KALADIN

Two quotes to begin.
The first: “In general, it is absurd to make the fact that the things of this earth are observed to change and never to remain in the same state, the basis of our judgment about the truth. For in pursuing the truth one must start from the things that are always in the same state and suffer no change.”
- Aristotle, Book 11, from his Metaphysics.
Now the second: “Serenity comes from the ability to say ‘Yes’ to existence.”
- Ayn Rand, 1973, from her essay “The Metaphysical versus the Man-Made”.
Any science of first principles rightly supposes that the justificatory structure of our schemas and assertions are terminal. It would seem then that there ought to be a terminus of judgment also, for how is one to judge a thing which can not be justified, even in principle? Justification surely is a form of explanation, namely one which identifies a cause whose identification itself deals in adherence to a kind of normativity appropriate to the production of human knowledge. Aristotle points out that all explanation is in terms of something more fundamental, and nothing is truly capable of explaining itself, for nothing is more fundamental than itself - it simply is itself. It has seemed strange then to philosophers throughout history that those concepts and principles occupying the base of human knowledge, being capable neither of having explanation or justification, should still be the ultimate source of both, hence the perennial quest for and atheological concerns towards an explanation of something like Being as such. This sort of meta-attitude is not confined to metaphysics or what calls itself metaphysics. Indeed in Hume’s infamous passage about the inescapable bifurcation or rather the inexplicable marriage of descriptive and normative statements, we see the presence of an anxious, “something from nothing” worry more familiar to us in the context of discussions about God. We may find this sort of sentiment just as easily in epistemologies also of the last century, where neo-Kantians like Wilfred Sellars marshal the notion of inference as constitutive of the perceiving act so as to escape the undesirable conclusion that the perceptually given could at once be justificatory and non-propositional, i.e., not itself justified or justifiable.
The ability of certain things to be a power unto themselves has always been met throughout history with skepticism and derision, especially by philosophers. While this fact may owe some to the prevalence and intuitive attractiveness of a naive necessitarian conception of causality (which itself necessarily invokes a prime mover), where the supposed constant conjunction of motion is appropriated as identifying the form of epistemic relations or ethical systems, I believe the source is more complicated in matter if not in form, and partly social. Namely, that in human interaction we constantly seek the identification of a final cause to explain the behavior of the human agents we interact with. And insofar as these motivations are explicit - as is the case with more noticeable, determined action - the cause can be expressed in propositional form, and we are thus loathe to think that any cause ought not to be able to expressed to one another someway, somehow. Even in relations lacking humans altogether, say perhaps the evolutionary development of an alternative organism, we identify the final cause of species survival and propagation as an explanatory summation of the efficient - and principally chemical - causes responsible for an organism’s biological integrity. We understand our mature language to be capable of reaching all corners of nature, both now, before, and forevermore.
We understand and believe then that if there are no reasons to accept something, then there can certainly be no reasons not to reject it. And it is precisely here, in elevating a particularly - and this is key - conceptual mode of grasping existence to legislate what is and is not permissible to treat as existent that all philosophical hell breaks loose. The explicit error is thus: the holding of the man-made, for no conceptual artifact is necessary, to constrain the metaphysically given. That is, the total inversion of epistemological primacy, of treating not perception but conception as cognitively basic. There is really only one tradition in the history of philosophy which explicitly recognizes a kind of metaphysical acquiescence as the source of epistemological accuracy, and that is the Aristotelian one, of which Objectivism is a part. Just as Aristotle refuted logical determinism by affirming the direction of truth to move from the metaphysically given to the man-made, so we may chastise those anti-foundationalist tendencies which make much ado about the fact that those so-called primaries of cognition cannot be explained or justified, yet serve as the source of both; the primaries, insofar as they constitute an identification of the relation of man's necessary formatic apprehension (for to be aware is not merely to be aware of something, but to be aware of something somehow) of existence to existence are not to be judged. The man-made can not arbitrate how the metaphysically given ought to be, or how its epistemic status ought to present itself, indeed the very concept of “ought” is inapplicable.
It as arbitrary to assert that because primaries are inexplicable they are somehow invalid or untrustworthy as it is to rule out the concept of “inertia” with Aristotelian physics. In both cases, perception, our primitive and primary contact with and awareness of reality - because it is metaphysically given and the identities of the human, sensory apparatus as well as the existents which act upon them are outside the power of human volition, of human making - vindicates what may be thought of as possible and trustworthy, and no more and no less. You may recall that I mentioned that there can be no reasons given not to reject the metaphysically given, and this is true unless those reasons are tied to some normative conception of what it is thought should be about and what it should serve. Indeed one is always free to ask: “why shouldn't I contradict myself?”. Objectivism has no answer to give this question save: man shall not live on thought alone, and if he is to acquire his bread also, he will need non-contradictory thought and a non-contradictory method to achieve it. Objectivism does not judge the metaphysically-given precisely because its recognition, its identification, is the means of making proper judgments about it, its very precondition. To say “yes” to the metaphysically-given is not to judge it as true or good, but to acknowledge the metaphysically-given fact that correspondence between and conformity of the metaphysically-given to the man-made is good or otherwise conducive to the survival of the man-made, and moreover still that the content of this relation is itself metaphysically-given. Objectivism does not promote an attitude of metaphysical acquiescence as true because it is good, but as good because it is true. Power over nature does not come from asserting man's omnipotence, but from asserting where and indeed how power is possible to him. To paraphrase Bacon: Nature, to be commanded, must not be judged.

From a recent discussion:
"Nietzsche also rejects the need for a world beyond the world of appearances (the thing-in-itself)..."
Rand does not merely reject the "need" for noumena. She regards the very concept as invalid: "But 'things-in-themselves' as separated from consciousness and yet discussed in terms of a consciousness—is an invalid equivocation" (Introduction to Objectivist Epistemology, Appendix Discussions). It is an equivocation on "consciousness" because in order to metaphysically sunder an object from its appearance, and posit corresponding gradations of Being (letting the "thing-in-itself" alone participate the Real), the form of conscious awareness must be taken to constitute its object - there is precisely nothing else to be aware of - and more this formatic apprehension must be taken as the "disqualifying element" (Rand's terminology) in coming to know the Real. In other words, in order to make sense of "separated from consciousness" or a principle of absolute unknowability, we have to make recourse to this appearance-object distinction which is itself a form of coming to know the object that is the apparently Real relationship between consciousness and existence ("everything is done from the human perspective" - Rand). Awareness is always awareness of something somehow, and there is an equivocation in treating awareness or identification of the Real with the Absolute - out of all relation to awareness - as something not also thereby distanced from the Real. For it treats of awareness as both capable and not of grasping something independent of what it constitutes - beyond the bounds of representation - just like how Rand sees "consciousness" (in the aforementioned quote) being used to capture a principle of separation and not. In truth, it is simply a category error to speak of "things-in-themselves" or "things-as-they-really-are" - let alone have them alone participate the Real - because the form and object of perception are incommensurable; to offer the objects of perception as "things-as-they-really-are-not" is to completely fail to grasp that there is no magically privileged perspective on anything whatsoever, and no standard of veridicality which does not grip the world with a specific identity. Attempts to evade, subvert, or negate these facts are attempts to judge or re-write the metaphysically given.
...
Unfortunately, Kant does not posit the relation of his transcendental schema to the world as an accidental one, or some potentially interesting hypothesis. The principle of transcendental idealism is not merely offered as a reflection on phenomenal awareness simpliciter. Kant must be committed to the knowability of the self-in-itself as beyond mere representation if he is indeed to affect the reality of a world of representational content (which is "nothing but representations, and they cannot exist at all outside our minds.” Critique of Pure Reason, B235) whose subject is the seIf-in-itself, i.e., the noumenal mind, which he attempts to establish only indirectly by deduction or inference more generally. But inference is radically dependent upon causality, and for Kant causality is imposed. One does not and can not properly infer the simple existence and operation of those activities which are already a necessary precondition of any right to the concept, performance, and meaning of inference - this is simply another consequence of the illicit character of Kant's epistemological vehicle(s). Indeed Kant is not even allowed some unknown explanans as the cause of the unity of experience precisely because causality is not something to mediate the phenomenal and noumenal worlds. To be imposed is to be of one. To infer the so-called activities of the self-in-itself is to make use of them here, so there is no way to make sense of the notion that their cause could be something beyond representational content, beyond the mere elucidation of an explanatory schema. Knowledge is a causal relation, and the utter incoherence of Kant's transcendental psychology is a consequence of him holding the mind to be constitutive of its contents except where those contents concern the cause of constitution, so as to be offered as something beyond the mere recognition of representational content. The distinction between noumena and phenomena is not synonymous with nor as innocuous as proclaiming the metaphysical independence and priority of the object of awareness, something all realists do. For the realist, form and object are naturally commingled, and the form of awareness is the identity of that specific relationship between consciousness and its objects, the somehow of being aware of something. Think for a moment about the contrapositive of this principle and just how perverse it is to understand the means of awareness as a metaphysical bar to awareness of the Real - that in order to be aware of the Real, of things as they "really" are, you would have be aware of it nohow (I am well aware that Kant doesn't regard our knowledge of the phenomenal world as something delusory). This fashioning the domain of the Real as metaphysically outside the purview of experience and reason is fundamentally Platonic in spirit, and its ruthless philosophical opposition is the basic spirit of Aristotelian epistemology - an unrelenting acquiescence before the evidence of the senses, and a principled recognition that "consciousness is the faculty of perceiving that which exists" (Atlas Shrugged, John Galt's Speech). To quote Marc Champagne:
"Aristotle was able to make change intelligible because he shunned facile recourse to 'appearances' and made it a sort of methodological compact to always strive for concordance with the data that set his inquiries into motion. By our lights, this is the aetiologic posture all philosophers should adopt: to eschew ladder-discarding." [emphasis mine]
And from Leonard Piekoff, who Champagne quotes immediately after giving the above quote:
"According to Aristotle, the question to start with is not: What must reality be like in order to make it possible for us to acquire knowledge of it? But simply: What, as a matter of fact, is reality?"
For Rand there are no boundaries of pure intuition. There is no such thing as anything "in-itself", no das Ding an sich Selbst betrachtet. Objectivism does not hold that we perceive things as they really are because there is no such thing as something as it "really is" or "in itself". Things as perceived by your mind - to paraphrase Galt - are not things as they really are but simply things as they are. There is no such thing as the noumenal world, or the completely unknowable Real. Knowledge is prior to ignorance and skepticism for the same reason existence is prior to consciousness; the latter in each case is itself a relational phenomenon, having meaning only in virtue of being commingled with or otherwise actualized through the former. As such, queries like "is knowledge possible?" or "can we be aware of reality as it really is?" are completely invalid. There is no vehicle for these questions that, to be a vehicle - to have weight, does not necessarily depend upon some form of knowledge and some prior apprehension of the real. There is always and everywhere substance before the void, and all voids are simply an absence of substance. Epistemology is never properly about the possibility of entangling the real, of asking when and how our "ladders" can be "discarded", but only of that entangling's norms and reproduction. Recognizing that we have consciousness or knowledge of the real is the starting point of true and efficacious cognition in general. Consciousness is a faculty of knowing reality; consciousness is conscious.

Sure, it's from his dissertation. Link below.
Champagne, Marc. (2007). Atomism, Wholism, and the Search for a Tenable Third Way.
https://www.researchgate.net/publication/32049136_Atomism_Wholism_and_the_Search_for_a_Tenable_Third_Way/link/5b2e63dfaca2720785dc6302/download
 

From a recent discussion:
"Nietzsche also rejects the need for a world beyond the world of appearances (the thing-in-itself)..."
Rand does not merely reject the "need" for noumena. She regards the very concept as invalid: "But 'things-in-themselves' as separated from consciousness and yet discussed in terms of a consciousness—is an invalid equivocation" (Introduction to Objectivist Epistemology, Appendix Discussions). It is an equivocation on "consciousness" because in order to metaphysically sunder an object from its appearance, and posit corresponding gradations of Being (letting the "thing-in-itself" alone participate the Real), the form of conscious awareness must be taken to constitute its object - there is precisely nothing else to be aware of - and more this formatic apprehension must be taken as the "disqualifying element" (Rand's terminology) in coming to know the Real. In other words, in order to make sense of "separated from consciousness" or a principle of absolute unknowability, we have to make recourse to this appearance-object distinction which is itself a form of coming to know the object that is the apparently Real relationship between consciousness and existence ("everything is done from the human perspective" - Rand). Awareness is always awareness of something somehow, and there is an equivocation in treating awareness or identification of the Real with the Absolute - out of all relation to awareness - as something not also thereby distanced from the Real. For it treats of awareness as both capable and not of grasping something independent of what it constitutes - beyond the bounds of representation - just like how Rand sees "consciousness" (in the aforementioned quote) being used to capture a principle of separation and not. In truth, it is simply a category error to speak of "things-in-themselves" or "things-as-they-really-are" - let alone have them alone participate the Real - because the form and object of perception are incommensurable; to offer the objects of perception as "things-as-they-really-are-not" is to completely fail to grasp that there is no magically privileged perspective on anything whatsoever, and no standard of veridicality which does not grip the world with a specific identity. Attempts to evade, subvert, or negate these facts are attempts to judge or re-write the metaphysically given.
...
Unfortunately, Kant does not posit the relation of his transcendental schema to the world as an accidental one, or some potentially interesting hypothesis. The principle of transcendental idealism is not merely offered as a reflection on phenomenal awareness simpliciter. Kant must be committed to the knowability of the self-in-itself as beyond mere representation if he is indeed to affect the reality of a world of representational content (which is "nothing but representations, and they cannot exist at all outside our minds.” Critique of Pure Reason, B235) whose subject is the seIf-in-itself, i.e., the noumenal mind, which he attempts to establish only indirectly by deduction or inference more generally. But inference is radically dependent upon causality, and for Kant causality is imposed. One does not and can not properly infer the simple existence and operation of those activities which are already a necessary precondition of any right to the concept, performance, and meaning of inference - this is simply another consequence of the illicit character of Kant's epistemological vehicle(s). Indeed Kant is not even allowed some unknown explanans as the cause of the unity of experience precisely because causality is not something to mediate the phenomenal and noumenal worlds. To be imposed is to be of one. To infer the so-called activities of the self-in-itself is to make use of them here, so there is no way to make sense of the notion that their cause could be something beyond representational content, beyond the mere elucidation of an explanatory schema. Knowledge is a causal relation, and the utter incoherence of Kant's transcendental psychology is a consequence of him holding the mind to be constitutive of its contents except where those contents concern the cause of constitution, so as to be offered as something beyond the mere recognition of representational content. The distinction between noumena and phenomena is not synonymous with nor as innocuous as proclaiming the metaphysical independence and priority of the object of awareness, something all realists do. For the realist, form and object are naturally commingled, and the form of awareness is the identity of that specific relationship between consciousness and its objects, the somehow of being aware of something. Think for a moment about the contrapositive of this principle and just how perverse it is to understand the means of awareness as a metaphysical bar to awareness of the Real - that in order to be aware of the Real, of things as they "really" are, you would have be aware of it nohow (I am well aware that Kant doesn't regard our knowledge of the phenomenal world as something delusory). This fashioning the domain of the Real as metaphysically outside the purview of experience and reason is fundamentally Platonic in spirit, and its ruthless philosophical opposition is the basic spirit of Aristotelian epistemology - an unrelenting acquiescence before the evidence of the senses, and a principled recognition that "consciousness is the faculty of perceiving that which exists" (Atlas Shrugged, John Galt's Speech). To quote Marc Champagne:
"Aristotle was able to make change intelligible because he shunned facile recourse to 'appearances' and made it a sort of methodological compact to always strive for concordance with the data that set his inquiries into motion. By our lights, this is the aetiologic posture all philosophers should adopt: to eschew ladder-discarding." [emphasis mine]
And from Leonard Piekoff, who Champagne quotes immediately after giving the above quote:
"According to Aristotle, the question to start with is not: What must reality be like in order to make it possible for us to acquire knowledge of it? But simply: What, as a matter of fact, is reality?"
For Rand there are no boundaries of pure intuition. There is no such thing as anything "in-itself", no das Ding an sich Selbst betrachtet. Objectivism does not hold that we perceive things as they really are because there is no such thing as something as it "really is" or "in itself". Things as perceived by your mind - to paraphrase Galt - are not things as they really are but simply things as they are. There is no such thing as the noumenal world, or the completely unknowable Real. Knowledge is prior to ignorance and skepticism for the same reason existence is prior to consciousness; the latter in each case is itself a relational phenomenon, having meaning only in virtue of being commingled with or otherwise actualized through the former. As such, queries like "is knowledge possible?" or "can we be aware of reality as it really is?" are completely invalid. There is no vehicle for these questions that, to be a vehicle - to have weight, does not necessarily depend upon some form of knowledge and some prior apprehension of the real. There is always and everywhere substance before the void, and all voids are simply an absence of substance. Epistemology is never properly about the possibility of entangling the real, of asking when and how our "ladders" can be "discarded", but only of that entangling's norms and reproduction. Recognizing that we have consciousness or knowledge of the real is the starting point of true and efficacious cognition in general. Consciousness is a faculty of knowing reality; consciousness is conscious.

In general, we know patterns of inference as codifications of regularly successful mental policies. In particular, we know logically valid inference patterns as means to certain conclusions, the denial of which results in contradiction. But seeing as conceptual knowledge and method are indivisible, valid forms of inference are less what we may know than that by which we know (conceptually). The knowing of logic and of basic inference patterns are in large part the faculty of knowledge turning back in on itself, and stating the implicit causal relations by which one knows as explicit propositional forms or rules for one to know.
Modus ponens is an explicit statement of the indivisibility of cause and effect, a principle implicit in every mental consequence as caused by the apprehension of some object of consciousness. "p therefore q" underscores the premise behind all valuation and recognition, for it is in recognizing the necessary connection between q and its cause that motivation may find real purchase.

In general, we know patterns of inference as codifications of regularly successful mental policies. In particular, we know logically valid inference patterns as means to certain conclusions, the denial of which results in contradiction. But seeing as conceptual knowledge and method are indivisible, valid forms of inference are less what we may know than that by which we know (conceptually). The knowing of logic and of basic inference patterns are in large part the faculty of knowledge turning back in on itself, and stating the implicit causal relations by which one knows as explicit propositional forms or rules for one to know.
Modus ponens is an explicit statement of the indivisibility of cause and effect, a principle implicit in every mental consequence as caused by the apprehension of some object of consciousness. "p therefore q" underscores the premise behind all valuation and recognition, for it is in recognizing the necessary connection between q and its cause that motivation may find real purchase.

Two quotes to begin.
The first: “In general, it is absurd to make the fact that the things of this earth are observed to change and never to remain in the same state, the basis of our judgment about the truth. For in pursuing the truth one must start from the things that are always in the same state and suffer no change.”
- Aristotle, Book 11, from his Metaphysics.
Now the second: “Serenity comes from the ability to say ‘Yes’ to existence.”
- Ayn Rand, 1973, from her essay “The Metaphysical versus the Man-Made”.
Any science of first principles rightly supposes that the justificatory structure of our schemas and assertions are terminal. It would seem then that there ought to be a terminus of judgment also, for how is one to judge a thing which can not be justified, even in principle? Justification surely is a form of explanation, namely one which identifies a cause whose identification itself deals in adherence to a kind of normativity appropriate to the production of human knowledge. Aristotle points out that all explanation is in terms of something more fundamental, and nothing is truly capable of explaining itself, for nothing is more fundamental than itself - it simply is itself. It has seemed strange then to philosophers throughout history that those concepts and principles occupying the base of human knowledge, being capable neither of having explanation or justification, should still be the ultimate source of both, hence the perennial quest for and atheological concerns towards an explanation of something like Being as such. This sort of meta-attitude is not confined to metaphysics or what calls itself metaphysics. Indeed in Hume’s infamous passage about the inescapable bifurcation or rather the inexplicable marriage of descriptive and normative statements, we see the presence of an anxious, “something from nothing” worry more familiar to us in the context of discussions about God. We may find this sort of sentiment just as easily in epistemologies also of the last century, where neo-Kantians like Wilfred Sellars marshal the notion of inference as constitutive of the perceiving act so as to escape the undesirable conclusion that the perceptually given could at once be justificatory and non-propositional, i.e., not itself justified or justifiable.
The ability of certain things to be a power unto themselves has always been met throughout history with skepticism and derision, especially by philosophers. While this fact may owe some to the prevalence and intuitive attractiveness of a naive necessitarian conception of causality (which itself necessarily invokes a prime mover), where the supposed constant conjunction of motion is appropriated as identifying the form of epistemic relations or ethical systems, I believe the source is more complicated in matter if not in form, and partly social. Namely, that in human interaction we constantly seek the identification of a final cause to explain the behavior of the human agents we interact with. And insofar as these motivations are explicit - as is the case with more noticeable, determined action - the cause can be expressed in propositional form, and we are thus loathe to think that any cause ought not to be able to expressed to one another someway, somehow. Even in relations lacking humans altogether, say perhaps the evolutionary development of an alternative organism, we identify the final cause of species survival and propagation as an explanatory summation of the efficient - and principally chemical - causes responsible for an organism’s biological integrity. We understand our mature language to be capable of reaching all corners of nature, both now, before, and forevermore.
We understand and believe then that if there are no reasons to accept something, then there can certainly be no reasons not to reject it. And it is precisely here, in elevating a particularly - and this is key - conceptual mode of grasping existence to legislate what is and is not permissible to treat as existent that all philosophical hell breaks loose. The explicit error is thus: the holding of the man-made, for no conceptual artifact is necessary, to constrain the metaphysically given. That is, the total inversion of epistemological primacy, of treating not perception but conception as cognitively basic. There is really only one tradition in the history of philosophy which explicitly recognizes a kind of metaphysical acquiescence as the source of epistemological accuracy, and that is the Aristotelian one, of which Objectivism is a part. Just as Aristotle refuted logical determinism by affirming the direction of truth to move from the metaphysically given to the man-made, so we may chastise those anti-foundationalist tendencies which make much ado about the fact that those so-called primaries of cognition cannot be explained or justified, yet serve as the source of both; the primaries, insofar as they constitute an identification of the relation of man's necessary formatic apprehension (for to be aware is not merely to be aware of something, but to be aware of something somehow) of existence to existence are not to be judged. The man-made can not arbitrate how the metaphysically given ought to be, or how its epistemic status ought to present itself, indeed the very concept of “ought” is inapplicable.
It as arbitrary to assert that because primaries are inexplicable they are somehow invalid or untrustworthy as it is to rule out the concept of “inertia” with Aristotelian physics. In both cases, perception, our primitive and primary contact with and awareness of reality - because it is metaphysically given and the identities of the human, sensory apparatus as well as the existents which act upon them are outside the power of human volition, of human making - vindicates what may be thought of as possible and trustworthy, and no more and no less. You may recall that I mentioned that there can be no reasons given not to reject the metaphysically given, and this is true unless those reasons are tied to some normative conception of what it is thought should be about and what it should serve. Indeed one is always free to ask: “why shouldn't I contradict myself?”. Objectivism has no answer to give this question save: man shall not live on thought alone, and if he is to acquire his bread also, he will need non-contradictory thought and a non-contradictory method to achieve it. Objectivism does not judge the metaphysically-given precisely because its recognition, its identification, is the means of making proper judgments about it, its very precondition. To say “yes” to the metaphysically-given is not to judge it as true or good, but to acknowledge the metaphysically-given fact that correspondence between and conformity of the metaphysically-given to the man-made is good or otherwise conducive to the survival of the man-made, and moreover still that the content of this relation is itself metaphysically-given. Objectivism does not promote an attitude of metaphysical acquiescence as true because it is good, but as good because it is true. Power over nature does not come from asserting man's omnipotence, but from asserting where and indeed how power is possible to him. To paraphrase Bacon: Nature, to be commanded, must not be judged.

Two quotes to begin.
The first: “In general, it is absurd to make the fact that the things of this earth are observed to change and never to remain in the same state, the basis of our judgment about the truth. For in pursuing the truth one must start from the things that are always in the same state and suffer no change.”
- Aristotle, Book 11, from his Metaphysics.
Now the second: “Serenity comes from the ability to say ‘Yes’ to existence.”
- Ayn Rand, 1973, from her essay “The Metaphysical versus the Man-Made”.
Any science of first principles rightly supposes that the justificatory structure of our schemas and assertions are terminal. It would seem then that there ought to be a terminus of judgment also, for how is one to judge a thing which can not be justified, even in principle? Justification surely is a form of explanation, namely one which identifies a cause whose identification itself deals in adherence to a kind of normativity appropriate to the production of human knowledge. Aristotle points out that all explanation is in terms of something more fundamental, and nothing is truly capable of explaining itself, for nothing is more fundamental than itself - it simply is itself. It has seemed strange then to philosophers throughout history that those concepts and principles occupying the base of human knowledge, being capable neither of having explanation or justification, should still be the ultimate source of both, hence the perennial quest for and atheological concerns towards an explanation of something like Being as such. This sort of meta-attitude is not confined to metaphysics or what calls itself metaphysics. Indeed in Hume’s infamous passage about the inescapable bifurcation or rather the inexplicable marriage of descriptive and normative statements, we see the presence of an anxious, “something from nothing” worry more familiar to us in the context of discussions about God. We may find this sort of sentiment just as easily in epistemologies also of the last century, where neo-Kantians like Wilfred Sellars marshal the notion of inference as constitutive of the perceiving act so as to escape the undesirable conclusion that the perceptually given could at once be justificatory and non-propositional, i.e., not itself justified or justifiable.
The ability of certain things to be a power unto themselves has always been met throughout history with skepticism and derision, especially by philosophers. While this fact may owe some to the prevalence and intuitive attractiveness of a naive necessitarian conception of causality (which itself necessarily invokes a prime mover), where the supposed constant conjunction of motion is appropriated as identifying the form of epistemic relations or ethical systems, I believe the source is more complicated in matter if not in form, and partly social. Namely, that in human interaction we constantly seek the identification of a final cause to explain the behavior of the human agents we interact with. And insofar as these motivations are explicit - as is the case with more noticeable, determined action - the cause can be expressed in propositional form, and we are thus loathe to think that any cause ought not to be able to expressed to one another someway, somehow. Even in relations lacking humans altogether, say perhaps the evolutionary development of an alternative organism, we identify the final cause of species survival and propagation as an explanatory summation of the efficient - and principally chemical - causes responsible for an organism’s biological integrity. We understand our mature language to be capable of reaching all corners of nature, both now, before, and forevermore.
We understand and believe then that if there are no reasons to accept something, then there can certainly be no reasons not to reject it. And it is precisely here, in elevating a particularly - and this is key - conceptual mode of grasping existence to legislate what is and is not permissible to treat as existent that all philosophical hell breaks loose. The explicit error is thus: the holding of the man-made, for no conceptual artifact is necessary, to constrain the metaphysically given. That is, the total inversion of epistemological primacy, of treating not perception but conception as cognitively basic. There is really only one tradition in the history of philosophy which explicitly recognizes a kind of metaphysical acquiescence as the source of epistemological accuracy, and that is the Aristotelian one, of which Objectivism is a part. Just as Aristotle refuted logical determinism by affirming the direction of truth to move from the metaphysically given to the man-made, so we may chastise those anti-foundationalist tendencies which make much ado about the fact that those so-called primaries of cognition cannot be explained or justified, yet serve as the source of both; the primaries, insofar as they constitute an identification of the relation of man's necessary formatic apprehension (for to be aware is not merely to be aware of something, but to be aware of something somehow) of existence to existence are not to be judged. The man-made can not arbitrate how the metaphysically given ought to be, or how its epistemic status ought to present itself, indeed the very concept of “ought” is inapplicable.
It as arbitrary to assert that because primaries are inexplicable they are somehow invalid or untrustworthy as it is to rule out the concept of “inertia” with Aristotelian physics. In both cases, perception, our primitive and primary contact with and awareness of reality - because it is metaphysically given and the identities of the human, sensory apparatus as well as the existents which act upon them are outside the power of human volition, of human making - vindicates what may be thought of as possible and trustworthy, and no more and no less. You may recall that I mentioned that there can be no reasons given not to reject the metaphysically given, and this is true unless those reasons are tied to some normative conception of what it is thought should be about and what it should serve. Indeed one is always free to ask: “why shouldn't I contradict myself?”. Objectivism has no answer to give this question save: man shall not live on thought alone, and if he is to acquire his bread also, he will need non-contradictory thought and a non-contradictory method to achieve it. Objectivism does not judge the metaphysically-given precisely because its recognition, its identification, is the means of making proper judgments about it, its very precondition. To say “yes” to the metaphysically-given is not to judge it as true or good, but to acknowledge the metaphysically-given fact that correspondence between and conformity of the metaphysically-given to the man-made is good or otherwise conducive to the survival of the man-made, and moreover still that the content of this relation is itself metaphysically-given. Objectivism does not promote an attitude of metaphysical acquiescence as true because it is good, but as good because it is true. Power over nature does not come from asserting man's omnipotence, but from asserting where and indeed how power is possible to him. To paraphrase Bacon: Nature, to be commanded, must not be judged.

Two quotes to begin.
The first: “In general, it is absurd to make the fact that the things of this earth are observed to change and never to remain in the same state, the basis of our judgment about the truth. For in pursuing the truth one must start from the things that are always in the same state and suffer no change.”
- Aristotle, Book 11, from his Metaphysics.
Now the second: “Serenity comes from the ability to say ‘Yes’ to existence.”
- Ayn Rand, 1973, from her essay “The Metaphysical versus the Man-Made”.
Any science of first principles rightly supposes that the justificatory structure of our schemas and assertions are terminal. It would seem then that there ought to be a terminus of judgment also, for how is one to judge a thing which can not be justified, even in principle? Justification surely is a form of explanation, namely one which identifies a cause whose identification itself deals in adherence to a kind of normativity appropriate to the production of human knowledge. Aristotle points out that all explanation is in terms of something more fundamental, and nothing is truly capable of explaining itself, for nothing is more fundamental than itself - it simply is itself. It has seemed strange then to philosophers throughout history that those concepts and principles occupying the base of human knowledge, being capable neither of having explanation or justification, should still be the ultimate source of both, hence the perennial quest for and atheological concerns towards an explanation of something like Being as such. This sort of meta-attitude is not confined to metaphysics or what calls itself metaphysics. Indeed in Hume’s infamous passage about the inescapable bifurcation or rather the inexplicable marriage of descriptive and normative statements, we see the presence of an anxious, “something from nothing” worry more familiar to us in the context of discussions about God. We may find this sort of sentiment just as easily in epistemologies also of the last century, where neo-Kantians like Wilfred Sellars marshal the notion of inference as constitutive of the perceiving act so as to escape the undesirable conclusion that the perceptually given could at once be justificatory and non-propositional, i.e., not itself justified or justifiable.
The ability of certain things to be a power unto themselves has always been met throughout history with skepticism and derision, especially by philosophers. While this fact may owe some to the prevalence and intuitive attractiveness of a naive necessitarian conception of causality (which itself necessarily invokes a prime mover), where the supposed constant conjunction of motion is appropriated as identifying the form of epistemic relations or ethical systems, I believe the source is more complicated in matter if not in form, and partly social. Namely, that in human interaction we constantly seek the identification of a final cause to explain the behavior of the human agents we interact with. And insofar as these motivations are explicit - as is the case with more noticeable, determined action - the cause can be expressed in propositional form, and we are thus loathe to think that any cause ought not to be able to expressed to one another someway, somehow. Even in relations lacking humans altogether, say perhaps the evolutionary development of an alternative organism, we identify the final cause of species survival and propagation as an explanatory summation of the efficient - and principally chemical - causes responsible for an organism’s biological integrity. We understand our mature language to be capable of reaching all corners of nature, both now, before, and forevermore.
We understand and believe then that if there are no reasons to accept something, then there can certainly be no reasons not to reject it. And it is precisely here, in elevating a particularly - and this is key - conceptual mode of grasping existence to legislate what is and is not permissible to treat as existent that all philosophical hell breaks loose. The explicit error is thus: the holding of the man-made, for no conceptual artifact is necessary, to constrain the metaphysically given. That is, the total inversion of epistemological primacy, of treating not perception but conception as cognitively basic. There is really only one tradition in the history of philosophy which explicitly recognizes a kind of metaphysical acquiescence as the source of epistemological accuracy, and that is the Aristotelian one, of which Objectivism is a part. Just as Aristotle refuted logical determinism by affirming the direction of truth to move from the metaphysically given to the man-made, so we may chastise those anti-foundationalist tendencies which make much ado about the fact that those so-called primaries of cognition cannot be explained or justified, yet serve as the source of both; the primaries, insofar as they constitute an identification of the relation of man's necessary formatic apprehension (for to be aware is not merely to be aware of something, but to be aware of something somehow) of existence to existence are not to be judged. The man-made can not arbitrate how the metaphysically given ought to be, or how its epistemic status ought to present itself, indeed the very concept of “ought” is inapplicable.
It as arbitrary to assert that because primaries are inexplicable they are somehow invalid or untrustworthy as it is to rule out the concept of “inertia” with Aristotelian physics. In both cases, perception, our primitive and primary contact with and awareness of reality - because it is metaphysically given and the identities of the human, sensory apparatus as well as the existents which act upon them are outside the power of human volition, of human making - vindicates what may be thought of as possible and trustworthy, and no more and no less. You may recall that I mentioned that there can be no reasons given not to reject the metaphysically given, and this is true unless those reasons are tied to some normative conception of what it is thought should be about and what it should serve. Indeed one is always free to ask: “why shouldn't I contradict myself?”. Objectivism has no answer to give this question save: man shall not live on thought alone, and if he is to acquire his bread also, he will need non-contradictory thought and a non-contradictory method to achieve it. Objectivism does not judge the metaphysically-given precisely because its recognition, its identification, is the means of making proper judgments about it, its very precondition. To say “yes” to the metaphysically-given is not to judge it as true or good, but to acknowledge the metaphysically-given fact that correspondence between and conformity of the metaphysically-given to the man-made is good or otherwise conducive to the survival of the man-made, and moreover still that the content of this relation is itself metaphysically-given. Objectivism does not promote an attitude of metaphysical acquiescence as true because it is good, but as good because it is true. Power over nature does not come from asserting man's omnipotence, but from asserting where and indeed how power is possible to him. To paraphrase Bacon: Nature, to be commanded, must not be judged.

Two quotes to begin.
The first: “In general, it is absurd to make the fact that the things of this earth are observed to change and never to remain in the same state, the basis of our judgment about the truth. For in pursuing the truth one must start from the things that are always in the same state and suffer no change.”
- Aristotle, Book 11, from his Metaphysics.
Now the second: “Serenity comes from the ability to say ‘Yes’ to existence.”
- Ayn Rand, 1973, from her essay “The Metaphysical versus the Man-Made”.
Any science of first principles rightly supposes that the justificatory structure of our schemas and assertions are terminal. It would seem then that there ought to be a terminus of judgment also, for how is one to judge a thing which can not be justified, even in principle? Justification surely is a form of explanation, namely one which identifies a cause whose identification itself deals in adherence to a kind of normativity appropriate to the production of human knowledge. Aristotle points out that all explanation is in terms of something more fundamental, and nothing is truly capable of explaining itself, for nothing is more fundamental than itself - it simply is itself. It has seemed strange then to philosophers throughout history that those concepts and principles occupying the base of human knowledge, being capable neither of having explanation or justification, should still be the ultimate source of both, hence the perennial quest for and atheological concerns towards an explanation of something like Being as such. This sort of meta-attitude is not confined to metaphysics or what calls itself metaphysics. Indeed in Hume’s infamous passage about the inescapable bifurcation or rather the inexplicable marriage of descriptive and normative statements, we see the presence of an anxious, “something from nothing” worry more familiar to us in the context of discussions about God. We may find this sort of sentiment just as easily in epistemologies also of the last century, where neo-Kantians like Wilfred Sellars marshal the notion of inference as constitutive of the perceiving act so as to escape the undesirable conclusion that the perceptually given could at once be justificatory and non-propositional, i.e., not itself justified or justifiable.
The ability of certain things to be a power unto themselves has always been met throughout history with skepticism and derision, especially by philosophers. While this fact may owe some to the prevalence and intuitive attractiveness of a naive necessitarian conception of causality (which itself necessarily invokes a prime mover), where the supposed constant conjunction of motion is appropriated as identifying the form of epistemic relations or ethical systems, I believe the source is more complicated in matter if not in form, and partly social. Namely, that in human interaction we constantly seek the identification of a final cause to explain the behavior of the human agents we interact with. And insofar as these motivations are explicit - as is the case with more noticeable, determined action - the cause can be expressed in propositional form, and we are thus loathe to think that any cause ought not to be able to expressed to one another someway, somehow. Even in relations lacking humans altogether, say perhaps the evolutionary development of an alternative organism, we identify the final cause of species survival and propagation as an explanatory summation of the efficient - and principally chemical - causes responsible for an organism’s biological integrity. We understand our mature language to be capable of reaching all corners of nature, both now, before, and forevermore.
We understand and believe then that if there are no reasons to accept something, then there can certainly be no reasons not to reject it. And it is precisely here, in elevating a particularly - and this is key - conceptual mode of grasping existence to legislate what is and is not permissible to treat as existent that all philosophical hell breaks loose. The explicit error is thus: the holding of the man-made, for no conceptual artifact is necessary, to constrain the metaphysically given. That is, the total inversion of epistemological primacy, of treating not perception but conception as cognitively basic. There is really only one tradition in the history of philosophy which explicitly recognizes a kind of metaphysical acquiescence as the source of epistemological accuracy, and that is the Aristotelian one, of which Objectivism is a part. Just as Aristotle refuted logical determinism by affirming the direction of truth to move from the metaphysically given to the man-made, so we may chastise those anti-foundationalist tendencies which make much ado about the fact that those so-called primaries of cognition cannot be explained or justified, yet serve as the source of both; the primaries, insofar as they constitute an identification of the relation of man's necessary formatic apprehension (for to be aware is not merely to be aware of something, but to be aware of something somehow) of existence to existence are not to be judged. The man-made can not arbitrate how the metaphysically given ought to be, or how its epistemic status ought to present itself, indeed the very concept of “ought” is inapplicable.
It as arbitrary to assert that because primaries are inexplicable they are somehow invalid or untrustworthy as it is to rule out the concept of “inertia” with Aristotelian physics. In both cases, perception, our primitive and primary contact with and awareness of reality - because it is metaphysically given and the identities of the human, sensory apparatus as well as the existents which act upon them are outside the power of human volition, of human making - vindicates what may be thought of as possible and trustworthy, and no more and no less. You may recall that I mentioned that there can be no reasons given not to reject the metaphysically given, and this is true unless those reasons are tied to some normative conception of what it is thought should be about and what it should serve. Indeed one is always free to ask: “why shouldn't I contradict myself?”. Objectivism has no answer to give this question save: man shall not live on thought alone, and if he is to acquire his bread also, he will need non-contradictory thought and a non-contradictory method to achieve it. Objectivism does not judge the metaphysically-given precisely because its recognition, its identification, is the means of making proper judgments about it, its very precondition. To say “yes” to the metaphysically-given is not to judge it as true or good, but to acknowledge the metaphysically-given fact that correspondence between and conformity of the metaphysically-given to the man-made is good or otherwise conducive to the survival of the man-made, and moreover still that the content of this relation is itself metaphysically-given. Objectivism does not promote an attitude of metaphysical acquiescence as true because it is good, but as good because it is true. Power over nature does not come from asserting man's omnipotence, but from asserting where and indeed how power is possible to him. To paraphrase Bacon: Nature, to be commanded, must not be judged.

Not reliably dependent.  The elements of an invalid concept or an anti-concept are integrated by a non-essential.  Quoting Rand  "...a 'package-deal' whose (approximately) defining characteristic is always a non-essential. This last is the essence of the trick."   (Which implies that the elements of an anti-concept need not be contradictory, merely incongruous or incommensurate.)
Remember that the entire point to thinking in concepts is to use the property of universality  (as in the 'problem of universals, "All men are mortal").  An invalid or anti-concept won't have the property of universality, which makes using them in logical structures such as a syllogism impossible because logical necessity does not exist without universality.   So what happens in debate is that if you pin down an advocate for an anti-concept by attacking a particular element then that element is simply omitted from the anti-concept (it was nonessential after all).  True socialism has never been tried.

This level of context-dropping is near impossible to believe. I will simply assume you are a troll and move on.

Introduction:
By "epiphenomenonal" I do not mean those perfectly valid descriptions appropriate to the context of physics and biology to articulate those phenomena which can be termed non-primary insofar as their effects are correlated with some relevant primary effects, but are not suspected to be their cause (see: Epiphenomenon subsections "Medicine" and "Electromagnetism"). Instead I mean the usage common to materialist theories of mind, i.e. the doctrine that consciousness exists, but is fundamentally acausal in the physical sense (as though there could exist some rupture between physicality and causality). In this sense consciousness does not affect the brain in any meaningful way, but is "epiphenomenal" - an illusory and metaphysically impotent byproduct of our third-person ontology.
Argument:
"Epiphenomenon" in this sense is an anti-concept, and more specifically, a stolen concept. When speaking to the referents of the concept of "nothing" in the appendix to Introduction to Objectivist Epistemology, Ayn Rand describes such negative concepts as "purely relative". She remarks later on that "[n]on-existence - apart from what it is that doesn't exist - is an impossible concept. It's a hole - a literal blank, a zero". In our case of the concept "epiphenomenon", the relative distinction has been collapsed - the referent in question is both "non existent" and the "what it is". The omissions relevant to the formation of the concept "nothing" are the totality of the measurements belonging to the existents whose absence is being signified. The omissions relevant to the the formation of the concept "being" are the the totality of the measurements of the measurements belonging to the existents whose existence is being signified. In collapsing the just-mentioned distinction, the measurements and the measurement's measurements become one, absolving the relative character needed to produce anything of sense about an absence of being. This "sense" derives from the existent (read: causal) nature of all productions of knowledge and principles known. Put very simply, the attribution of acausality contradicts the requirements of knowing an existent to attribute. The absoluteness of reality and the principle of no metaphysical hierarchies guarantees the nonexistence of any gradations of existence, including the gradations of existence relative to putatively known existents.
Conclusion:
The adjectival form of "epiphenomenon" common to those materialist fetishizations of the human mind's nonexistence is an anti-concept, and just another poor way (albeit a fashionable one) of attempting to side-step the axiom of consciousness.

I've taken a look at everyone else's replies but the answer seems rather simple: the domains of emotion and evaluation are not the sole cause of their correlated physiological responses, e.g., nocturnal erections, tearing from sulfur compounds (onions), circadian clocks, etc. For these examples there are no reasons to attribute lust, sadness, or boredom as cause.
With the utter normality in the animal kingdom of infant vocalizations being an invitation for caregiving I see no reason to chalk up to an emotional faculty what can be attributed to evolution.

I've taken a look at everyone else's replies but the answer seems rather simple: the domains of emotion and evaluation are not the sole cause of their correlated physiological responses, e.g., nocturnal erections, tearing from sulfur compounds (onions), circadian clocks, etc. For these examples there are no reasons to attribute lust, sadness, or boredom as cause.
With the utter normality in the animal kingdom of infant vocalizations being an invitation for caregiving I see no reason to chalk up to an emotional faculty what can be attributed to evolution.

The missing link is causality.  Perception links the causal interactions of the external world into our cognitive realm by causal means.  If we came to know something, that knowledge was caused by some chain of causal events and then willful inferences that traversed the distance between existence and our recognition of that existence.  To accept something for a reason necessarily entails it is knowable, but if you accept something for no reason then sure all bets are off and that isolated proposition might be unintegratable and incompatible with other knowledge.  Uncaused knowledge is unjustified knowledge, and so is merely opinion which threatens nothing.
In my signature is a link to Notes on "Unity in Epistemology and Ethics" by Dr. Leonard Peikoff, lecture one touches on this.
 

This is an assertion that contradictions exist in particular specific existents.  It is a completely valid response to dismiss this as an wild hypothetical without a shred of evidence to support it.  Another response is to identify the stolen concept at work here: "diction" is speech, "contra" is against, but existence does not speak so it cannot speak against itself.  Contradiction is inapplicable to existence.
Ought implies can. Therefore "Cannot implies ought-not". Epistemology is as normative a field as is ethics.

In ITOE, (Concepts as Mental Existentents, p. 153) Rand says in response to Prof. F.:
"Because in a metaphysical sense only concretes exist.  Therefore, when we form a concept, we cannot say that we have removed it in a certain sense from individuality or the existence of concretes.  Isn't there a Platonic element in the question?
The basic overall point would be always to keep in mind that this is a cognitive process, not an arbitrary process; it's a process of perceiving reality and is governed by the rules of reality.  Nevertheless, it's our way of grasping reality; it isn't reality itself; it's only a method of acquiring knowledge, a method of cognition."
Why this is so is well summed up on p. 63:
"Since consciousness is a specific faculty, it has a specific nature or identity and, therefore, it's range is limited: it cannot perceive everything at once; since awareness, on all its levels, requires an active process, it cannot do everything at once.  Whether the units with which one deals are percepts or concepts, the range of what man can hold in the focus of his conscious awareness at any given moment, is limited.  The essence, therefore, of man's incomparable cognitive power is the ability to reduce a vase amount of information to a minimal number of units--which is the task performed by his conceptual faculty.  And the principle of unit-economy is one of that faculty's essential guiding principles."
 
 

Query one and Two:
What is the purpose of philosophy to you?  How is it a value to you and how do you benefit from it? 
Answers to the above may be "meta" this discussion, but it is important at the widest levels of Objectivism.  Certain types are psychologically attracted to "philosophy" because of a mistaken belief that it is "above" the base considerations of things like science, economics, biology, ... engineering... that it is a "higher" exercise into abstractions... the implicit belief being one akin to the "ideal versus practical" false dichotomy.  I have seen this mentality over and over and over... it's the one that revels in flights of fantastical imaginative fancy playing at thought by attempting to apply logic to floating abstractions and complete fictions... the kind of mentality which so engrossed in their insanity of the unfounded "possible" (products of the untethered imagination) are offended when the subject of evidence of the senses or perception of reality are brought up.  As if the idea that which they think needed to be bounded by that which IS were some distasteful morsel foisted upon their platter of ineffable morsels, spoiling their a la carte... carte blanche that is.
Granted, you and this type of mentality may not be related but there is an element of this momentum at play in many who are drawn to ideas as an escape from rather than an acceptance and discovery of reality.
 
Question one: 
Your query implies the need to accept either: 1) contradictions IN reality itself or 2) man's faculty of consciousness i.e. the faculty of identification is inherently flawed -> it will identify a contradiction where none exists.
If there were any evidence to support either of these now would be the time to raise it.
As for your questions re. epistemology they seem elliptical and unspecific.  Man forms concepts and uses forms of logic to gain knowledge solely on the basis of evidence of the senses which are the form of the direct causal connections between reality and his mind.
Query two:
The arbitrary is literally something for which there is no, i.e. absolutely zero evidence.  The onus falls on one to prove i.e. show some evidence tending to show, the positive.  There is no onus on anyone to prove a negative i.e. prove the non existence of what is arbitrarily asserted.  For example, take the arbitrary assertion that the Devil exists.  Now imagine the proponent of the Devil asking for you to prove the Devil does not exist.  There is no evidence in reality to point to which disproves the existence of the Devil.  The non existence of the Devil cannot leave behind any little red flags, any footprints, any little notes saying "The Devil wasn't here" to point to.  Only what IS constitutes evidence and only evidence in some form supports an assertion of what is.  The onus is on he who asserts the positive.
This is not the same issue as some philosophers adopting a standard of omniscience as the standard of knowledge.  There is and never was an omniscience.  There only are men, with finite time, finite memory, finite capacity.  The concept knowledge does not apply to trees, they do not have it.  The concept knowledge does not apply to Planets or Galaxies, they do not have it.  The concept of knowledge does not apply to Gods, they simply are NOT.  The concept knowledge is applicable to Man, and is defined in the context of man because it is the only kind of knowledge there is... that knowledge is finite.  As such any self-aware computer, or alien (if ever proven to exist) could have knowledge of the same kind (although of different degree) as man, but because of the nature of existence it would be finite.  Omniscience however, lies outside of the concept of knowledge.  It is an impossible fiction.  To state that because man cannot have a faculty of omniscience, i.e. cannot possess an impossible fiction he cannot have knowledge, is an attempt to steal the concept knowledge from the realm of reality and ascribe it to the unreality and to redefine the finite as required to be infinite.
 
 

Is this thread a joke? I don't think I've ever seen such a messy hodpodge of personal misunderstandings, clunky symbolism, and arbitrary assertions cobbled together to posture as a "critique". 

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.

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.

Is this thread a joke? I don't think I've ever seen such a messy hodpodge of personal misunderstandings, clunky symbolism, and arbitrary assertions cobbled together to posture as a "critique". 

Is this thread a joke? I don't think I've ever seen such a messy hodpodge of personal misunderstandings, clunky symbolism, and arbitrary assertions cobbled together to posture as a "critique". 

Is this thread a joke? I don't think I've ever seen such a messy hodpodge of personal misunderstandings, clunky symbolism, and arbitrary assertions cobbled together to posture as a "critique".