Concepts consist of the "mechanism" needed to output statements. And since statements are composed of words, a concept is best understood as a word-making mechanism. Concept itself is a word, therefore there must be some kind of a superconcept, a prime mover mechanism which either outputted itself or has always existed, and which originally outputted the very first statement to ever exist, which of course would have been about itself.

This stuff really isn't that hard to figure out. It's not like you're the first person to come up with this garbage.

Edited by MisterSwig

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11 hours ago, SpookyKitty said:

What relevance does this have to the thread?

It has everything to do with this post if you believe that language, math, logic and physics are about the world and the universe that we live in and not just a nominalist game of symbol manipulation that may or may not end up having some meaningfulness or "truth-value" with regards to the real world.

From a previous post of yours:

"Imagine that the world was such that everything lay in the same plane. Nothing would be above anything else, but that does not mean that the concept of "aboveness" would be meaningless."

In this imagined 2-d world of yours (see Flatland, which is probably what Plasmatic was thinking about) you axiomistized  a world where "aboveness" would in fact be be meaningless.  But when Plasmatic pointed this out, your response was to arbitrarily throw in another axiom that space would be 3-d - thus preserving "aboveness".

Quote:

"As for the second part, just because everything happens to lie in a 2d plane, does not mean that space is not 3-dimensional, just that everything happens to lie in some 2d plane of a 3d space."

This type of thinking is the reason why I posted the Bertrand Russell quote regarding inconsistent logical systems.  In such systems, you can provide a proof for any theorem.  Because inconsistent systems have no limits, they also have no value with regards to reality.

Regarding String Theory and extra-dimensional hyperspaces, this represents the blurring of the line between mathematics and physics (but that's another post).  But related to this, you asked me if I doubted mathematics:

"Your mistrust and lack of understanding of logic is your own. That an argument is formalized is not a point against it. Do you seriously doubt mathematics, or something?"

Your problem is that you are unknowingly blurring the line between three different domains: mathematics, formal logic and language - all of which, to be useful, must have limits.  I replied that I do understand the limits of formal systems (such as mechanics used in engineering).  Without these limits, these systems would be meaningless.  They would be inconsistent and could "prove" anything.  We could not tell a right answer from a wrong answer, true from false.  Beams may or may not resist loads....

In structural engineering, for example, the "axioms" that is, the abstract generalized understanding of the behavior of beams, columns, and footings, are derived inductively by subjecting different materials (steel, wood, concrete) to tests that measure their capacity to resist such stresses as shear, bending, buckling, modulus of elasticity, etc.  These empirically derived properties of the different materials are the limits imposed on our more abstract and  mathematized understanding of how beams behave in general i.e. abstractly.

From your paper:

"Before proceeding, let us explain what is meant here by “axiom” and what role they serve in the overall analysis. An axiom here is simply a common sense, although completely explicit, assumption we must make about concepts.
I do not claim that these axioms are self-evident nor that everyone must accept them. Rather, I hold that they are implictly regarded as true by any reasonable person, just as the axioms of arithmetic or geometry are implicitly regarded as true by any reasonable person."

This is precisely how not to form "axioms".  Axioms are arrived at through induction - that is from concretes to abstractions, and then by further abstracting from abstractions in order to form even more broad generalizations -  all via concept formation.  But without defined limits imposed by concrete reality, any deductive reasoning from these axioms would result in meaningless statements.  This is true for formal logic, mathematics, mechanics and language.

Your understanding of how knowledge is acquired is exactly backwards.

Edited by New Buddha

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1 hour ago, MisterSwig said:

..... Your definition of it is incorrect. ....

I am free to make my own definitions when making a point. Is my definition not grammatically correct? Does it not connect a subject and a predicate? I have used SK's process. You must deal with my definition. It is consistent with the proposed philosophy in question.

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2 hours ago, MisterSwig said:

Dragon is not an invalid concept. Your definition of it is incorrect. A dragon is a mythological creature often depicted as a large, lizard-like monster that can fly and breathe fire. This concept does have representative units in reality, in fictional books and movies.

The nicest way to put this is that this topic is out of your league. Referents are things in reality, and that's a main interest - concepts and referents. A drawing or description of a dragon is not a dragon in reality, they're (supposed to be) creatures, not abstractions like math theorems. This goes back to your form of dualism no one else here thinks makes sense.

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4 hours ago, aleph_1 said:
5 hours ago, MisterSwig said:

..... Your definition of it is incorrect. ....

I am free to make my own definitions when making a point.

You're not free to steal a concept and then deny its origin. The concept of dragon comes from it being a fictional creature. You cannot now pretend that it's supposed to be real. That would be committing the stolen concept fallacy, as Rand identified.

Of course, you could be joking around. If that's the case, then touché!

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Just now, MisterSwig said:

You're not free to steal a concept and then deny its origin. The concept of dragon comes from it being a fictional creature. You cannot now pretend that it's supposed to be real. That would be committing the stolen concept fallacy, as Rand identified.

Of course, you could be joking around. If that's the case, then touché!

 

Maybe you should consult an authority on dragons? Maybe Tolkein or Rowling?

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SpookyKitty said: You know it would be a lot more helpful and persuasive to point at least one thing that you think is a misunderstanding or an arbitrary assertion. At least then we could have  a meaningful discussion about it.

From your paper (blue is mine):

"Abstract: We show that Rand’s theory of concept formation, more specifically, the requirement that every concept subsume at least two entities..."

That requirement is not a part of Ayn Rand's theory of concept formation. Rand endorses metaphysical pluralism and never legislates entities as the only kind of existent which can serve as a unit. Because the argumentative vehicle for your criticism of Objectivism is (entirely) the rejection of this requirement you fundamentally miss the mark.

"Definition 1. A set of statements Σ is philosophically neutral with respect to some set of philosophical positions Π if and only if all of the statements in Σ are logically independent..."

If indeed "the truth is the whole" then logical independence makes since only as a concept referring to a subject's lack of knowledge (like 'randomness'). This means then that only when you can not identify, say, the logical dependence of higher-abstractions upon more primitive ones is it possible to be philosophically neutral towards those more complex abstractions. Interesting.

"Both true and false statements are representations of reality."

One wonders at the standard of appeal by which we come to distinguish truth and falsity.

"If subjects represent things, then predicates represent concepts."

Your entire section pertaining to "Definition 3." is very confused. It is merely because the three statements you make use of in turn make use of proper nouns (which can not represent concepts) as subjects that you feel licensed to regard subjects as necessarily non-representative of concepts. Subjects are things. Predicates are composed of concepts.

"Definition 4. A concept is a mental phenomenon that which, given a subject, outputs a statement about the subject."

This definition, if held also as an operational definition and in conjunction with your "Definition 2.", leads to the impossibility of the beginning of concept-formation; one would require the constituent concepts of the outputted statement before one could have the concept which outputs that statement. Or maybe you think concepts output things to and exist apart from knowing subjects.

"It is possible to apply the concept “a red planet” to Earth and thereby obtain the false statement, 'The Earth is a red planet'."

This whole passage is ridiculously messy and your quotation actually makes pretense to concepts and predicates being identical but a concept is not the kind of thing that can be "said of some subject" unless you consider, per your own phraseology, every phenomenon "a mental phenomenon".

"The third is that a concept does not represent anything . . .Instead, a concept is what connects statements to subjects."

How is something which represents nothing capable of connecting or "outputting statements" about anything? And moreover how does a concept connect "statements to subjects" if, again by our own definition, a statement is already essentially composed in part by a subject? Perhaps what you meant was to connect statements to subjects which are alien to the ones of the original statement's composition but then again what would your non-representational, non-referential connective tissue even mean?

"The role that these axioms serve in the overall analysis is to . . . 3) establish the truth of the conclusion."

See: Rationalism.

"For example 'red and a planet' and 'not neither red nor a planet' are equivalent predicates because: 'Mars is red and a planet' is true if and only if 'Mars is not neither red nor a planet' is also true, 'Earth is red and a planet' is true if and only if 'Earth is not neither red nor a planet' is true, ... , and so on for every other such statement."

Therefore, according to you (in virtue of logical dependency being a bar to neutrality), the determination of any equivalent predicates can not be philosophically neutral and must necessarily be "biasing the investigation beforehand". Also interesting.

"Axiom 7. (Axiom of Concept Representation) For all concepts c and all predicates ϕ and all predicates ψ, if ϕ represents c and if ϕ is equivalent to ψ, then ψ also represents c. What the above axiom basically comes down to is that people understand logic. If one understands every statement like 'Mars is red and a planet' then one cannot also fail to understand any logically equivalent statement such as 'Mars is not neither red nor a planet'."

Did you forget earlier where you said "Note that the word 'is' is not part of the predicate"? Note that the logical equivalence of these statements depends exclusively on "predicates ϕ and ψ" containing forms of the verb to be.

"Since there is an infinite variety of predicates equivalent to each predicate..."

Being allowed to say this means rejecting your "Note that..." assertion just quoted above insofar as the very possibility of pairs of equivalent predicates depends precisely on what you've already banished from the predicate.

I admit to being bored at this point and have decided to skip to the part of your paper where you supposedly actually talk about Objectivism.

" The Objectivist theory of concept formation makes at least the following claims:"

Here we go...

"Claim 20. For every concept, there are at least two (non-mental) subjects subsumed by the concept."

I guess the concept of concept isn't possible in Objectivism. *facepalm*

"Claim 21. Existence exists. That is, the concept represented by the predicate 'has existence' exists."

First, the theory of concept formation does not claim "existence exists". Second, that is perfectly not what the existence axiom means and your characterization of "has existence" makes pretense to existence as an attribute of things, an assertion which is clearly repudiated in Chapter 6 of ITOE where Rand says, "Existence and identity are not attributes of existents, they are the existents." [emphasis original]

"Claim 22. A is A. That is, the concept represented by the predicate 'has identity' exists."

See again response to "Claim 21" and substitute "existence exists" with "A is A" and "has existence" with "has identity".

"The predicate 'has existence' will be denoted by ex and the predicate 'has identity' will be denoted by id."

So we finally get to the part in your paper where you actually deal with Objectivism and you present three claims its theory of concept formation makes - all of them being abjectly wrong and clearly contradicted by primary Oist literature - then finish your "criticism" with three theorems all resting on perfectly inadmissible predications (e.g. "has identity", "has existence"). I don't know what it is you are critiquing (and I'm fairly sure you aren't either) but it isn't Objectivist Epistemology and it definitively isn't definitive.

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3 hours ago, Eiuol said:

The nicest way to put this is that this topic is out of your league.

What do you mean by this, Eiuol?

It seems like you're saying MisterSwig ought not participate in this conversation because you and he disagree with respect to some more fundamental matter. Perhaps in the same way that someone who doesn't believe in angels isn't welcome in the thread devoted to discovering how many of 'em can Lindy hop on the head of a pin.

But I thought what MisterSwig said about dragons was sensible. (Just like I think the person in the angels thread who says, "angels don't exist" is right, even if no one else in the thread appreciates the contribution, because they don't think it helps them answer their question.)

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39 minutes ago, SpookyKitty said:

Maybe you should consult an authority on dragons? Maybe Tolkein or Rowling?

Been there done that. But you reminded me of the Heaney translation of Beowulf that I still need to read. Thanks.

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