I will try to organize your responses by topic.
It is true that concepts and definitions cannot be proven correct, based on the definitions I’m using
Proof by contradiction.
I’m sorry but I don’t understand this question. [Re: What would you have to count on?]
In light of what I’ve written above, what (according to you) have I assumed that I wish to disprove?
Your proof by contradiction fails because you are, and openly admit to, using definitions to prove that definitions cannot be proven correct. What you have to count on in order for your argument to work is definitions (and concepts and logic, which I will treat below) in your very attempt to show they cannot be proven correct. This is a classic skeptical argument collapsing into self-contradiction and absurdity.
What makes “A” the “correct” symbol to use there?
Here’s another example. Which is the correct word to use to describe electromagnetic energy with wavelength between 440 and 490 nm – “blue”, “azul”, or “sininen”?
My point is that words are mere symbols.
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it implies that specific words are necessarily tied together with specific concepts.
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I thought you were implying that the word “value” necessarily points to a particular concept. In other words, I thought you were saying “the word ‘value’ must necessarily mean this: …” If instead you were simply talking about something that (you believe) has been inferred from observation and given (by you) the label “value”, I stand corrected
I see now where your confusion is coming from with regard to your asking my to prove my conception of “value.” Yes, words qua symbols (i.e. combinations of letters and sounds) are “arbitrary” in a sense that they strictly depend on the discoverer and labeler of a concept and whatever pronunciations and rules of grammar of the language he uses. You learn the correct existing word-unit relationship from others who already know the words (“cow”, “torque” and so on). When you invent a word to go with some concept (e.g. because you’ve invented some nifty new tool and you need a name for it), you have to make a choice. “Cow” is one word in English meaning a specific group of bovine animals, while " 牛" is the Japanese word meaning the same thing. It makes absolutely no difference epistemologically what sounds, letters, or symbol(s) is chosen to name things, provided that symbol refers to a clearly defined aspect of reality. Words and their definitions, however, are not “arbitrary” in a sense that they are used for a specific cognitive reason, and thus if I start using “cow” to refer to a random hash of things “cow, chicken, dog, cat, round, loud, gravity, inflation, property, law” then utter mental chaos results and language is useless and now does the opposite of what it is for (designating and retaining concepts, thus enabling you to think and deal with broad, complex information that otherwise would be impossible.)
From your objection that you thought I was trying to prove that there was something metaphysically in a concept which necessitated that particular combination of letters for a word leads me to believe that you think a definition states the meaning of a word and somehow necessitates a particular word in a given instance. But this is false because a word is merely a visual-auditory symbol used to represent a concept. In order for logic to even function, you have to have words to denote things. A word has no meaning other than that of the concept it symbolizes, and the meaning of a concept consists of its units. So a word is not a concept, a word is merely a perceptual symbol that stands for a concept.
The purpose of a definition is to distinguish a concept from all other concepts and thus to keep its units differentiated from all other existents. A definition helps us retain a long chain of knowledge about a concept’s units by means of organizing and condensing its characteristics. Without words and definitions, reason would be practically impossible to use (you would have to start anew the entire process of abstracting every time you needed to think about any one given thing, there would be no way to order thoughts, any higher level concepts would be impossible to reach.)
However, inductive principles can never be said to be proven, as they rely upon empirical evidence and observation. As any scientist knows, the set of empirical evidence and observation is never complete.
It’s not true that the set of evidence is never complete. It depends on the context. But what you are saying is true in a sense that all knowledge is contextual. A way to picture this is like a skyscraper. The base is the fundamental axioms and perceptual observations, then first-level concepts are formed by isolating and integrating perceptually observed concretes, then wider concepts can be abstracted by isolating and integrating those, and so on. Higher level concepts consist of long chains of abstractions and classifications (this is impossible without precise definitions), but they are always reducible to their base in perceptual reality (that is actually what I meant by “anyone can understand it” earlier, not that that constituted the proof.) So the skyscraper has its base and gets more and more bricks added on to it as knowledge expands, as we become aware of more things, and as more things confront our awareness, or new knowledge is discovered. This means knowledge is hierarchical in nature because wider concepts derived from earlier narrower concepts (which constitute its “genetic roots,” and the attempt to ignore or invalidate a concept’s genetic roots constitutes a stolen concept fallacy.) e.g. If you haven’t grasped “parent” then you couldn’t grasp “orphan.”
So, the point I’m trying to explain here is that the structure of man’s knowledge is contextual and hierarchical, therefore so are definitions. We are not even talking about Ayn Rand now, but Aristotle and his “rule of definitions,” which is that a proper definition must consist of a genus and differentia. Words in a definition used to denote genus and differentia have definitions too, e.g. definition of “man” as “rational animal” depends entirely on the definition of “rational” (differentia) and “animal” (genus.) The precision of the definition depends on this structure and the structure of the definitions of its genus and differentia. So, as knowledge grows, context grows (concepts are open-ended), definitions are simply updated, refined, expanded, etc. with the expansion of one’s knowledge. If done correctly, a newer definition won’t contradict the older one. A definition can only reflect the context of knowledge available at that time, and a the definition which is objective is the one that does exactly that. (An example Rand gives is a child who in effect defines “man” as “a thing that moves and make noises.” This is obviously correct, and all that is possible given the child’s context. It doesn’t contradict Aristotle’s more essential definition of “rational animal” because “animal” includes “thing that moves and make noises” in its referents.)
My own definition of “logic” is such that it doesn’t necessarily adhere to reality. It only adheres to consistency of the symbols under consideration and their interactions. Neither those symbols nor their interactions need to have any connection to reality in order for what I call “logic” to still work.
The doctrine of empiricism is that analytical statements are independent of experience. They are just symbols under consideration, “castles in the air,” with no connection to reality, e.g. all bachelors are married. Thus, a true analytic statement is necessarily true, because it follows from logical necessity due to the symbols used, but they bear no relation to experience. Empirical statements, by contrast, are devoid of logical necessity, and thus “contingent” on experience. e.g. All bachelors are happy. A true empirical statement bears no logical necessity however, because the symbols involved, and it could have been otherwise in reality. (If this is to be taken as an empirical statement itself, then it has no connection to reality on its own terms, or else it is an analytical statement and yet contradicts itself, but I will dispense with that criticism in order to explain the Objectivist view of logic.)
Since we have seen that knowledge is contextual, there can be no such thing as “out of context knowledge” because it would have no bearing on reality, like a floating skyscraper without a base. All knowledge is acquired on the basis of previous knowledge, which means it has to be integrated into a non-contradictory whole. The method used is logic, which means logic is applied to experience to gain true and valid knowledge. If logic doesn’t adhere to reality, then you are stating logic is meaningless because there is nothing else for logic to adhere to. There is nothing else for something to be “logically true” of. A statement without connection to reality is arbitrary, i.e. without rational basis, i.e. meaningless. This is a failure to grasp the metaphysical basis of laws of logic.
All truth involves adherence to the law of identity. Logic is never divorced from reality because the law of identity forms the basis of the laws of logic. It is not merely just “A is A,” again the symbol itself is not relevant. The point is what it means: “What is is, what is not is not. A thing is itself.” and then we can deduce its corollaries, the law of non-contradiction, and the law of excluded middle, and so forth. All truths are “tautological” in the sense that all truths reflect the fact that A is A. By the same token, all falsehoods are self-contradictions. Therefore there is no “necessary versus contingent” or “analytic versus synthetic,” only “true versus false.” Experience will always bear out what it logically must and it could not be another way. The laws of nature are inherent in the identities of the entities that exist. The violation of a law of nature would require that an entity act in contradiction with its nature, that is, it would require a contradiction.
Secondly, the implicit assumption in the “logic versus experience” dichotomy is that a concept consists only of its definition. But above we have seen this is false, as a concept consists of its units, and all their characteristics and referents in reality. “X is: one more more of that things which it is.” The predicate in that proposition states some characteristics of the subject, but since it is a characteristic of the subject, the concept designating the subject, X, includes the predicate from the outset. Therefore an “empirical” statement such as X does Y is “tautological” in a sense because Y is within the nature of the entity X, it is one of the ways in which X can act by its nature. X cannot not act according to its nature, or violate its nature.
Thus, there is no such thing as “empirically true versus logically true.” A true proposition is necessarily, empirically, logically, true, all these being redundancies. A “contingent truth” or “logical, but not factual” or “factual by not logical” or “logical but not empirical” truth is a self-contradiction. All truth is a product of the logical identification of the facts of reality (experience), because reason identifies and integrates observations into concepts. Reason itself is the application of logic to experience, the fundamental base of which is the law of identity. Without the use of logic, man has no way of drawing conclusions solely from his perceptual data. e.g. if you see a lamp, your eyes alone won’t give you “lamp.” Logic must be employed at every step of concept formation, from induction from observation, to deduction from previously-known facts. The same eliminates the dichotomy between a priori and a posteriori, which is an actual disagreement with some Austrian economists’ epistemology.
the fundamental distinction between Objectivism and Austrianism is in their treatment of “value”.
According to Rand, “the market value of a product does not reflect its philosophically objective value.” By “philosophically objective value” she means morally right value: those things that people ought act to gain and/or keep based on the biological and psychological requirements and needs of human survival and flourishing. But rather, Rand states, “its socially objective value,” i.e. “the sum of the individual judgments of all the men involved in trade at a given time, the sum of what they valued, each in the context of his own life.” (Cf. Capitalism: The Unknown Ideal.) This is pretty much parallel with Menger’s original explanation. Here, Rand agrees that prices in the aggregate are rhe sum of all individual choices about valuations and exchanges. She apparently just doesn’t like the term “subjective value theory” because that has certain implications. Other Objectivists simply use the term “economically subjective” just to differentiate between ethics and economics.
Thus it should be clear that the Objectivists don’t really treat value any different in the field of economics. In ethics, it a different case, but this is not “a main difference with Austrians” because again Menger, Bohm-Bawerk, Rothbard, Reisman among other Austrian economists and intellectuals do not disbelieve in objective moral values to different extents (they have different opinions on morality.) So it’s not even that Objectivists treat value different, it’s just that some of the people in this thread apparently have a strange inability to isolate economics from ethics and apparently think they’re the same thing.
Anyone who can’t grasp this can simply read the first chapter of Human Action, or Man, Economy, and State, Chapter 1: “The Fundamentals of Human Action,” p. 73-74
“Praxeology, therefore, differs from psychology or from the philosophy of ethics. Since all these disciplines deal with the subjective decisions of individual human minds, many observers have believed that they are fundamentally identical. This is not the case at all. Psychology and ethics deal with the content of human ends; they ask, why does the man choose such and such ends, or what ends should men value? Praxeology and economics deal with any given ends and with the formal implications of the fact that men have ends and employ means to attain them. Praxeology and economics are therefore disciplines separate and distinct from the others.
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To sum up the relationship and the distinctions between praxeology and each of the other disciplines, we may describe them as follows:
Why man chooses various ends: psychology.
What men’s ends should be: philosophy of ethics. also: philosophy of aesthetics.
How to use means to arrive at ends: technology.
What man’s ends are and have been, and how man has used means in order to attain them: history.
The formal implications of the fact that men use means to attain various chosen ends: praxeology.”
Man, Economy, and State, Chapter 12: “The Economics of Violent Intervention in the Market,” p. 1029 n141, Rothbard explains that economics is Wertfrei and does not make value-judgments. But that doesn’t mean that he, qua ethicist, won’t make value-judgments, just that they are outside of the scope of economics and praxeology (and thus the current volume.) “Ultimate ethical principles and choices are outside the scope of this book. This, of course, does not mean that the present author deprecates their importance. On the contrary, he believes that ethics is a rational discipline.”
I mean, for all the people insisting oh, those Objectivists just don’t think and are just dogmatic robots, (I know because Rothbard said so in an article I read on LRC, yay independent thought!) it strikes me as ironic that some of these “Austrians” have no clue what Austrian economics even says before pronouncing knowledge about it, and even less clue of what Rand says before condemning her.