Len Budney: Jon Irenicus:As for Mises' praxeological system being non-rigorous and mathematical, what do you mean? Mathematics is reasoning logically from axioms--no more, no less. It has very little to do with equations. In fact many areas of mathematics don't have any equations at all. So whenever someone reasons logically from axioms, he's doing math. Mises attempts to do just that in Human Action, so he's doing math. He thought he wasn't, though, because he wasn't using equations. It was non-rigorous because he didn't pin down his axioms and definitions well enough to make them airtight. A cranky mathematician might call that "bad" mathematics, but ALL mathematics was "bad" in that sense up until about 150 years ago. Mises was a pioneer, and plowed ahead rather than stopping to dot his i's and cross his t's. Praxeology can be made rigorous, and I'd like to see it done (but it's bloody hard, so I've basically given up looking for low-hanging fruit there). --Len
Jon Irenicus:As for Mises' praxeological system being non-rigorous and mathematical, what do you mean?
Mathematics is reasoning logically from axioms--no more, no less. It has very little to do with equations. In fact many areas of mathematics don't have any equations at all. So whenever someone reasons logically from axioms, he's doing math. Mises attempts to do just that in Human Action, so he's doing math. He thought he wasn't, though, because he wasn't using equations.
It was non-rigorous because he didn't pin down his axioms and definitions well enough to make them airtight. A cranky mathematician might call that "bad" mathematics, but ALL mathematics was "bad" in that sense up until about 150 years ago. Mises was a pioneer, and plowed ahead rather than stopping to dot his i's and cross his t's. Praxeology can be made rigorous, and I'd like to see it done (but it's bloody hard, so I've basically given up looking for low-hanging fruit there).
--Len
There's more that distinguishes mathematics than just deriving conclusions from axioms. It's a mistake to equate mathematics and praxeology on this score as if this were their essential characteristic. It's the modern rationalists following Descartes who want to construe philosophy and the social sciences on the model of mathematics.
Yours in liberty,Geoffrey Allan Plauché, Ph.D.Adjunct InstructorBuena Vista University
"Quis custodiet ipsos custodes?"(Who watches the watchmen?)-Juvenal, Satires VI.347
I think you're speaking in ignorance here. Aristotle, for example, never tried to prove any axiom.
Aristotle was a mathematician. You philosophers use a very broad definition of "philosophy," and claim lots of ancient mathematicians for your own. Mathematics is logical reasoning from axioms. Aristotle actually documented the laws of logic; in doing so, he was acting as a mathematician as distinct from a philosopher.
If he took a break from that and argued with his disciples whether 5 is a noun or an adjective, he would be doing philosophy. If he paused to motivate his axioms by explaining why they were plausible, he would be doing philosophy. So long as he confined himself to reasoning logically from axioms, he was doing mathematics.
And how does Hoppe try to prove any axiom for that matter?
Hoppe, like Rand and too many others, attempts to prove (in effect) that aggression is morally wrong. In Hoppe's case, he attempts to prove self-ownership--and he tries to do it, not from axioms, but by "proving" that any alternative is self-contradictory. His argument fails. No argument will ever succeed, because self-ownership is an axiom.
If we grant his proof that you "own" yourself, that still fails to prove that there's any reason I can't eat you. He sometimes equivocates on the meaning of "ownership" to derive that self-ownership implies exclusivity.
His entire ethical argument falls to earth if you reply, "Besides, who gives a d*mn about minimizing conflict?"
The NAP is not an axoim, btw; it is a conclusion derived from a long chain of reasoning.
You're being a philosopher now, not a mathematician.
Some attempt to prove the NAP as a theorem. All of their attempts either (1) are invalid, like Hoppe's self-ownership argument, or (2) depend on some other moral axiom. In the latter case, the other moral axiom is equivalent to the NAP. If Hoppe and others were just slightly less philosophical, and slightly better mathematicians, they would realize that the reason they're in a quagmire is that they're trying to prove axioms.
This is mistaken in a number of ways. And I think it's based on mistaken assumptions about metaphysics, epistemology, and ethical theory. Yes, any argument in favor of the NAP will lead back to discussions of metaphysics and epistemology because the NAP is not an axiom. And no, the NAP will not be at the base of all premises.
Rest assured, ANY attempt to get TO the NAP logically must start from SOME axioms. And at least ONE of those axioms must be a moral assertion of the form: X is wrong. If no axiom has that form, then it will be impossible to conclude that aggression is wrong. Once you've identified that axiom, you'll realize that X is a synonym for aggression. QED
Trust me on this one. I am not confused.
Your approach may be good for persuading people, good rhetorically, but it doesn't suffice for providing a philosophical defense of the NAP.
It is impossible to prove any assertion of the form "X is wrong," as I've just proven with fair rigor. You will always be found, at the bottom of it, either assuming that X is wrong, or else assuming that Y is wrong and then proving that X implies Y. There's no way around it; that's how aristotelian logic works.
But it's also impossible to prove that "X is wrong" empirically. Sometimes crime pays. To argue that crime is still wrong, even when it pays, even when nobody ever realizes a crime was committed, you must either sneak in an assertion (and hence beg the question), or else invoke some notion analogous to karma, whereby the criminal or others are harmed even if nobody is ever conscious of harm. A eudaimonist would say that the criminal in that case is "not flourishing fully as a human," which is somewhere between begging the question and meaningless.
The NAP can't be "proven." Anyone who attempts to prove the rightness of a moral code is trying to prove axioms without realizing it. Rand was an egregious offender in this area: her "proof" was garbage even IF you grant her axiom that "life is the standard of value." Which we don't grant: who says that life is the standard of value?
Geoffrey Allan Plauche:There's more that distinguishes mathematics than just deriving conclusions from axioms.
No. Trust me on this one. That's the definition of the field in which I earned my doctorate.
The entire discussion is moot. We're not in the business of judging minds and hearts. If one "really believes in" the NAP, he's a libertarian. It doesn't matter whether he does so because he believes it will maximize prosperity, or because it's "just right," or because he thinks it will protect him from others' aggression, or keep him out of hell, or lead him to Nirvana, or give him washboard abs. It suffices that the NAP is embraced.
I have to agree with Len, here. One of the most liberating and illuminating aspects of praxeology for me, was discarding people's intentions as irrelevant, as compared to their actions. You really can understand people when you ignore the fluff and watch the silent movie. I've come to believe that regardless of what people think about themselves, they could be lying to themselves, or believing a fantasy they've created. Watch a person, track what they actually do, and you'll get the best, non-biased sense of who, what they are. Compare that then, with what they say, or what they actually think about themselves, and you have a firm basis from which to learn about them.
Len Budney: Geoffrey Allan Plauche:It's not a trap. It's sound ethical theory. We're not concerned here with epistemic problems like whether we can tell someone is really virtuous. But from the standpoint of ethical theory, he doesn't count as virtuous if he only does it out of fear of punishment. Then you're setting yourself an unsolveable problem. The depths of the human psyche are vast and murky--you yourself can't even say whether you do something "only" for this reason or that. It's extremely rare that a person has "only" one reason anyway. I'm honest to my wife, not only because I uphold that virtue, but also because I know I won't like the consequences if I don't. So am I virtuous? Evil? 30% virtuous? 50%? God alone knows--I sure don't, and you certainly have no idea. The whole quest is a fool's errand. But I'm leery of entering into conflict with you on this point, because we're also on the boundaries of a religious war between philosophers and mathematicians. I think that most of what philosophers do is a fool's errand, because it always boils down to arguing definitions through an infinite regression.
Geoffrey Allan Plauche:It's not a trap. It's sound ethical theory. We're not concerned here with epistemic problems like whether we can tell someone is really virtuous. But from the standpoint of ethical theory, he doesn't count as virtuous if he only does it out of fear of punishment.
Then you're setting yourself an unsolveable problem. The depths of the human psyche are vast and murky--you yourself can't even say whether you do something "only" for this reason or that. It's extremely rare that a person has "only" one reason anyway. I'm honest to my wife, not only because I uphold that virtue, but also because I know I won't like the consequences if I don't. So am I virtuous? Evil? 30% virtuous? 50%? God alone knows--I sure don't, and you certainly have no idea.
The whole quest is a fool's errand. But I'm leery of entering into conflict with you on this point, because we're also on the boundaries of a religious war between philosophers and mathematicians. I think that most of what philosophers do is a fool's errand, because it always boils down to arguing definitions through an infinite regression.
No. Again you're confusing theorertical considerations with a separate epistemic issue pertaining to what we can know about another person in practice. The latter doesn't vitiate the necessity and usefulness of the former.
Are you a mathematician? That would explain much.
Len Budney:Aside from the philosopher/mathematician thing, I have a pragmatic question: would you rather get your theory just right, and die in slavery, or would you rather be free, though you don't finish your theory? Does your theory matter more to you, or the reality of freedom? Having watched Christians go through the same tail-chasing regression, I can tell you: first, you'll end up either concluding that nobody is a "real" libertarian, or divorcing your model from reality and accepting us at face value despite your theory to the contrary; second, you'll not get much closer to attaining actual freedom while you try to chase this recursion to its bottom. It has no bottom. It should suffice for me to assure you that I embrace non-aggression. If I turn out to be a liar, call me on it. Otherwise, take me at my word.
Your pragmatic question doesn't prove what you seem to want it to prove here. The pragmatic question just poses two seemingly mutually exclusive alternatives, as if theoretical work isn't necessary and useful for promoting liberty. But the alternatives aren't necessarly mutually exclusive. True, one has to make trade-offs and sometimes one might have to give up the theorizing for a while, say to become a freedom fighters. It would be foolish to argue against a division of labor in promoting and defending liberty though.
Do you realize that your claim that there is no bottom runs counter to treating that NAP as an axiom? Axioms are the bottom. Lack of a bottom means infinite regression or vicious circularity, both of which Aristotle rejected. The problem is the NAP is not an axiom.
There is a sense in which it suffices for me that you embrace non-aggression, that is, as a fellow human being living in society with you. But from a philosophical and ethical standpoint, it matters why you embrace it.
gplauche: Are you[Len] a mathematician?
February 17 - 1600 - Giordano Bruno is burnt alive by the catholic church. Aquinas : "much more reason is there for heretics, as soon as they are convicted of heresy, to be not only excommunicated but even put to death."
a separate epistemic issue pertaining to what we can know about another person
What we can know about ourselves, I believe I said. Your own motives are mixed, impure, and often not what you thought they were. Given that, your concept of "virtue" is fairly useless, since for practical purposes nobody satisfies it.
Sorry, I thought everyone knew that by now.
Different sense of "bottom." An axiom is what you get when you've tried to prove something long enough, realized that you've been reasoning in circles for, say, 1500 years, and finally admit, "I will assume this." What's bottomless is the circular argument itself--but philosophers seem to love chasing the circle till they find its end.
That being the case, it's helpful to distinguish "practical" libertarianism from the ivory-tower version that you're trying to construct and haven't yet. Especially since construction will never finish, and a moving van just pulled into the driveway.
As for why I embrace it, I embrace it because it's "just plain right." But perhaps that only means that I'm genetically disposed to certain brain functions which lead me to think that. Or maybe that's a response to childhood trauma. Or maybe there's no such thing as free will, and hence no such thing as virtue--after all, we're basically machines are we not?
Len Budney: Geoffrey Allan Plauche:There's more that distinguishes mathematics than just deriving conclusions from axioms. No. Trust me on this one. That's the definition of the field in which I earned my doctorate. --Len
Nah. So it's not essential to the concept of mathematics that it deals with magnitudes, quantities, etc.? Mathematics is just anything involving the deduction of conclusions from axioms? How imperialistic of your discipline to stretch its meaning beyond recognition and usefulness. And I suppose it's not essential to the concept of praxeology that it deals with human action. Let's apply it to other animals and inanimate objects too! After all, since its essential characteristic is that it deduces conclusions from axioms any subject matter this applies to can be considered praxeological!
Juan: Danno: Libertarian ideals hit a very solid grey area in this - indoctrination of the children is not ideal, but anyone preventing the parents from doing so is even worse. I'm not at all advocating such intervention. I'm just pointing out that the way parents deal with 'their' children is arbitrary most of the time. That is a fact, and it probably has consequences.
Danno: Libertarian ideals hit a very solid grey area in this - indoctrination of the children is not ideal, but anyone preventing the parents from doing so is even worse.
No doubt it does, but, like the weather - it's interesting to note, but I fail to see what can be done about it on other than a small scale. Debating particular instances of indoctrination that you object to, in the venues in which you may have an effect on actual parents who are interested in those topics, is probably a more efficient use of your energies. You're likely to be called a troll in such venues as well, though - no matter how heartfelt your contribution. It's probably best to develop a thick skin for such things, and recall Carroll on the misuse of words when you're mislabeled by the ignorant:
""When I use a word," Humpty Dumpty said in a rather a scornful tone, "it means just what I choose it to mean -- neither more nor less. "The question is," said Alice, "whether you can make words mean different things." "The question is," said Humpty Dumpty, "which is to be master -- that's all."" -- Lewis Carroll in _Through the Looking-Glass_.
many Libertarians fairly froth at the mouth (as do I) at the abuses of Church Rule in history and today, but even worse is the idea of any authority making a particular faith mandatory or prohibited. My ideal size of government is zero - so I can hardly be advocating political control of religion. On the other hand, church and state have always been partners in crime - a fact that the paleos here are quite glad to ignore.
many Libertarians fairly froth at the mouth (as do I) at the abuses of Church Rule in history and today, but even worse is the idea of any authority making a particular faith mandatory or prohibited.
I don't know that anyone ignores it so much as acknowledges that there's little to be done about it. In either an anarchist or libertarian society, interfering with someone who is voluntarily following the dictates of a religion without aggressing against a third party would be viewed as aggression itself. If the follower were committing aggression against a third party, the reason would be immaterial - it'd still be viewed as aggression.
This may be more important to you than to others here, because of simple geography. My information on current Argentinian society is regrettably scant, but I'm under the impression that the Church is a much more potent force there than it is in the USA. (Here, we have demagogues and rabble-rousers, but they're often not attached to any large, traditional church.)
maxpot46: Danno: An all-meat diet would be even unhealthier than a vegetarian diet. Facts: Eskimoes and other aboriginal tribes live today on all-meat diets, and are among the healthiest people on the planet. So the golden rule on vegetables wasnt't true after all ? =]
maxpot46: Danno: An all-meat diet would be even unhealthier than a vegetarian diet. Facts: Eskimoes and other aboriginal tribes live today on all-meat diets, and are among the healthiest people on the planet.
Danno: An all-meat diet would be even unhealthier than a vegetarian diet.
Eskimoes and other aboriginal tribes live today on all-meat diets, and are among the healthiest people on the planet.
It may well be so - I haven't looked at the evidence, or reviewed the counter-evidence yet. If it is so, it probably won't have much effect on diet around here - vegetables are tasty, too - we're planning on deep-fried cauliflower tonight. It does need to be looked at before I claim that an all-meat diet is unhealthy again, eh?
Danno, making himself hungry again.
The avatar graphic text:
"Are you coming to bed?"
"No, this is important"
"What?"
"Someone is wrong on the internet."
So it's not essential to the concept of mathematics that it deals with magnitudes, quantities, etc.?
GIVE THE MAN A CIGAR! You've hit it exactly! Mathematics has nothing specially to do with magnitudes, quantities, etc. Graph theory is mathematics, and vast chunks of it do not involves magnitudes, quantities or even numbers. Group theory is mathematics, and again most of it doesn't involve magnitudes, quantities or even numbers. The coolest field in all of mathematics is point-set topology, which has nothing whatsoever to do with numbers. Non-mathematicians uniformly think that mathematics is about measuring--but in fact it's easy for a doctoral candidate to finish a PhD without having done any calculations of any sort in years.
The common denominator in all branches of mathematics is that we reason logically from axioms. We don't really care about numbers, unless our area of inquiry happens to involve them, and many do not.
How imperialistic of your discipline to stretch its meaning beyond recognition and usefulness.
I bet you don't realize how much of chemistry is graph theory. Is it "imperialistic" of us that we teach chemists graph theory so they can do their jobs? And that, when they do graph theory IN their jobs, we comment, "He's doing mathematics?" When he blows junk up, he's not doing mathematics. But when he draws the graph and decides whether it's embeddable in the plane, say, then he IS doing mathematics.
Len Budney: a separate epistemic issue pertaining to what we can know about another person What we can know about ourselves, I believe I said. Your own motives are mixed, impure, and often not what you thought they were.
What we can know about ourselves, I believe I said. Your own motives are mixed, impure, and often not what you thought they were.
Even so.
Len Budney:Given that, your concept of "virtue" is fairly useless, since for practical purposes nobody satisfies it.
I disagree.
Len Budney: Do you realize that your claim that there is no bottom runs counter to treating that NAP as an axiom? Axioms are the bottom. Lack of a bottom means infinite regression or vicious circularity, both of which Aristotle rejected. The problem is the NAP is not an axiom. Different sense of "bottom." An axiom is what you get when you've tried to prove something long enough, realized that you've been reasoning in circles for, say, 1500 years, and finally admit, "I will assume this." What's bottomless is the circular argument itself--but philosophers seem to love chasing the circle till they find its end.
This confuses continued debate with the failure to discover any truths.
Len Budney: There is a sense in which it suffices for me that you embrace non-aggression, that is, as a fellow human being living in society with you. But from a philosophical and ethical standpoint, it matters why you embrace it. That being the case, it's helpful to distinguish "practical" libertarianism from the ivory-tower version that you're trying to construct and haven't yet. Especially since construction will never finish, and a moving van just pulled into the driveway.
It's not an ivory-tower version that has no practical application. I'm concerned both with the seach for truth and with promoting liberty. I don't see the former as a waste of time or as having no practical import.
Len Budney:As for why I embrace it, I embrace it because it's "just plain right." But perhaps that only means that I'm genetically disposed to certain brain functions which lead me to think that. Or maybe that's a response to childhood trauma. Or maybe there's no such thing as free will, and hence no such thing as virtue--after all, we're basically machines are we not?
I find none of that philosophically satisfactory. If that's satisfactory to mathematicians, so be it.
`Would you tell me, please, which way I ought to go from here?' `That depends a good deal on where you want to get to,' said the Cat. `I don't much care where--' said Alice. `Then it doesn't matter which way you go,' said the Cat. `--so long as I get SOMEWHERE,' Alice added as an explanation. `Oh, you're sure to do that,' said the Cat, `if you only walk long enough.' Alice felt that this could not be denied, so she tried another question. `What sort of people live about here?' `In THAT direction,' the Cat said, waving its right paw round, `lives a Hatter: and in THAT direction,' waving the other paw, `lives a March Hare. Visit either you like: they're both mad.' `But I don't want to go among mad people,' Alice remarked. `Oh, you can't help that,' said the Cat: `we're all mad here. I'm mad. You're mad.' `How do you know I'm mad?' said Alice. `You must be,' said the Cat, `or you wouldn't have come here.'
I'm curious of Geoffrey: What do you think your main contribution, or set of contributions to libertarian theory are? I'm wondering where you're coming from. Perhaps asked a different way, where do you find current libertarian theory problematic?
Geoffrey Allan Plauche:I find none of that philosophically satisfactory. If that's satisfactory to mathematicians, so be it.
As a theist, I think it's impossible to be virtuous without sincerely embracing morality, but it's further necessary that you pick the right morality--namely, God's. So not only is what I suggested unsatisfactory, but whatever morality you come up with will be equally unsatisfactory to me.
Therefore, I submit that it's a good idea not to pack too much into liberty, other than liberty itself. Most everyone on this forum is on the same page, and I'm glad to be a part of it. In so doing I'm associating expansively, beyond my religious circle, and hence outside the ambit of those who fully agree with me philosophically. Your approach strikes me like someone coming along and saying, "OK, you're all kinda libertarians--but if you want to be the real deal, you also have to join my church."
Len Budney: So it's not essential to the concept of mathematics that it deals with magnitudes, quantities, etc.? GIVE THE MAN A CIGAR! You've hit it exactly! Mathematics has nothing specially to do with magnitudes, quantities, etc. Graph theory is mathematics, and vast chunks of it do not involves magnitudes, quantities or even numbers. Group theory is mathematics, and again most of it doesn't involve magnitudes, quantities or even numbers. The coolest field in all of mathematics is point-set topology, which has nothing whatsoever to do with numbers. Non-mathematicians uniformly think that mathematics is about measuring--but in fact it's easy for a doctoral candidate to finish a PhD without having done any calculations of any sort in years. The common denominator in all branches of mathematics is that we reason logically from axioms. We don't really care about numbers, unless our area of inquiry happens to involve them, and many do not.
I left out graphs and sets, but I did end the sentence with an 'etc.' What is group theory? The word group implies a quantity of something.
At any rate, the concept of mathematics is delimited; it can't encompass everything that involves deduction from axioms. Mathematics is not synonymous with logical deduction for that matter. It's a fundamental mistake to view praxeologicy as mathematical simply because it involves deduction from an axiom. Praxeology is not by any stretch of the imagination a subset of mathematics.
Len Budney: Geoffrey Allan Plauche:I find none of that philosophically satisfactory. If that's satisfactory to mathematicians, so be it. As a theist, I think it's impossible to be virtuous without sincerely embracing morality, but it's further necessary that you pick the right morality--namely, God's. So not only is what I suggested unsatisfactory, but whatever morality you come up with will be equally unsatisfactory to me. Therefore, I submit that it's a good idea not to pack too much into liberty, other than liberty itself. Most everyone on this forum is on the same page, and I'm glad to be a part of it. In so doing I'm associating expansively, beyond my religious circle, and hence outside the ambit of those who fully agree with me philosophically. Your approach strikes me like someone coming along and saying, "OK, you're all kinda libertarians--but if you want to be the real deal, you also have to join my church." --Len
This is confusing something. I don't know what you think I'm packing into liberty. It's bizarre if you think I'm arguing that you don't have liberty if other people aren't really virtuous. Liberty in the strict libertarian sense is freedom from the threat or use of initiatory physical force. From the point of view of the moral recipient all that matters is that his rights are respected.
Nope, nothing to do with quantities. The integers do form a group, but that's only one example of a group. The theory has no reference to measuring or quantifying. Believe me, there's a lot more to mathematics than you imagine. Sadly, undergrads almost never get to any of the good stuff, because there's no time in their programs for much outside the algebra->calculus->differential-equations sequence. So they never get a glimpse outside the world of numbers and equations.
Mathematicians in general do not give a DARN about measuring things. We care about proving theorems, using logic, from axioms. Calculations of any sort are purely incidental.
Praxeology is not by any stretch of the imagination a subset of mathematics.
You find my characterization limiting (or hubristic) because you have no real conception what mathematics IS. Not an insult; as I said, few ever get to find out unless they do graduate work, or need it in their field. Plus it's taught so incompetently on every level that it's no wonder people think it's little more than a fuzzy nightmare of numbers whacking them with rulers.
spires: I'm curious of Geoffrey: What do you think your main contribution, or set of contributions to libertarian theory are? I'm wondering where you're coming from. Perhaps asked a different way, where do you find current libertarian theory problematic?
That would take a long time to get into. I'm coming from the burgeoning tradition of Aristotelian libertarianism, which is about 30-40 years old or so and includes Henry Veatch, Douglas Rasmussen and Douglas Den Uyl, Fred Miller, and Roderick Long.
To put it in a nutshell, I think the thin conception of libertarianism is inadequate for bringing about and maintaining a free and flourishing society. And I think that libertarians haven't been successful in grounding an obligation to respect the rights of others.
You might check out my website for my dissertation research proposal and the chapter on rights.
This is confusing something. I don't know what you think I'm packing into liberty. It's bizarre if you think I'm arguing that you don't have liberty if other people aren't really virtuous.
What I mean is: here we both are, two solid anarcho-capitalists, and you're prepared to argue with me whether I'm virtuous or not. I think I am, mostly; I doubt that anybody really is, often; and I'm certain it's none of your d*mn business to be sticking your nose up my virtue. If your definition of libertarianism compels you to do that, there's something wrong with it. (And going about it that way, you'll never see liberty anyway. We'll all be too busy scrutinizing each other--in rather the same way that Muslims, given their druthers, would rather be killing Muslims from other sects than infidel dogs.)
Len Budney: I left out graphs and sets, but I did end the sentence with an 'etc.' What is group theory? The word group implies a quantity of something. Nope, nothing to do with quantities. The integers do form a group, but that's only one example of a group. The theory has no reference to measuring or quantifying. Believe me, there's a lot more to mathematics than you imagine. Sadly, undergrads almost never get to any of the good stuff, because there's no time in their programs for much outside the algebra->calculus->differential-equations sequence. So they never get a glimpse outside the world of numbers and equations. Mathematicians in general do not give a DARN about measuring things. We care about proving theorems, using logic, from axioms. Calculations of any sort are purely incidental. Praxeology is not by any stretch of the imagination a subset of mathematics. You find my characterization limiting (or hubristic) because you have no real conception what mathematics IS. Not an insult; as I said, few ever get to find out unless they do graduate work, or need it in their field. Plus it's taught so incompetently on every level that it's no wonder people think it's little more than a fuzzy nightmare of numbers whacking them with rulers. --Len
I still see no reason to equate mathematics and praxeology, or to consider praxeology merely a subset of mathematics, or to equate mathematics with axiomatic-deduction.
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