NameYourAxioms

Hopefully this is sufficient proof that your comment that Ayn Rand rarely used the term “metaphysics" is way off. Has anyone in this forum actually read anything that Ayn Rand wrote? From "Philosophy: Who Needs It?" by Ayn Rand: Concepts serve as units and are treated epistemologically as if each were a single mental concrete- always remembering that metaphysically each unit stands for an unlimited number of actual concretes of a certain kind. Aristotle held that definitions refer to metaphysical essences, which exist in concretes Aristotle regarded essences as metaphysical; Objectivists regard essences as epistemological. The metaphysical referent of man’s concepts is not a special, separate metaphysical essence, but the total of facts of reality he has observed. Although axiomatic concepts designate fundamental metaphysical facts, they are products of an epistemological need. Metaphysically, the referents of “5” are any 5 existents of a specified kind; epistemologically, they are represented by a single symbol, “5”. Each of an existent’s characteristics has the same metaphysical status. The characteristics designated as “essential”- and the definitions which express them- may alter as one’s cognitive context expands. Thus essences are not intrinsic to entities in the Platonic or Aristotelian manner; they are epistemological, not metaphysical. A definition is a device of man’s method of cognition. Metaphysically, all facts are inherent in the identities of the entities that exist, i.e., all facts are necessary. The concept of “necessity” in a metaphysical context, is superfluous. A major source of confusion is the failure to distinguish metaphysical facts from man-made facts. Metaphysical facts are unalterable by man and limit the alternatives open to his choice. “Infinity” in the metaphysical sense, as something existing in reality, is an invalid concept. The concept “infinity” in that sense, means something without identity, something not limited by anything, not definable; Therefore, the measurements omitted here are all measurements and all reality. Furniture exists on the same metaphysical level as tables and chairs; the hierarchy is epistemological. In asking yourself whether any concept is of a metaphysical primary, you have to ask yourself: to what does that concept refer? Locke, Berkeley, and Hume didn’t have a concept of existence as a metaphysical fact. If anything is metaphysical, attributes are. The only thing that concerns philosophy is that we can say: whatever it is, it will have to be what it is, it will be and no contradictions claimed about it will be valid-as for instance, the current theories about a particle that goes from one place to another without crossing the places in between (quantum entanglement?). That is metaphysically impossible, and you don’t have to be a scientist to know that. The alternative of what “had to be” versus what “didn’t have to be” doesn’t apply metaphysically. It applies only to the realm of human action and human choice. From "The Virtue of Selfishness" by Ayn Rand: Most philosophers are not concerned with discovering the metaphysical cause or objective validation of ethics. Ethics is a metaphysical necessity of man's survival. Men do not live in lifeboats so a lifeboat is not the place on which to base one's metaphysics.

In regard to tautologies, nominalists don't get it that concepts refer to metaphysical referents, not definitions. It is an error to think that a concept is equal to its definition (nominalism). The Russellian paradoxes arise because philosophers have attempted to treat truth as if it were a matter of correspondence between words and facts. The word is not the object of cognition, but its form. According to Wittgenstein "To say that John and Paul are both men is to say nothing more than we apply the word “man” to each." The word is not what the units have in common; what they have in common is the distinguishing characteristics. A concept represents knowledge, not a social practice in the use of words. The metaphysical component of concepts is regarded as their content. The available context of knowledge determines the referents of the concepts. A definition of “man” as “a two-legged animal” is too broad because that definition would include birds. But how are we to know prior to defining “man” that birds aren’t men? We do not begin with a definition. We do not begin with a concept. We begin with perception, including perceived similarities and differences. Concept-formation precedes definition. We start from observation of reality, not from definitions. The definition is the final step in the process, not the first.

Go to page 88 of Introduction to Objectivist Epistemology and read the chapter entitled "The Analytic-Synthetic Dichotomy" where the claim you are making is thoroughly destroyed. According to Kantian believers of the analytic-synthetic dichotomy, tautologies are propositions that repeat the same thing. To them, Ayn Rand's oft-repeated proposition (that she borrowed from Aristotle) “Man is a rational animal” means nothing more than “A rational animal is a rational animal”. Objectivism rejects the analytic-synthetic dichotomy as false.

The universe is EVERYTHING THAT EXISTS. There can be NOTHING outside of the universe (including "other universes") since nothing is excluded from the concept "universe". Existence, the universe, is a self-sufficient primary. There is nothing that causes there to be something rather than nothing; there is nothing prior to existence, beneath existence, or outside of existence. To grasp the axiom that existence exists, means to grasp the fact that nature, i.e., the universe as a whole cannot be created or annihilated. Matter is indestructible, it changes forms, but it cannot cease to exist. The universe- the entirety of that which is- neither came into being nor it can go out of existence. There is no time at which nothing existed; the universe is not in time or space; time and space are relationships among things in the universe. Philosophers are the guardians of scientific epistemology. Philosophy, in identifying the nature of existence (metaphysics) and the rules of cognition (epistemology), is the base of physics. Scientists work from a philosophic base and much research that scientists have done has been distorted by wrong philosophical premises. “String theory” is an arbitrary construct based on playing with mathematics rather than supported by observational data and its concepts including “11-dimensional space” are invalid.

MPH is a man-made mathematical ratio. Mathematical division is epistemological. Numerators (miles) are infinitely divisible by denominators (hour) but you mustn’t forget that mathematics is only a tool devised by men to help answer questions about matter. A number system, to be manageable, must be open-ended. Mathematical infinities (that do not exist in the world) are an indispensable part of mathematics. An arithmetical sequence extends into infinity without implying that infinity actually exists. Is your car traveling 33 MPH or is it traveling 33.333333333333333333333333333333333333333333333 MPH? The standard of precision that a given man chooses is an epistemological matter (man chooses whether to round the infinite mathematical sequence at 40 digits or 0 digits). You have mistakenly taken the infinite mathematical precision possibilities afforded by our man-made decimal number notation system (epistemology) as proof for the existence of actual infinity (metaphysics). The distinction between rational numbers and irrational numbers is not a metaphysical distinction pertaining to magnitudes. It is rather, a mathematical distinction pertaining to the means of identification of quantitative relationships. You are confusing the means of measurement (which are dependent on man's consciousness) with the objects of measurement (objects are what they are independent of man's consciousness). The need for irrational numbers arises from a difference between mathematics and engineering. In engineering (applied physics) with a concrete application in mind, one can always identify the required precision in advance. But the application of mathematics is open-ended. There is simply no way to anticipate the level of precision that may, someday be required for some reason. Geometric propositions have infinite precision but all of our measurements have finite precision. Don't believe that our decimal number notation system is man-made? Try expressing an irrational number to the precision of 40 decimal places using Roman numerals.

SL, let's examine the validity of your anti-Objectivist rejection of the Law of Identity. When you claim that there are an "infinite number of 'speeds' between 0 MPH and 55 MPH", what you are really saying is that an object can travel somewhere between 0 miles and 55 miles (no more, no less) in one hour. 55 miles is a finite range, not infinite.

You have asked me 30 questions in one day. That is beyond ridiculous. I'm not answering one more G-D question. Get to the damn point. State your case or this conversation is over. 1. Question: How would you address the statement: In the 10 seconds it took my car to accelerate from 0 mph (relative to the pavement) to 55 mph, my car travelled at different speeds, in fact an infinite number of speeds between 0 mph to 55 mph." 2. Is the statement true or false or meaningless and why? 3. Could it be corrected by tweaking language? 4. Is there something fundamentally different about trying to speak of aspects of something continuous versus speaking of discrete things? 5. Are you saying "speed" is epistemological rather than metaphysical? 6. What about "distance" (as a relationship between two entities)? 7. You claim "Speed" is only a measurement... a measurement of *what* in reality? 8. An epistemological measurement has as its object some aspect of metaphysical reality, no? 9. If you consign the concept "speed" to the epistemological what then do you identify as its object in metaphysical reality to which it refers? 10. Care supply some label (i.e. a word) for it? 11. If your premise that "speed" is only epistemological is true, what does that imply about momentum (a physical quantity or attribute possessed by entities)? 12. What property does an entity posses (you need to supply a word for it) and has identity, which manifests itself in what you eventually measure as "speed"? 13. How do you keep in your mind the distinction between the attribute or property in reality possessed by entities and your identification of them in terms of some measurement? 14. Are you claiming all continually changing properties or attributes of reality with magnitudes are not metaphysical but instead merely epistemological? 15. Does the metaphysical property "motion" of an entity have identity? 16. Is the identity of the "motion" of an entity at time A when we "measure" its speed at 10MPH , different in reality from the "motion" of the entity at time B when we "measure" its speed at 20MPH? 17. As a part of reality, does your "motion" need to exist as particular, concrete, and specific. 18. In other words, although motion can have any magnitude and direction in general at any time it must exist having a specific magnitude and direction? 19. Or does it remain... identy-less until measured? 20. Do you hold that attributes and properties of systems of entities such as "distance" between object A and object B and relative "motion" between them are not metaphysical? 21. i.e. are you claiming A and B moving away from each other at 10 MPH is not metaphysically distinct from A and B moving away from each other at 20 MPH? 22. Do you hold that all such properties, attributes, relationships between existents are merely epistemological? 23. If so is the knowledge thereof valid i.e. having some referents in reality and if so.. what in reality are the referents? 24. Can you identify them with a label or a word? 25. And what finally could possibly "be" (i.e. exist) independent of human consciousness, other than something of metaphysical reality? 26. Do you take a relationship in reality between two objects such as distance to be metaphysical? 27. Do you hold that metaphysically there is no difference between a system of object A and object B spaced apart by 5 inches and a system of object A and object B spaced apart by 10 inches? 28. Are all relationships between objects in a system are not metaphysical what are they? If we can identify them in reality what can they be other than metaphysical? 29. Do you hold that a system of object A and object B in a state of "acting" to move away from each other at 10mph is metaphysically different from a system of object A and object B in a state of "acting" to move away from each other at 20mph? 30. BTW have you read ITOE?

Look, if you have some point to make let's get on with it. You have done nothing but carpet bomb me with a never-ending stream of questions, many of which are completely unrelated to my statement that "Infinity cannot exist per the Law of Identity." If you believe that the universe is infinite, then out with it. Either explain to me why you believe that the Law of Identity is false or why you believe that an infinite universe would not violate the Law of Identity. I will not play this game any longer with you.

Distance is not a property of an entity as you say. That is absurd. Neither is motion. You are wrong on both counts. Distance is a relationship between separate entities. Motion is an action of a metaphysical entity. It is not a property.

Motion cannot have a magnitude or direction. Objects are in motion. Motion is not an entity; it is an action of an entity. Attributes, motions, and relationships cannot exist without entities. Motion does not exist by itself. Things are in motion relative to each other. The error you are making is called reification. Reification is the fallacy of taking an aspect of a thing (motion) as if it were capable of a separate existence. You are trying to make an action of an entity (motion) into a substance.

Speed is a measure of motion. Motions are metaphysical actions of entities. Speed is a measurement of that motion and, therefore, epistemological. Motion is what it is independent of human consciousness. Measurement is an act of human consciousness making it epistemological. Measurement, the essential purpose of mathematics, ultimately involves an identification of a quantitative relationship between concretes. Man, wishing to understand motion, measures it using the following epistemological device: Speed = Distance divided by Time.

Yes, all the gold in the universe is finite (limited) per the Law of Identity. EVERYTHING that exists is limited. There is no such thing as an infinite quantity because "infinite" means a quantity without any specific identity. The universe- the entirety of that which is- neither came into being (from what?) nor can go out of existence. Matter is indestructible, it changes forms but it cannot cease to exist.

Finite means limited. It is a metaphysical fact that the amount of gold on planet earth is finite. This would be a metaphysical fact whether human consciousness existed or not. How much gold exists on planet earth is a matter of measurement which requires human consciousness and is therefore epistemological. See the difference now?

"Finite" is not a measurement. It makes no reference to a unit. Saying "This pencil is 3 times longer than that one" is an objective verifiable statement unlike the example you gave "this is long".

Rather than explaining how to reach abstractions that integrate perceived concretes, philosophers have offered us the choice of empty abstraction (rationalists) or disintegrated concretes (empiricists). Rationalists (mystics) declare that the constructs of their imaginations are validated by their "beauty" or "clarity". Empiricists (skeptics) denounce the very goal of discovering causal theories and demand that researchers settle for describing appearances. It has been said that Kant merged rationalism and empiricism but he actually combined the worst in both. He combined the arbitrary method of the rationalists with the skeptical content of the empiricists.

Speed is a measurement (distance divided by time, such as miles per hour) and, therefore, epistemological. When I look at a distance as being 5 miles, I am looking at it numerically (measurement requires human consciousness so it is epistemological). If I say that this particular pencil is 3 times longer that particular pencil, I am looking at it geometrically. My focus is on the quantitative relationship between the 2 pencils (the relationship exists metaphysically independent if human consciousness). The concept, "place", refers to a relationship among bodies.

Our senses cannot perceive cosmic rays, or genes, or electrons, or ultraviolet but each of these concepts is reducible to perceptual data. They have no direct referents on the perceptual level of awareness but each can be grasped by following a long antecedent chain of concepts that ultimately reduce to first-level concepts that can be pointed at. Gravity is an abstract concept; not a first-level concept like a dog that can be pointed at. Abstract = farther from perceptual reality.

Your question is epistemological. We must draw a distinction between the metaphysical and epistemological. Mathematics, in Newton's view, is only a tool devised by men to help answer questions about matter (mathematics is a man-made epistemological device). In mathematics we must embrace the the possibility of an infinite set of numbers. MPH is a ratio and, mathematically, man may choose to divide it in an unlimited number of infinitesimally small units depending on his desired precision requirements. Mathematical infinity is valid epistemologically but infinity in the metaphysical sense, as something existing in reality like an unlimited universe, is an invalid concept.

Infinity cannot exist per the Law of Identity. Everything that exists is finite. Infinity in a metaphysical sense is an invalid concept; there is no actual infinity. It would mean something without identity, something not limited by anything. Everything that exists is limited. There is no such thing as an unlimited quantity or an unlimited number of attributes because "infinite" means a quantity without any specific identity. In mathematics, we must embrace the possibility of an infinite set of numbers but neither numbers nor sets of numbers exist in the world as such; there is no actual infinity. All multiplicity is finite. An infinite number would have to be one that could not be reached by counting (infinity to the power of infinity +1, 2, 3....).

"The earth is flat" was NEVER true since it DID contradict reality. The truth did NOT evolve.

Truth pertains to something mental in its relationship to the external world. Truth is an awareness of the facts. Man determines the truth or falsehood of his judgments by whether they correspond to or contradict the facts of reality. New knowledge can contradict old mistaken beliefs but not old knowledge. Knowledge is a mental grasp if the facts of reality. Newly grasped facts cannot contradict previously grasped facts. This rules out such notions such as "For the medieval, the world was flat; for us, it is round"- as is Columbus' voyage somehow curved it.

Measurement doesn't produce identity. Measurement is a act of human consciousness. Measurement identifies a quantitative relationship between concretes in the world. Quantities exist whether you measure them or not. An arithmetic expression can be changed by a choice of units but the relationship among magnitudes remains the same. "This pencil is twice as that one" identifies a quantitative relationship between 2 metaphysical existents but it's not a measurement since it makes no reference to a man-made standard. It's true whether I measure it in centimeters or inches.

You are committing Heidegger's error of reifying "nothing", treating it as a thing rather than the absence of a delimited positive. Existence has no contrary: there is no nothing. Existence exists; non-existence does not. According to the Law of Identity: to be something is to have a specific identity. To be nothing in particular is to be nothing at all.