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Source link: http://archive.mises.org/10711/private-propertys-philosopher/

Private Property’s Philosopher

September 25, 2009 by

Professor Hans Hoppe, in his outstanding new introduction to the reissue of The Ethics of Liberty, hits the nail on the head. He contrasts Murray Rothbard with Robert Nozick, a much more famous figure among academic philosophers and political theorists. Although both writers embrace libertarianism (Nozick much less ardently or consistently than Rothbard), their styles of thinking differ entirely. Nozick, according to Hoppe, is impressionistic and given to flights of fancy. Rothbard, by contrast, reasons by strict deduction from self-evident axioms.

Agree with him or not on Nozick, no one can dispute the accuracy of Professor Hoppe’s characterization of Rothbard. FULL ARTICLE

{ 16 comments }

Daniel Coleman September 25, 2009 at 8:48 am

This article is appearing at a nice time to supplement the debate between Edward Feser and Gerard Casey over Rothbard’s merits as a philosopher — especially on the issue of self-ownership. Dr. Casey’s recent paper in the Libertarian Papers is especially good to read. (Feser responds on his personal blog.)

John Deal September 25, 2009 at 11:05 am

New to the blog. I have a question re: self-ownership. Does Mr. Rothbard’s objection to selling oneself into slavery mean he rejects all contracts based on future production? Would he allow the sale of organs but not “the will?” And does anyone think that saying we cannot sell our will imply we don’t actually have one? And if I want to deal with a certain person selling me their will shouldn’t I be able to assume the risk that the will isn’t really as valuable as I perceive it? There is something fishy here or I am mistaken in my understanding of Mr Rothbard.

Weingarten September 25, 2009 at 4:34 pm

Gordon’s discourse (about Hoppe) on Rothbard is quite thoughtful and provocative. Rothbard notes that freedom of contract is not an absolute, but is subordinate to the axiom of self-ownership. This is reminiscent of the Founders who wrote of the ‘inalienable’ rights of the individual, meaning that it cannot be transferred to another. Thus Rothbard and the Founders might well agree on the lack of justification for a contract on slavery. However, whereas the Founders took this as self-evident, Rothbard derives his axiom on the basis of what exists.

The first question is how does Rothbard develop this ‘ought’ from an ‘is’? He does so, by including within ‘is’ an objective characterization of the moral realm. So to quote our former President “It depends on what the meaning of the word ‘is’ is.” If ‘is’ denotes a strictly material realm, such as is the case within physics, then one cannot derive an ‘ought’ from it, but if ‘is’ includes a defined moral realm, an ought can logically follow. I believe that this is the way in which Ayn Rand derives an ‘is’ from an ‘ought’ by her characterization of the nature of man. Rothbard does this however on the basis of natural law, which might not be as fundamental as an axiom that derives from a purely philosophical foundation. So philosophers can debate whether the true foundations are from the self-evident, from philosophy, from natural law, or elsewhere.

At any rate, I presume that all would arrive at the same Lockean conclusion, that one does not acquire ownership by first encountering some land, but only after mixing his body (or person) with it, and bringing it into use.

Gordon writes “I fear that I have tried my readers’ patience by too-frequent reminiscence.” I for one would appreciate more of his insights.

Max Drax September 25, 2009 at 6:54 pm

Very well-written, Mr. Gordon. I’m left with one question, though, particularly in regard to the question of self-ownership.

I will put aside the potential logical problems that come from deriving an “ought” from an “is.” The problem, I think, is what happens when we do in fact start doing this. After all, while it is true that each man’s will is his own, and always remains his own, there is also no question that human beings CAN physically dominate their peers. They CAN use force to subjugate them. They CAN enslave them. And they do. Men are not all the same. Some are smarter, faster, and stronger.

So while the will always does remain free, the body does not, and need not. Does Rothbard ignore this? If not, what is his reasoning for accepting one “is” but not another?

I suspect that if there is an answer here, it lies in Weingarten’s discussion above – that we have to be very careful in how we define precisely what “is” – that what “is” is must include not strictly a physical dimension, but also a moral one My only question then is how we define that (without begging the question).

Weingarten September 26, 2009 at 3:29 am

Max Drax suggests that there are potential logical problems which come from deriving an “ought” from an “is”, and asks how we can provide “is” with a moral dimension (without begging the question).

I submit that when Rothbard derives self-ownership from natural law, he attributes a moral dimension to nature, and when Ayn Rand derives self-ownership from the nature of man, she does so as well. Thus “is” is characterized as including what “ought to be”. Although I respect both of them for their views and applications, I believe there is a flaw in their epistemology. *By including what “ought to be” within what “is”, they are conflating the two components of a dichotomy, which should be kept separate.* Allow me to clarify this by some examples.

There is a dichotomy between the ‘analytic’ and the ‘synthetic’, where for example a logical (or analytic) argument is basically different from an empirical (or synthetic) proof. Thus, from the premise that a man is a bachelor, it follows logically that he is not married, in contradistinction with evidence that shows he has never had a marriage license. (Similarly, from the definition of a free-market one can show the unlikelihood of the development of a monopoly, which is in contradistinction to the fact that a monopoly rarely occurs within a generally free-market.) So when some thinkers claim that the synthetic includes the analytic, they make an error in definition, for these components must be defined by their contrast.

The same thing occurs when people fail to notice the fundamental difference between ‘mind’ & ‘body’, ‘culture’ & ‘government’, or ‘subjective’ & ‘objective’. Although these components of a dichotomy are metaphysically inseparable, they are epistemologically distinct. (I do fear that I have tried my reader’s patience by being unable to describe these esoteric matters in a briefer and clearer manner.)

In sum, “is” & “ought” are epistemologically distinct, as are “same” & “different” (or “yin” & “yang”).

Weingarten September 26, 2009 at 6:28 am

I should add however, that the error of deriving the “ought” from the “is” does not violate the validity of the principle of self-ownership. Given the traditional meanings for ‘justice’ and ‘morality’, the experience of natural law, or the imperative of man’s reason, or the sense of the self-evident, make a telling case for establishing this principle.

Bala September 27, 2009 at 4:54 am

Weingarten,

I thought the analytic-synthetic dichotomy had been long since disposed off. Just to put it in simple terms, depending on where you start from – definitions or observable facts – either all truths are analytic or all truths are synthetic.

Take the pair of statements “Man is a rational animal – Man has two eyes”

A lot of philosophers start by saying that the definition of man is “a rational animal”. Starting from here, they say that the statement “Man is a rational animal” is analytic because it is like saying that “A rational animal is a rational animal” and that the concept of “rational animal” is implicit in the definition of man. The same philosophers however go on to say that the idea that “man has two eyes” is not implicit in the definition of man as “a rational animal” and has to hence be verified by observation, thus making the statement “Man has two eyes” a synthetic truth.

The fundamental flaw here is the error in the understanding of the process of concept formation. When we say that the phrase “rational animal” is a definition of man, we would be incorrect in assuming that the concept “man” refers to a “rational animal” and nothing else. In reality, the concept “man” subsumes all discovered and yet to be discovered characteristics of man. This includes physical characteristics that man (leaving out those born with physical deformities) has two eyes, two ears, one nose, one heart and so on and mental characteristics like the fact that he has a conceptual faculty, that he is solely dependent on his rational faculty to form concepts and decide on a course of action and so on.

The statement “Man is a rational animal” therefore only identifies a specific attribute of the concept “man” to define man’s nature. A definition is an identification of a characteristic of an entity that makes the explains or makes possible the maximum number of other characteristics of that same entity. For instance, various actions of man such as that he chooses cooperation over conflict, right over might, etc., can be explained by the definition of the concept “Man” as “a rational animal”. His rationality explains these behaviours that man displays.

This does not mean that the concept “Man” does not include all the other physical characteristics of man. Excluding those born with deformities, the concept “Man” subsumes the physical characteristics common to all men living at a point in time, men in the past and all men yet to be born.

Thus, the statement “Man has two eyes” is also analytic if one were to start from the concept “Man”. To call it synthetic would be equivalent to saying that the concept “man” stands for the characteristics identified in the definition “rational animal” and nothing else. To claim otherwise that all characteristics should be included in the definition is to defeat the very purpose of definition – as an aid to concept formation and integration of new knowledge into one’s existing body of knowledge. Such long definitions are by nature unwieldy and not suitable for man.

At another level, both statements are synthetic. That man has two eyes is identified by first observing a large number of men. When one is convinced that possession of two eyes is the normal state of most men, one concludes that man (as in any normal member of the species) has two eyes. Similarly, that man is a rational animal is identified similarly by observing the behaviour of a large number of men and then identifying that characteristic as common to all members of the species “man”. Thus, both the statements are synthetic.

Please do feel free to correct any error I may have made, but then I think that by accepting the “analytic-synthetic dichotomy” as a valid proposition, we are making a big mistake.

Weingarten September 27, 2009 at 9:10 am

Bala, you wrote “I thought the analytic-synthetic dichotomy had been long since disposed off. Just to put it in simple terms, depending on where you start from – definitions or observable facts – either all truths are analytic or all truths are synthetic.” You then said “Please do feel free to correct any error I may have made, but then I think that by accepting the “analytic-synthetic dichotomy” as a valid proposition, we are making a big mistake.”

The error is contained in your statement “the concept “Man” subsumes the physical characteristics common to all men living at a point in time, men in the past and all men yet to be born.” Here, you have included within what is purported to be an analytic statement, the synthetic characteristics of man. (You have assumed what you try to prove, by defining ‘analytic’ as exactly what it is meant not to be.) That is precisely the error that is made when deriving the “ought” from the “is”, namely presuming that the “is” contains the moral dimension.

Now, I grant the ultimate consistency that the ‘truth’ is a combination of the analytic and the synthetic, so that they are metaphysically inseparable. Yet at the same time, they are epistemologically distinct. Note that your demonstration that the analytic and the synthetic cannot be separated, has presupposed being able to view them independently. It reminds me of the argument given by an Objectivist which ‘proved’ that from an analytic point of view, and from a synthetic point of view, there can be no dichotomy. Therein, I responded that he had found it necessary to use the logically prior notion of differentiating between them, which by his view could not be justified, since there was no dichotomy.

Allow a clarification of what is meant by ‘epistemologically distinct’. *In a course in logic or mathematics, one can only use defined axioms and logical derivations.* Given that there are two ‘children’, whose product of ages is 6, where one child is a year older than the other, an integer answer is that one is 2 and the other is 3. However, mathematically another answer is -3 and -2. Unless some additional information is given, all that is considered mathematically is that x (x+1) = 6, where x is an integer. Consequently, either x= 2 or x= -3. Nor does the mathematician consider that in reality an age is not exactly integral for more than an instant, for if at the beginning of a question a child is 2 years old, by the end of the question, he is 2 years old plus 5 seconds. Now an empiricist might say that the mathematician or logician has no right to speak of perfectly integral numbers, or perfectly straight lines, etc. Yet such methods are at the heart of the analytic disciplines. To deprive them of analytic constructs would destroy logic and mathematics. If the analytic and the synthetic were not epistemologically different from the synthetic, we could not have courses in mathematics, as opposed to say courses in history or geography.

From an analytic point of view, the logic of derivation from fully defined premises, is different from the derivation from observations; from a synthetic point of view, the existence of courses in mathematics differ from extant courses in history.

The method of denying a dichotomy by showing that its components are ultimately the same, does not merely refute the analytic-synthetic dichotomy, but ends up refuting all dichotomies. Thus the nominalism-realism dichotomy is denied by saying that there is: no difference between the existence of individual cats and the class of all cats; no difference between mind and body; no difference between culture and government; no difference between “is” and “ought”; and no difference between you and me.

In sum, the error of denying a dichotomy (by saying that one component is essentially the same as the other) is based on disregarding the disparity between metaphysics (which is the ultimate reality) and epistemology (which is how reality is modeled). This raises the question as to whether there is a dichotomy between reality and its models. Reality and its models are metaphysically inseparable (for both are real), but epistemologically distinct (since a model is a portrayal of the reality).

As an aside, I greatly respect and appreciate someone who opens his views to criticism. Let me respond in kind, and perhaps you might wish to email me at allen7777@comcast.net

Weingarten September 27, 2009 at 12:42 pm

A briefer statement is that if within a dichotomy one component is defined to include the other, there is no longer a dichotomy (but only the need for that component).

With regard to the analytic/synthetic dichotomy, what would be a definition for ‘analytic’ (that does not include the synthetic)? It would be that the derivation of its conclusions could in principle be checked by a computer.

Bala September 27, 2009 at 5:37 pm

Weingarten,

You said

” The error is contained in your statement “the concept “Man” subsumes the physical characteristics common to all men living at a point in time, men in the past and all men yet to be born.” Here, you have included within what is purported to be an analytic statement, the synthetic characteristics of man. ”

I am unable to agree. One shall be able to use the word “Man” only after one has formed the concept “Man”. In fact, it is possible to form the concept “Man” long before and even without creating or knowing the word “Man”. The word is just a visual-auditory symbol representing the concept one has formed.

This brings us to the point “What is a concept?”. In simple terms, a concept is a mental picture of a an element of reality we encounter. As I use it, it is a mental integration of two or more units possessing the same distinguishing characteristic(s) with their particular measurements omitted.

(I am using the Objectivist definition of “Concept” because that is the epistemology based on which I am denying the very existence of the “analytic-synthetic dichotomy”)

The first step in concept formation is perception. The transition from perception to cognition involves a process of identifying an entity as apart from its surroundings, understanding its identity and then seeing that particular entity as one of a larger family of identical entities, i.e., as one unit of a larger family with similar characteristics. When one has thus reached the stage of dealing with percepts as units, one is ready to form a concept.

The key in concept formation is measurement omisison. While one learns to identify any element of the (yet-to-be-formed) concept “Man”, one goes through a process of measuring the characteristics of the entity being perceived and then omitting most specific measurements of all such entities and retaining only those that set all entities of that unit apart from all other entities of all other units.

One thus identifies a set of characteristics with their measurements as the “concept” being formed.

This omission does not, however, mean that these omitted measurements do not exist. The do and that is implicit in the concept.

This brings us to a very important point – That the starting point of all concepts formation is the process of receiving stimuli from the outside environment in the form of “percepts” which we then transform through a process of differentiation and integration into “concepts”. Every concept, therefore, represents a particular element of reality that one has encountered directly or indirectly (in the case of transmitted knowledge). Even in the latter case, someone encountered it at some point in time.

Thus, all concepts have their roots in reality and are formed out of an attempt to organise the perceived characteristics of entities that exist and have an identity of their own independent of the entity that perceives them (in this case, the human being trying to form a concept of that entity).

Without a perception of an entity, concept formation is either not possible or loses its touch with reality. One should be careful not to confuse the category of higher level concepts as not being connected to reality. They are related to perceptual concretes through many layers of lower level concepts. However, at some stage, one reaches a concept, to explain which one needs to point at some entity in reality and say “This is what this concept stands for”.

Concept formation divorced from or contradictory to objective reality would be fantasising. While such fantasising may, by reference to some aspect of reality at some later stage, attain the status “concept”, until it does so, it cannot be considered seriously.

This aspect of concepts and the process of concept-formation is what, according to Objectivists like me, makes a “Analytic-Synthetic Dichotomy” a false dichotomy. To me, all concepts are formed by measuring various characteristics of observed aspects of reality and are hence synthetic in origin. I would not be able to agree with a study which tries to omit this important aspect of concept formation because doing so would be an attempt to separate concepts from the aspects of reality they were created to help us have a mental image of. Such an approach would risk being guilty of creating an imaginary world cut-off from all reality and is a step towards insanity. Hence, I think we should not give credence to such attempts.

You further said

” no difference between “is” and “ought” ”

I will say in brief that “ought”s exist only for living beings, that too only for living beings with a volitional consciousness. So, the ought is implicit not in the “is” but in what the “is” means to the being of volitional consciousness that is encountering it. This (as I understand it) is what Ayn Rand meant when she said “Every “is” implies an “ought” “.

You also said

” Reality and its models are metaphysically inseparable (for both are real), but epistemologically distinct (since a model is a portrayal of the reality). ”

This misses the point that the portrayal always starts with perception of specific aspects of reality and hence are always “synthetic” in nature.

In summary, I submit that the starting point of concept formation is always synthetic (if it is to be rooted in reality) and these synthesised concepts may then be used analytically to develop more concepts and constructs that explain more aspects of reality and explain them better. However, the link to reality is never lost and exists through that layer of concepts in then chain that was formed directly from reality.

You continued in another post

” With regard to the analytic/synthetic dichotomy, what would be a definition for ‘analytic’ (that does not include the synthetic)? ”

If you go by the explanation I have given above, the synthetic alone makes the analytic possible, especially if one wishes to keep the connection with reality strong.

It was very kind of you to give me your contact. However, I would be more loath to (what I would consider) intruding and am more comfortable discussing this on this forum.

Once again, I would be happy to have any errors pointed out.

Weingarten September 28, 2009 at 6:11 am

Bala:

You define the concept “Man” in an open form, whereas an analytic portrait of “man” must be in closed (i.e., self-contained) form. Similarly, you define ‘concept’ itself in a synthetic form. By so doing you preclude the very nature of what it means to be analytic. The problem with that argument is that it assumes what is to be proven, namely whether there can be disciplines that are purely rigorous. Note that the ‘king’ in chess is solely defined by the moves it may make, and takes the attribute of being important by being able to be mated. One cannot say that by the concept of a king, it can move anywhere it pleases, for that is how a king behaves. *The existence and success of purely closed form analyses is undeniable, and more fundamental than any philosophy.* If a rock exists, and a philosophy ‘proves’ that it does not, it is not the rock that disappears, but the philosophy that is refuted.

However, we agree that if you assume that ‘analytic’ contains the synthetic, it follows
that there is no such thing as an analytic-synthetic dichotomy. I would add that there is then no meaning to being ‘analytic’, and no sound definition for logic or mathematics. To you, the concept of orders of infinity, and fractional dimensions, which are accepted in mathematics are merely fantasies. You might as well deny any analysis performed by a computer.

One side point is that realists, such as yourself, paid no attention to non-Euclidean geometries, since everyone ‘knew’ that reality was Euclidean. Nonetheless, mathematicians developed these forms, because they were not concerned with being realistic, but only with being sound from an analytic point of view.

In sum, by presuming that the meaning and test of a concept is strictly synthetic, you are denying the soundness and effectiveness of purely closed form analyses.

Weingarten September 28, 2009 at 12:51 pm

Bala, let us consider how statements can be validated or refuted. I wrote that ‘in mathematics, given that x (x+1) = 6 (where x is an integer) either x= 2 or x= -3.’ Can there be a synthetic validation or refutation of this statement? Is there anything empirical that can validate or refute it? Similarly, ‘if “is” is defined to include “ought”, then there is no ‘is-ought’ dichotomy.’ Is there anything empirical that can validate or refute that statement? On the other hand, consider the statement that ‘There are departments of mathematics & logic which are not the same as departments of physics & chemistry.’ Can anyone claim that this statement could be validated or refuted by purely analytic means? To belabor the point, can the statement that ‘non-Euclidean geometry is as consistent as Euclidean geometry’ be validated or refuted by studying whether or not physical space is Euclidean?

In short, is your position that there are different methods of validation, between what is logically derived from premises, and what is found empirically? Or is it your position that there is no difference between these methods?

Bala September 28, 2009 at 9:24 pm

Weingarten,

Please give me a day’s time. I am extremely tied up. I have the time to read what you have said but not to reply in detail right now. I will do it in a day or two.

Thanks (in advance) for the patience. :)

Bala September 29, 2009 at 9:14 pm

Weingarten,

Firstly, let us keep a fundamental point in mind – Mathematics is not a set of mindless abstractions with no necessary link to reality. It is most closely connected with our attempts to understand reality (which we always fails to do because our perceptual faculty is limited while reality is not constrained to be within our perceptual range).

Mathematics’ link to reality lies in its very definition, as given by Ayn Rand (I don’t know if she has taken it from some source, but I have encountered in a book of hers).

Mathematics is the Science of Measurement.

Measurement is always measurement of something. Thus, the link that Mathematics has to reality is undeniable. There is always something in reality that Mathematics helps us measure. It is the need to measure, distinguish one object (or one attribute) from another, form distinct concepts and then integrate various concepts into a larger body of knowledge that triggers our interest in the science of measurement. Without this science, man cannot form any concepts.

Taking the specific example you have given

x(x+1) = 6

What is “x”? It clearly represents the value of some physical or non-physical element in reality that you are trying to measure. “x” is always an attribute of some physical object. Attributes are those special traits of each object that give it its identity and distinguish it from others around it. Attributes always exist in the entity. They exist in some measure. This is what you state as “x” since you do not know it and are trying to measure it. Further, this attribute can take only one value at a time because not doing so would (to us) violate a basic axiom that nature abhors contradictions. It can’t simultaneously take a value of 2 and -3 because nature does not allow anything to do so.

” Is there anything empirical that can validate or refute it? ”

Yes. Finding something (empirical evidence) that can simultaneously take values 2 and -3. Until that day, I will have to take only one of the 2 values.

Your example of the king in chess is most misplaced because the word “king” always implies the existence of a territory over which he is king. In this case, the territory is the chessboard and the rules of behaviour on the chessboard are defined for the king too. If the king were to violate these, the game would no longer be called chess. Chess players would refuse to play with a person who insists that his king is free to move whichever way he pleases (note that “he” implies the player and not the king since the “king” in chess has no mind of his own but that of the player wielding him).

To take the example further, you may call Roger Federer “King of the tennis courts”. That does not mean he can do anything with and on the tennis courts. The status of King is given to him by fans on account of his exceptional performance over the years. The title whall be withdrawn if he falls or is surpassed by someone else. He may still be remembered as the “king of the tennis courts” in his era, but just that.

I am just showing that missing out parts of the meaning can lead to serious errors.

You also said

” One side point is that realists, such as yourself, paid no attention to non-Euclidean geometries, since everyone ‘knew’ that reality was Euclidean. ”

Nothing could be more incorrect than this. The frame of reference in which we study space is a matter of choice. For long, it was felt that Euclidean Geometry is sufficient because it explains every aspect of space. They were also based on certain axioms (4 to be precise) which Euclid laid out many centuries ago.

The fundamental problem with axioms is that they are self-evident and cannot be proved or disproved. To prove or disprove an axiom, you will have to refer to the axiom itself, a process that we would call circular reasoning. However, since they are real, it is futile to ignore them. They therefore form the best starting point of a study.

Which statements to take as axioms and which not to is what, as I understand it, is the difference between Euclidean and non-Euclidean geometry. When you drop the 4th axiom (that there is only 1 line that can be drawn passing though a given point and which would be parallel to a given straight line), you get non-Euclidean geometry. As I understand it, non-Euclidean geometry also serves to explain certain aspects inexplicable within the framework of Euclidean geometry.

In any case, Euclidean and non-Euclidean geometry are not reality. They are frameworks created by human minds in order to better understand reality. Human beings will continue to study them further and use them as per their relevance.

The same applies to “fractional dimensions”. The frame of reference is an arbitrary choice and is dicated by the ability of the chosen frame to explain observations and simplify analysis. These are not apsects of reality. Fractional dimensions are gaining acceptance today because they explain certain aspects of reality that conventional 3-dimensional analysis fails to explain.

In all these, you are guilty of confusing perception and choices for reality.

Talking of “closed form analysis”, I am not in the know. However, I am quite sure that if you apply the same reasoning above and ask fundamental questions about the terms and ideas you are using in a particular “closed form analysis”, the links to reality would be obvious and undeniable.

In summary, there is (I believe) no mathematics without a connection with reality.

Weingarten September 30, 2009 at 2:55 am

Bala, we fundamentally disagree. You claim “Mathematics is not a set of mindless abstractions with no necessary link to reality.” I aver that that is precisely what the operation of mathematics is about. Again, you are addressing what mathematics is metaphysically, but I am speaking about its method, i.e., epistemologically. Although ultimately it is applied to reality, the very essence of its method is to take completely defined axioms and rules of inference, and derive conclusions whose proof could be validated or refuted by a computer (and never by physical measurement).

Yet even if you deny that that is what the operation of mathematics is, suppose we defined a discipline to be precisely that. *Do you deny that such a discipline would have value?*

So again, you have presumed a definition of mathematics that includes reality, whereas it is precisely the exclusion of reality, in contradistinction to the physical sciences that contains its essence.

Your example of denying the values of x as 2 and -3 misses the point. Take for example, the case where x must be positive, so that only the answer 2 occurs. *Can you find any empirical evidence that can refute it?* Or similarly, there are straight lines, which never change in geometry. Can you refute this by measurement, since there are no straight lines in nature (not even geodesics), but only things that are imperfect, and change over time? Why not say ‘Since my ruler is not perfectly straight, and since it changes physically every second, I have refuted the existence of a straight line’? Or else say that ‘If I am able to manufacture a ruler that is perfectly straight, and does not change at all, then I have validated the existence of a straight line’? The same holds for its infinite length.

To my statement “realists, such as yourself, paid no attention to non-Euclidean geometries, since everyone ‘knew’ that reality was Euclidean” you say that “Nothing could be more incorrect than this.” However, that is not a statement of theory, but of historical fact. It does not apply to yourself (since it is past tense), but to those who denounced the soundness of mathematics precisely because it did not appear to meet the requirements of reality. This has occurred continually in history, so kindly tell me whether those realists were correct or not.

Next, you have not addressed whether the study of various geometries is sound mathematics. Instead you address real space. I again raise the question as to whether it has been proven that non-Euclidean geometries are as consistent as is Euclidean geometry. This is a mathematical question, not a question of reality.

Most pertinent, I ask again “is your position that there are different methods of validation, between what is logically derived from premises, and what is found empirically? Or is it your position that there is no difference between these methods?” Note that this is not a question about Objectivist theory, but of what exists objectively. Either different methods exist, or they do not.

Weingarten September 30, 2009 at 10:14 am

Bala, Albert Einstein said “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” In other words: when he is addressing the synthetic (i.e., metaphysical) aspect of mathematics, it relates to reality; when he is addressing the analytic (i.e., epistemological) aspect of mathematics, it does not relate to reality.

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