One of the striking features of (propertarian) libertarianism, especially in the US, is its reliance on *a priori* arguments based on supposedly self-evident truths. Among[^1] the most extreme versions of this is the “praxeological” economic methodology espoused by Mises and his followers, and also endorsed, in a more qualified fashion, by Hayek.

In an Internet discussion the other day, I was surprised to see the deductive certainty claimed by Mises presented as being similar to the “certainty” that the interior angles of a triangle add to 180 degrees.[^2]

In one sense, I shouldn’t be surprised. The certainty of Euclidean geometry was, for centuries, the strongest argument for the rationalist that we could derive certain knowledge about the world.

Precisely for that reason, the discovery, in the early 19th century of non-Euclidean geometries that did not satisfy Euclid’s requirement that parallel lines should never meet, was a huge blow to rationalism, from which it has never really recovered.[^3] In non-Euclidean geometry, the interior angles of a triangle may add to more, or less, than 180 degrees.

Even worse for the rationalist program was the observation that the system of geometry (that is, “earth measurement”) most relevant to earth-dwellers is spherical geometry, in which straight lines are “great circles”, and in which the angles of a triangle add to more than 180 degrees. Considered in this light, Euclidean plane geometry is the mathematical model associated with the Flat Earth theory.

The discovery of non-Euclidean geometry led to the rise of formalism as the dominant philosophical approach in mathematics. The key point of formalism is that axioms like Euclid’s parallel postulate are neither true nor false. They are merely sentences in a formal language that can be combined and manipulated to form new sentences (theorems). A set of axioms may be useful if the theorems it yields turn out to provide a good model for some real world phenomenon, but this is not a mathematical question (though it helps keep mathematicians in work).

Mathematical formalism reached its high point with the Hilbert program in the early 20th Century. Despite the negative results of Godel, who showed that the more ambitious aims of the program could not be fulfilled, it was still dominant when I was taught mathematics in the 1970s.

I believe mathematical formalism has lost some ground since then, but if so, the effects have yet to filter through to economics. Mainstream (neoclassical and Keynesian) economics, since its mathematical reformulation by Samuelson and Arrow in the 1940s and 1950s, has been entirely formalist in its approach. Its axioms are not treated as self-evident. Rather the standard justification is that of modus tollens: if the theorems are descriptively false, we can trace our way back to work out what is wrong with the axioms.

The formalist program in economics hasn’t lived up to its expectations. It turns out to be much trickier than was hoped to work out what is important and what is not, and the formal clarity of deductive argument doesn’t necessarily translate into clear thinking. Still, this program is in far better shape than that of the Austrian School, and the methodological failure of a priori reasoning is a large part of the reason.

Having written this piece, I did a better Google search and found, as usual, that much of it is not new ~~and indeed goes back to Keynes. (Mises reply to Keynes seems entirely unconvincing)~~. But the point that Austrian economics is genuinely related to Flat Earth geography (as opposed to the use of this term as simple abuse) seems to be new.

**Update** The reference to Keynes above was the result of reading too quickly. The “Lord Keynes” in question isn’t John Maynard, but the contemporary blogger to whom I linked. And the weak reply is not from Mises but from one of his epigones, Hans-Herman Hoppe.

[^1]: As I read him, Nozick is equally extreme. An ethical theory that disregards consequences seems just like an economic theory that disregards data. Nozick seems to me to get more respect from other philosophers than Mises gets from economists. Reader

[^2]: Some presentations are more careful, referring to a triangle on a Euclidean plane. But that only shifts the problem one step back. Without the empirical proposition (false for the surface of the earth) that the subject of inquiry is a Euclidean plane, we don’t know (as Russell said) what we are talking about when we refer to Euclidean triangles. And, as Einstein showed, the situation isn’t improved by thinking of the earth as an object in three-dimensional Euclidean space.

[^3]: The most famous name here, immortalized by Tom Lehrer, is Nikolai Ivanovich Lobachevsky.

{ 108 comments }

Sandwichman 07.28.14 at 12:06 am

This from Henry Hazlitt,

The Failure of the “new Economics”: An Analysis of the Keynesian Fallaciesin response to Keynes’s remark in the General Theory that the classical theorists resemble Euclidean geometers in a non-Euclidean world.I’m sure Keynes had a better understanding of both geometry and economics than Hazlitt! BTW, I’m trying to find out if there is any confirmation for my suspicion that Keynes’s “non-Euclidean economics” is an unattributed allusion to J. M. Clark’s 1921 article, “Soundings on non-Euclidean economics.” Nothing definite yet.

Tabasco 07.28.14 at 12:10 am

The first sentence in your last paragraph is a mess.

John Quiggin 07.28.14 at 12:16 am

@1 Thanks!

@2 Thanks, again! Fixed now I hope

Sandwichman 07.28.14 at 12:19 am

SOUNDINGS IN NON-EUCLIDEAN ECONOMICS

The American Economic Review,Vol. 11, No. 1, Supplement, Papers and Proceedings of the Thirty-third Annual Meeting of the American Economic Association (Mar., 1921), pp. 132-143.…

Theophylact 07.28.14 at 12:22 am

Well, Keynes

didearn a first-class BA in Mathematics at Cambridge, so probably yes.ChrisH 07.28.14 at 12:24 am

The talk of mathematical formalism reminded me of an old joke in the vein of scientific disciplines ribbing each other:

There were two men taking a balloon ride, when fog came rolling in and the wind shifted. They soon had no idea where they were. The first man suggested they might be able to call out to the ground and someone could hear them.

They dropped their balloon as low as they felt safe too and then the first man called out into the mist “Where are we?” It echoed for a moment before a response came up from the ground. “You’re in a hot air balloon.”

The first man nodded and said “Well, at least we know there is a mathematician down there and we could try to reason where we are from that.”

The second man looked confused, “But how do you know he was a mathematician?”

The first man replied, “Because, he gave us an answer that was technically correct but totally useless.”

Neil Levy 07.28.14 at 12:37 am

Wherever did you get the idea that Nozick’s ethical theory ignores consequences? He is quite explicit: consequences matter, but rights act as side-constraints on how much they matter. When no rights are at stake, then consequences might matter more than anything else. It might be wrong (I’m damned sure it is, actually), but not because it ignores consequences.

Sandwichman 07.28.14 at 12:38 am

The six axioms that Clark presented and inverted were the following:

Matt 07.28.14 at 12:56 am

Mainstream (neoclassical and Keynesian) economics, since its mathematical reformulation by Samuelson and Arrow in the 1940s and 1950s, has been entirely formalist in its approach. Its axioms are not treated as self-evident. Rather the standard justification is that of modus tollens: if the theorems are descriptively false, we can trace our way back to work out what is wrong with the axioms.The formalist program in economics hasn’t lived up to its expectations. It turns out to be much trickier than was hoped to work out what is important and what is not, and the formal clarity of deductive argument doesn’t necessarily translate into clear thinking. Still, this program is in far better shape than that of the Austrian School, and the methodological failure of a priori reasoning is a large part of the reason.Do you have examples of axioms that were changed in the formalist mainstream after the 1950s, in response to descriptive failures of theorems founded on older axioms? As a layman I’m not sure if “hasn’t lived up to expectations” is a dryly humorous understatement or not.

Sandwichman 07.28.14 at 1:03 am

“hasn’t lived up to expectations” = “paper mechanisms whereby armchair theorists can grind out misleading results”

john c. halasz 07.28.14 at 1:15 am

Umm…IIRC Keynes thought of his work, in his more self-aggrandizing moments, as the equivalent of Einstein’s general relativity, whereby, the neoclassical economics, in the Marshallian version in which he was raised up, was a more specific case, “Newtonian”, of the broader framework. Deterministic vs. indeterminacy/uncertainty. Euclidian geometry vs. the curvature of space.

KZ 07.28.14 at 1:44 am

While the analog to geometry makes an argument against formalism, I think invoking it considering economics is missing the point. Say what you want about Euclidean geometry, when you try to measure the sum of the angles of a triangle, it is 180 degrees every time. Euclidean geometry only start to lose it power when you started working on something truly spherical, say a triangle connecting New York, London and Madrid. The point being the faith behind the formalism is based on irrefutable evidence at the time. I see nothing like that in economics. Hide behind formalism when the evidence is against you is not science.

Thornton Hall 07.28.14 at 1:44 am

There seems to be a distinction without a difference as far as economics is concerned. Frequently, economists will say “everything else being equal, which, of course, never happens.” Whenever this is said, the speaker is now committed to the exact same a priori endeavor as the Austrians (except Austrians don’t mock Austrians for their a priori system of economics).

John Quiggin 07.28.14 at 1:53 am

@KZ So, the angles sum to 180 except when they don’t. That’s pretty much irrefutable.

John Quiggin 07.28.14 at 1:56 am

@14 I don’t think this takedown works at all, unless you want to demolish physics and all the sciences derived from it as well eg

Newton’s First Law of Motion

Every object in a state of uniform motion tends to remain in that state of motion

unlessan external force is applied to it (emphasis added).John Quiggin 07.28.14 at 2:11 am

Matt @9 Most of my career as a theorist has been built on generalizations of the expected utility theory of choice under uncertainty (developed by von Neumann and Morgenstern, and later by Savage). The key idea in this literature has been to relax the independence axiom or its equivalent in Savage, the sure thing principle.

This is still a live issue – the EU model remains dominant in most applied work, but alternatives like cumulative prospect theory (prospect theory is Kahneman and Tversky, the ‘cumulative’ bit is me) are also widely used.

dahl 07.28.14 at 2:17 am

@John Quiggin (3)

Last para still a bit off. There are more opening parentheses than closing, and I think the concluding line of the first sentence is missing.

That said, it’s pretty clear you’re saying that the arguments are not new.

John Quiggin 07.28.14 at 2:22 am

Thanks again. I made the changes, I thought, but they don’t seem to have saved. I think it works now

Thornton Hall 07.28.14 at 2:22 am

@15 To put some meat on the bones of my point, economists predict that raising the minimum wage will result in fewer jobs, all else being equal. Then the empirical data proves this false and economists say “well, all else wasn’t equal.”

It simply is not the case that that is the role played by friction in Newton’s laws of motion. When I throw a ball down the street and it eventually comes to rest, Newton doesn’t say “Well, all else wasn’t equal.” He says, look at this equation (F=ma) which, when you look at the force of your arm and the force of friction and the force of gravity, predicts exactly the spot where the ball came to rest.

Thornton Hall 07.28.14 at 2:26 am

The point is that “the world is complicated” serves as an all purpose shield against the process in formalism that you describe where the world feeds back on the axioms. In fact, the process never happens in a way that changes the axioms. What happens, as a matter of practice, is that the economists claim that the world actually is the way their formal model predicts (there’s inflation if you know where to look) or there are ad hoc modifications to the model that aren’t, well, formal, that is, they are ad hoc.

Either way, a priori and real world never meet. And poor people die.

Thornton Hall 07.28.14 at 2:37 am

And what really sticks in my craw is the word “derived”. “unless you want to demolish physics and all the sciences derived from it as well e.g.”

I see this error all over the place. The fact that the equations in a theory are all consistent with each other does not mean that they are “derived from each other.”

There simply isn’t a process whereby science is deduced from other science. Observations generate equations and those equations lead to other equations and those new equations are exciting not because they are true, but because they can be tested!

Thornton Hall 07.28.14 at 2:44 am

@JQ I hope you see the parallel on the minimum wage theory versus reality and the Euclidian non-Euclidian geography question. The data tells us we live in a non-Euclidian world. It says the same thing about a theory that predicts job losses due to minimum wage increases. But economists don’t see that because human interaction is infinitely complicated. Therefore, by definition, there will always be an unaccounted for variable that (it can be argued by Neoclassical Euclidian Economists), if we could measure it, would demonstrate that we were right, the globe is governed by Euclidian economics.

John Quiggin 07.28.14 at 2:46 am

Have you been following the debate about minimum wages? Start here

http://www.nber.org/papers/w4509

Thornton Hall 07.28.14 at 2:52 am

Right, my understanding is that that is more or less where we’re at on the minimum wage. Good for them for going after the data.

Colin 07.28.14 at 3:17 am

My impression of mathematicians nowadays is that they mostly regard formalism, Platonism and so on as personal beliefs that don’t need to be discussed when doing mathematics. ZFC is a convenient ‘industry standard’ axiomatic foundation, but you’re not expected to truly believe in it or even think much about it. The general attitude seems to be that mainstream mathematics is ‘too big to fail’, so even if ZFC is found to be inconsistent, we will be able to simply replace it with a slightly weaker collection of axioms that retains all the ‘useful’ theorems of analysis, number theory, geometry and so on (many of which are already known to require much less than ZFC).

Sandwichman 07.28.14 at 3:30 am

Digging deeper into the Euclidean/non-Euclidean metaphor in economic thought, Pigou had this to say in

Economics of Welfare, published in 1920:Wesley Mitchell used the non-Euclidean metaphor even earlier, in a 1910 article, “The Rationality of Economic Activity.” Interestingly, Mitchell uses “non-Euclidean” to refer to rarified theoretical abstractions that have little to do with reality.

bad Jim 07.28.14 at 4:36 am

Two tangential irrelevancies:

Flat-earth thinking is still common in religious belief. People say God or Heaven is “up there” and gesture accordingly, even though they’re pointing at Vega in one season and Betelgeuse in another.

It’s been said that mathematics is like sex: it has a practical side, but that’s not the main reason people do it.

Sandwichman 07.28.14 at 4:46 am

Addendum to my comment @8 above:

In subsequent reworking of his essay (in

The Trend of Economics,edited by Rexford Tugwell 1924), Clark added two additional propositions to make the total eight .The additional propositions were: “A bargain between two persons concerns primarily those two persons, and only incidentally, under special conditions, becomes ‘affected with a public interest.'” (inserted between props 3 and 4) and “Private enterprise is necessary and efficient because people will work and sacrifice for their individual ends where they reap the fruits themselves and will not work as well for a collective end.” (inserted between props 4 and 5).

ZM 07.28.14 at 5:19 am

I hope that Keynes or anyone else’s work is not the equivalent of Einstein’s relativity work. I asked a professor if they could kindly quickly sum up for me what the referent of spacetime was since I couldn’t work it out from the writing, and they told me it would take at least 4 years to convey all the information since the referent was a whole bunch of interrelated empirical equations. So I still don’t know what the referent for spacetime is and have largely given up hope of ever knowing :(

Sandwichman 07.28.14 at 5:26 am

“I hope that Keynes or anyone else’s work is not the equivalent of Einstein’s relativity work.”

Relax — it’s a metaphor.

Jeremy 07.28.14 at 6:24 am

@7 Neil Levy: Doesn’t Nozick claim that, as long as people’s acquisitions and transactions are OK (as he defines OK), then whatever distribution results is OK no matter how lopsided it may turn out? Maybe that’s what the OP meant by Nozick not caring about consequences.

Zamfir 07.28.14 at 6:30 am

ZM, I have never heard about a concept called “referent of spacetime” in GR. In what context did you encounter that term?

John Quiggin 07.28.14 at 6:35 am

@7 What Jeremy said. Rights aren’t a side constraint for Nozick, they drive everything. So, whatever your attitude to consequences, there’s no scope for government action to improve them.

ZM 07.28.14 at 6:37 am

I think referent is just the word for the thing that a word refers to. So cat is the reverent of cat. I understand what space is and I understand what time is – but I cannot work out what Einstein is referring to when he writes spacetime…

Lee A. Arnold 07.28.14 at 6:41 am

Bit of a sidetrack, but Gödel wrote a very short and very interesting lecture on the current notions of the nature of math in 1961, “The modern development of the foundations of mathematics in the light of philosophy”, reprinted here:

https://www.marxists.org/reference/subject/philosophy/works/at/godel.htm

He had already concluded from his logic studies that there must be something else, an additional realm that needs to be let into science, a study of our own acts in the use of logical, mathematical and scientific concepts.

Some idea of what these acts of cogitation are — for example, what we are doing, when we are doing mathematics of any sort — is given in a list in Saunders Mac Lane’s remarkable survey book, Mathematics, Form and Function (Springer-Verlag, 1985): Collecting, counting, comparing, computing, rearranging, estimating, selecting, acting in succession, etc. It is not an endless list, so it might be possible to find some way to study it, and to formalize it, before logic, before maths.

Gödel thought that the beginnings of this new science were to be found in Husserl, whose phenomenology in turn begins in Kant, and Gödel’s lecture argues along the way that, although some of Kant’s formulations are wrong (e.g. in regard to Euclidean geometry), Kant’s underlying structure is still clearly valid.

There is indeed some interesting related stuff in Husserl’s book, Experience and Judgment (1939). Possibly the least jargon-laden and most practical…

It could be that Mises was onto the same sort of idea, although he had grabbed it by the wrong end. I personally find Mises tedious to read, and it could be because, as Gödel points out in his lecture, the idea that deductions can be made from these phenomenological concepts of actions seems terribly misplaced.

These acts are what we use to PERFORM deductions, which is a little different. Indeed even the verbal definitions of these acts are profoundly roundabout, and they are more easily understood as Wittgenstein said: ostensively, by demonstrating them and pointing to them. “This is how you count, this is how you make a collection,” and so on.

It may be recognized that this is the realm under discussion in Wittgenstein’s Remarks on the Foundations of Mathematics (1937-44), before it becomes part of his discussion in the wider application to “language games” in the Philosophical Investigations (1953). This phase of Wittgenstein has been dismissed in the philosophy of mathematics for decades, but I imagine that there is very bright future for it. If only we can start to get a hold of our new subject…

Collecting, counting, comparing, etc. etc., are used in the process of doing something else. We talk a lot about all the “something else’s”; they are the traditional subject matter of science — but very curiously so far, we have had very little discussion of what this set of actions is, on its own. It seems to be a fairly small set of things, but I cannot find whether anyone has attempted a definitive list, and, although the set appears to be small, I don’t know whether you could prove that it is finite.

One interesting thing is that these acts are applied to two things at a time, in the basic application. They are always capable of being pairwise or bipartite. Is this related to the fact that the human body is bilaterally symmetrical in form?

Another interesting thing is that there is another, subsequent set of distinctions, or categories, which are judgments or outcomes of the acts: Sames (usually called “identity”), difference, equals, unequals, opposites, negatives, before-and-after, cause-and-effect, subject-and-predicate, left-and-right, etc. These are also basically pairwise. Call it “pairwisdom”. This set of judgments also seems to be rather small, but I know of no attempt at a definitive list here either, although JS Mill was clearly on the case, with the concept of the “fundamentum relationis” in A System of Logic, Ratiocinative and Inductive (1843).

Both lists, the actions and the resulting distinctions, appear to be small in number, but the list of fields in which these can be applied is even fewer: space, time, and grammar. (And grammar makes use of space and time in symbolic format).

I believe that economics should be a normative science, describing what our overall goals should be: feed everybody, etc. This is prior to mathematics. Then we would back up a step to see how we can get to that, by individual intentions and by social institutions. “Choice” is only one of the phenomenological acts. But this overall program will be different than a positive and mathematical science.

The subject matter of economics is further complicated by the observation of the “economy of science” in Ernst Mach’s Science of Mechanics (1883). The doing of science, and even the construction of language, are efficient in some vague sense. this has soem relation to economics. Are the pairwise functions which compose the ways in which we think, susceptible to the same sorts of analysis as transactions in economics? Economic transactions have two sources of efficient gain: 1) specialization and trade, and 2) reduction of the trade costs by common understanding (i.e. the institution ruling the trade). Do these have analogies in the interior, pairwise acts of cogitation that produce mathematics?

Lord Keynes 07.28.14 at 7:22 am

A great post, but regarding this statement:

“Having written this piece, I did a better Google search and found, as usual, that much of it is not new andindeed goes back to Keynes”Slight misunderstanding here: the blog post “A Red Herring on Praxeology: A Reply to Lord Keynes” is a reply to my post you cite above.

“Lord Keynes” is a pen name I use for my blog:

http://socialdemocracy21stcentury.blogspot.com/

regards

Chris Bertram 07.28.14 at 7:48 am

Not quite true to say that Nozick disregards consequences entirely, since he entertains the possibility that rights may need to be overridden to avoid “catastrophic moral horror”. But respect, yes, because Nozick seemed to show that something like libertarian conclusions flowed from premises that many people were inclined to accept, and those people were disturbed by that and it was challenging to work out what had gone wrong.

The consequences/data analogy just seems wrong, in any case. Resistance to the facts is clearly a vice in a subject that purports to discover truths about the way the world contingently is. Philosophy is largely (or even entirely) about reasonable disagreement over non-empirical matters (to channel something that David Estlund was saying on Facebook recently). Even consequentialism doesn’t depend for its truth or falsity on the facts (consequences) being a particular way: if they were different it would recommend different actions, but that it recommends actions or policies as a function of consequences is a non-empirical matter.

George Berger 07.28.14 at 7:54 am

Let me add a bit to Lee A. Arnold’s comment. There are at least two notions of formalism. (1) As notions of pure logical syntax used to construct axiomatic theories of some subject. (2) As notions from proof theory used to evaluate existing axiomatic theories or to construct new systems of formal logic. Notion (1) was the standard approach to teaching logic, until ideas related to model theory and refutation trees became popular, around 1970, at least in the USA. I think you mean (1). As for (2), some of Husserl’s ideas have been used in the proof-theoretical intuitionism of Per Martin-Löf. I don’t know if he read ‘Experience and Judgement,’ (Erfahrung und Urteil), but some work of his combines Husserlian notions of evidence with a reasonably formalistic system of logical and mathematical rules of construction and deduction. Evidence is said to be

fundamental to these, as it is claimed to be the final source of conviction that his rules and

deductive principles are valid. His work all but replaced the looser intuitionism of

Brouwer and perhaps Bishop, with more tractable ideas. Gödelian and Husserlian intuition of mathematical items like numbers and some axioms becomes insight into basic applications of a rule. Per’s work is beautiful, as its basic principles can be seen as either logical or mathematical but are more fundamental than either.

reason 07.28.14 at 8:06 am

I always think that the problem is not a priori reasoning per se, but ignoring the importance in completeness in a priori reasoning. It is like reasoning in two dimensions and then assuming the result holds in three or four dimensions.

Scott Martens 07.28.14 at 9:02 am

I have some disagreements with your history of formalism, which doesn’t negate the main point at all. The basically Platonic conception of mathematics was not progressively undermined by non-Euclidean geometry, much of which can be understood as geometry on curved surfaces. It, and its associated notions about rationalism, were overthrown in an unexpected, violent, fairly quick revolution instigated by Frege’s Begriffsschrift, which suddenly threw the whole idea of timeless and eternal mathematical truths into chaos and replaced them with timeless and eternal

logicaltruths. The effect was rather to create an even stronger kind of rationalism, one that was mixed up in complex notations and obscure language that rendered it inaccessible to most people, but even more able to force counter-intuitive and often genuinely false conclusions on people in the name of “reason.”If I were telling the story, I would start with Gauss’ line about mathematics as the ‘queen of the sciences’ and ‘number theory’ (= arithmetic in Gauss’ era) as the queen of mathematics. (

Die Mathematik ist die Königin der Wissenschaften und die Zahlentheorie ist die Königin der Mathematikin OV) Think of early 18th century and early 19th century math as a divine right monarchy that appears eternal and stable just as modernism begins to expose the cracks in its foundation when faced with the increasing use of calculus and algebra in geometry – the development of modern analysis – and the problems created by calculus. Each mathematician exposing the cracks in the edifice swears up and down they are really trying to fix it, to eliminate the little nagging problems and contradictions, right up through men like Gauss. I would put this in parallel to the notion of economics as a theory of morality and justice as a thread running from Aquinas, Ibn Khaldun and the School of Salamanca right through Smith, Locke, Say, Ricardo, and Mill.Then Frege comes along and burns the entire damn thing down by giving the whole of arithmetic a basis in logic. The divinity of numbers, and the Platonic worldview, simply cannot recover from the revolution. You might put this in parallel with the second industrial revolution, the rise of the German Empire, and the entire rearrangement of economics around the needs of the state, and at the same time Frege’s contemporary Karl Marx, who seems to have been the first person to think the economy was about actually “production and reproduction of real life” (Engels’ words, so the analogy isn’t perfect) instead of moral sentiments. Bosanquet’s line about the “Empire of Logic” fits here.

The Empire reaches its peak in the

Hilbertprogrammand smashes up on the rocks of the Gödel incompleteness theorems, just as Marxism and imperialism were wrecked by the two World Wars. It is replaced in some quarters with a postmodern cynicism about the whole project, in others with a kind of quasi-socialist bureaucratic centralism led by the Bourbaki group in France (“math for the working mathematician” was their line), and to some degree by the advance of category theories and universal algebras in other places as a kind of mathematics version of the “managerial capitalism” of the post-war era in the west.This falls into a sort of Brezhnevite-stagflationary decadence by the 70s, when the computer appears on the scene and forces a kind of quasi-empiricist glasnost into mathematics. Today, as a result, math is dominated by a practical interest in getting rich quick, with the best minds and greatest talents going into quantitative finance, crypto, and Internet start-ups, and only a few

altermondialistslooking at building a kind of neofoundationalism out of algorithm theory – guys like Martin-Löf and Peter Grünwald representing its more respectable, intellectually coherent side, and a kinda of silly side represented by… someone I might need a job from someday and who knows how to Google.All of this makes hyperformalist economics in the Arrow-Debreu tradition look faceplamingly retro, like science fiction from the 20s or 30s, and the Mises-wannabes look like they’re the economics equivalent of neo-Confederates, or those people who think the 16th amendment was never legally ratified so they shouldn’t have to pay their taxes: People who never got over the 19th century, much less the 20th.

The general point about the sterility of

a priorireasoning is sound. Nearly everything of substance in math and science since the French revolution has come from abandoning it. You’re missing its appeal to the minds of college sophmores, who are just educated enough to see the beauty of simple formal logics, and not nearly educated enough to see their massive gaping flaws, and how very important that is to Austrian economics as a proselytizing faith. But I strongly encourage telling the history of mathematics and logic in strongly humanist terms: as a succession of crises and failures and recoveries that were doomed to fail from the outset – in short, math as politics. Doing that takes away its magic, and deprived of its magic power, it becomes a laughable basis for an economic theory.John Quiggin 07.28.14 at 9:27 am

@Chris I’m not asserting that consequentialism is factually true. I am, as you initially say, making an argument by analogy: consequences are to ethics as empirical experience is to epistemology. Resistance to consideration of the consequences is just as much a vice in ethics and political philosophy as resistance to facts in science (broadly defined to include pre-scientific domains of inquiry like economics).

In both case you can make a priori arguments (appealing, as Scott says, to college sophomores) that start from seemingly self-evident axioms and lead to bad (factually wrong or consequentially abhorrent) conclusions. As I said, I don’t see any difference between Nozick and Mises; can you spell out the distinction you want to make?

John Quiggin 07.28.14 at 9:59 am

@Scott I agree with a lot of this. But I don’t see the response to the problems created by calculus as being like a series of epicycles, which is the way I read you. Rather I see the replacement of intuitive concepts of infinitesimal by the rigorous foundations of Weierstrass and Riemann leading to growing confidence, which complemented the abandonment of Platonism in geometry.

And, as I see it, the success of that program is still largely intact. It was the C20 attempt (Frege and Hilbert among others) to dig even deeper in the hope of finding an utterly unshakable foundation that ended in disaster.

I think your characterization of Arrow-Debreu and Mises is spot on, made even sharper by the fact that many of the Mises crew are real neo-Confederates.

Chris Bertram 07.28.14 at 10:00 am

But consequences aren’t to ethics as empirical experience is to epistemology, not even close, even for a consequentialist ethical theory. Which consequences? How do you value them? What if the list of consequences includes heterogeneous elements: how do you reduce them to a common standard? All the work is going into answering those questions, and it isn’t anything like empirical inquiry. Bentham might have thought he had something like you appear to be referring to, but he didn’t. Economists might think that some version of “utility” might do the trick, but all such views beg the important questions and when operationalized involve looking for keys under the lamp-post.

As for Nozick, well, I think the reference to “sophomores” is just a bit of rhetoric there. The principles Nozick deployed (many of them, anyway) were the common currency of the left (including the Marxian left) and of many feminists (“our bodies ourselves”) and he pulled off the disturbing trick of showing (or seeming to) that those familiar principles which many of his opponents accepted led to libertarian conclusions. Some social democrats may have already thought those principles obviously wrong (Brian Barry) but a lot of other people wanted to both hang onto their intuitions and to reject the conclusions, hence a lot of hard work was needed from those people to show where Nozick went wrong. Hence Jerry Cohen’s well-known essay “Marxism and Contemporary Political Philosophy, or: Why Nozick Exercises some Marxists more than he does any Egalitarian Liberals”.

Billikin 07.28.14 at 10:42 am

@ZM

Leaving General Relativity aside for the moment, suppose that we live in a three dimensional Euclidean space. What is the referent for “three dimensional Euclidean space”?

Sam Clark 07.28.14 at 10:58 am

Just wanted to say thanks to Sandwichman for the reference to Clark’s fascinating ‘Soundings on Non-Euclidean Economics’.

ZM 07.28.14 at 11:35 am

Billikin,

I think that is a compound referent – the referent of three being the abstract quantity three + the referent of dimensional being dimension plus al making it an adjective qualifying the object to follow + the referent of Euclidean being the long dead fellow Euclid plus ean making it an adjective (likely about his geometry work rather than his bodily person) qualifying the object just ahead + the referent of space being space which is the object of the fragment and the object of Euclid’s work in geometry.

I cannot unpack spacetime in this sort off way and have been told it cannot be simply summed up to me but that I would have to spend four years to study the matter before understanding what the word is meant to refer to :(

Scott Martens 07.28.14 at 11:51 am

@John: I don’t mean to be read quite so cynically. My intent is less to suggest math is trapped in some kind of Toynbeeesque (am I allowed 3 e’s in English?) cycle of history as to suggest that, much like politics, progress may happen, but not with any clear narrative of progress and often it’s only progressive on the long run, in retrospect, sometimes, maybe. Math is made by people faced with historically rooted problems using historically rooted tools, just like politics. The analogy with political development over the last couple of centuries is not a theory of the history of math so much as an analogy that shows how the same story can be told in much more human terms. And, of course, to propose that true knowledge comes from some kind of rigorous axiomatic approach to reason, logic, mathematics, and truth in 2014 without addressing Frege, Gödel, and all the reasons why that program failed, is very much like proposing in 2014 to return to the gold standard and laissez-faire without ever addressing all the excellent reasons why every single country abandoned the gold standard and laissez-faire.

@Chris: I wasn’t thinking of Nozick when I made that remark, I was thinking of some teenage Reaganites I knew as a sophmore. Actually, I think Nozick on self-ownership is a little advanced for dorm rooms. His argument there is actually difficult enough to merit special consideration because “self-ownership” sounds simple and obvious and is neither. Self-ownership is only simple when it amounts to little more than a moral rejection of abject slavery, and I agree entirely in the value of reading Nozick on it as taking leftist sloganeering of the 70s to its logical ends.

But then, I think Nozick more or less admited he got self-ownership from Kant. And love him or hate him, Kant is not that easy. I still think Nozick is basically wrong, but at least there’s something worth not laughing at there.

Zamfir 07.28.14 at 12:55 pm

ZM, 4 years of study sounds way too much. The need for a combined “spacetime” concept is already clear in special relativity, and SR is really not that hard. At least, not “4 years of study” hard. It’s typically a single course for new physics students in their first year.

ZM 07.28.14 at 1:03 pm

The Professor said the final important equations that spacetime is incorporated of were not taught until the end of the course or honors from what I remember. I don’t know enough about the matter to comment on how long it would take. This is the same with how economics sums are taught in Australia also – the professors teach basic rudimentary versions of the sums at the start of the course but apparently these are all based on advanced calculus that is not taught until right at the end of the course and then only for one semester.

Billikin 07.28.14 at 1:12 pm

ZM: “I cannot unpack spacetime in this sort off way and have been told it cannot be simply summed up to me but that I would have to spend four years to study the matter before understanding what the word is meant to refer to :(”

Well, whoever said that to you thought that you meant something different. As a matter of fact, you can unpack spacetime in exactly the same way that you did Euclidean three space. Before the theory of general relativity, it was thought that there were three dimensions of space and one dimension of time, which could be graphed as though it were another dimension of space. You see such graphs all the time, where time is one dimension with years or minutes equally spaced on the time axis, for instance. Einstein showed that that view of things did not hold up. Time was not just like another spatial dimension. However, it was soon discovered that you could view time as just another dimension, but not a space-like dimension. It has different properties. Distance in space-time with three spatial dimensions is not like distance with four spatial dimensions. Also, the idea of a straight line in spacetime is not the same as that of a straight line in Euclidean space.

So if you want to understand spacetime, it can take years. But if you only want to refer to spacetime, then you can do it as you refer to Euclidean space, with time as one of the dimensions. Whoever told you what they did was thinking about how long it would take you to understand spacetime, which is difficult, not about refering to spacetime, which is easy. :)

J Thomas 07.28.14 at 1:29 pm

#34 ZM

I understand what space is and I understand what time is – but I cannot work out what Einstein is referring to when he writes spacetime…This is off-topic so I’ll try to keep it short. First, the idea is that time is another dimension, like the space dimensions but different. And there was the empirical observation that the time it took for light to travel some specific distance in vacuum appeared to be the same regardless of the velocity of the source and destination, provided they were stationary wrt each other. But if light traveled at some specific velocity c then when you added the velocity of the source you’d expect it to travel at v+c, and it appeared not to.

So time was not a normal dimension. For historical reasons it made sense to think of two kinds of time. Coordinate time t was the time you calculate should have passed for somebody given your newtonian assumptions. Proper time T was the time actually measured by a clock that experienced the time. Coordinate time was the real one, and proper time could be biased away from the reality of coordinate time by velocity.

It was esthetically pleasing to think that velocity was like a rotation between space and time. Acceleration would rotate, and velocity would be the amount of rotation. But with euclidean geometry, when dimensions are independent it turns out that total distance = X^2 + Y^2. Coordinate time is special, and they found the minkowki total distance = X^2 + Y^2 + Z^2 – T^2. To make that into a rotation it had to be a hyperbolic rotation which is weird and hard to think about. But the minkowski distance is the same independent of velocity. Each relativistic transform results in some conserved quantity.

It turns out that when you make T be the independent dimension, many of the complications that are hard to understand go away. t is total distance, a euclidean combination of T, X, Y, Z. Total velocity is a euclidean combination of proper time/t and distance/total distance. Momentum is a euclidean combination of rest energy and the momentum that comes from the velocity you arbitrarily assign the source.

It’s all pretty simple and straightforward but it doesn’t work quite like you’d expect euclidean geometry to work. Light travels at right angles to the direction anything else travels and so when you compare the time that light arrives someplace versus the time some piece of mass arrives, you need the pythagorean theorem.

The result appears to mostly fit measured observations, though there are always enough fudge factors that something could be a little bit off.

ZM 07.28.14 at 2:25 pm

Billikin,

Sorry, I didn’t explain the context. I was not at all interested in concepts of space – I can only remember geometry from high school and if I have misrepresented Euclid I am sorry – I didn’t know his work had a truth claim that space itself was 3 dimensional – I thought he just found a helpful way of representing bodies in space on paper. understanding Euclid’s conception of space was not what I was trying to learn about.

I was interested in changing concepts of time, historically and culturally, as related to social groups’ environmental sustainability and unsustainability.

So I was interested in different conceptions of time – and why Einstein put space and time together and referred to this as spacetime – and what spacetime as a concept meant. I was also interested in how Newton understood there to be real absolute unmeasurable time and representational measurable relative time – but Einstein said there was no real absolute time at all, not even relative time by itself, but only relative spacetime. Also I wanted to know how if spacetime was made up of empirical equations it was able to do away with unmeasurable absolute time which shouldn’t really be affected by empirical equations since it is unmeasurable.

To understand this the professor said I would need years of physics study, so I still don’t know what spacetime refers to as a 20th century concept of (some sort of version of) time.

J Thomas,

Thank you for trying to explain, but I think I would need to improve my understanding before I can understand your explanation. Maybe this is why it would take me 4 years but Zamfir could learn it quickly.

Bruce Wilder 07.28.14 at 3:05 pm

One Damn thing after another. Time is like history that way.

Billikin 07.28.14 at 3:11 pm

Thanks, ZM. Now I have a better idea of what you want.

You talk about Euclidean space as a way of “representing bodies in space on paper”. That’s what I thought you meant, and said that spacetime was a way of representing positions in space and time. At least, that’s what I was trying to get at.

But you want to understand different concepts of space and time and spacetime. I don’t think that you need a lot of physics for that. Philosophy and anthropology have a lot to say about those concepts. Before Einsteinian relativity there was Galilean relativity, which Newton understood quite well, OC. IIRC, Newton believed in absolute space, anyway, even though you had a choice where to put the origin of any coordinate system, and a choice of the directions of your dimensions. But there were other natural philosophers who thought that space did not exist, only distance. Leibniz? I am not sure.

As for the idea that time is unmeasurable, I don’t know what you mean by that. Galileo certainly measured time. Without doing so he could not have made all of his discoveries.

I don’t know about Einstein’s original idea of spacetime in general relativity, because it was quickly superceded by Minkowski spacetime, which J Thomas explained briefly.

Anyway, it sounds like you have been frustrated by the idea of taking four years of physics to understand spacetime. You may find philosophy and anthropology more relevant to your interests and more satisfying.

William Timberman 07.28.14 at 3:21 pm

1. Bravo Scott Martins @ 47. I could explain my applause, but like most art criticism, which is what my explanation would amount to, it would suffer by comparison with the original work. Just

bravowill do, I think.2. Doesn’t all of this thread, excellent though it has been, tend toward the ineffable? By which I mean, aren’t consequences always, inevitably, richer than the putative mechanisms which produce them? Or, put another way…if we’re humanists, and devoted for some purposes to a priori reasoning, and for others to empirical data collection and analysis, and always, inevitably given to extrapolating from the specific to the general, in the perhaps forlorn hope of broadening our horizons, don’t we at some point wind up as lost as Dante in the

selva oscuraof concepts like superstring theory, or the infinite regression of linguistic deconstruction?3. To make a long story short: so many variables, so little time — for each of us

pagliaccias individuals, it goes without saying, but even our cumulative wisdom is suspect, I think. I mean, libraries do help, but when it takes half a lifetime or more wandering in the stacks before we can say anything original, maybe they don’t help as much as we’d hoped when we first started compiling them.William Timberman 07.28.14 at 3:32 pm

Scott Martens. Apologies for the typo.

William Timberman 07.28.14 at 3:38 pm

And, oh yes, Scott Martens @ 40, 47. God forbid I should applaud the clarification before the thesis itself. (This comment-numbering thing is a bitch at the best of times, but doesn’t excuse my not paying attention to what I’m doing.)

Sebastian H 07.28.14 at 3:41 pm

“Doesn’t all of this thread, excellent though it has been, tend toward the ineffable? By which I mean, aren’t consequences always, inevitably, richer than the putative mechanisms which produce them?”

Yes. C.S. Lewis used the analogy of looking AT the telescope and looking THROUGH. The telescope. Looking at the telescope is a good thing, because it allows us to make the telescope better. But looking through the telescope is ultimately the point of building telescopes. A lot of social science gets so bogged down in looking at the telescope that it actively inhibits looking through it.

bianca steele 07.28.14 at 4:38 pm

Francis Bacon wrote, IIRC, that all the

socialscience we need is contained within the first pages of Genesis. But I suppose we may assume that Lewis was not being ironic.Jim Harrison 07.28.14 at 4:58 pm

Seems to me the thinking that characterizes economics is neither inductive nor deductive but procrustean. People endlessly argue about whether economics is a science or a prescience, but didn’t the subject actually grow out of a very different set of activities—business practices like accounting and what they call cameralistics in Europe, i.e. techniques that rationalize important aspects of human affairs by force or agreement? Doesn’t economics belong to Herrschaft rather than Wissenschaft?

Sasha Clarkson 07.28.14 at 5:32 pm

Because non-Euclidean space and Euclidean space seem the same when distances are “small”, length in both may be measured by means of the three-dimensional

Euclidean Metric(definition of what distance is):ds² =dx² + dy² + dz², wheredsis a small unit of space.This is basically using Pythagoras’ theorem with infinitesimally small measuring rods. One way of looking at space-time is to use a similar, four-dimensional metric:

ds² =dw² + dx² + dy² + dz²wheredw² = -c²dt²,cis the speed of light in a vacuum, anddtis an infinitesimal element of time. Thusdwis treated exactly like another spacial dimension in the measurement of space-time, but it is defined asdw = i.c.dt, whereiis the square root of -1.If this is mumbo-jumbo to you, don’t worry: that is inevitable unless you’ve met some of the concepts before. But if I make sense to even one person, I won’t have posted in vain! :D

TM 07.28.14 at 6:06 pm

ZM, have you tried Feynman’s essay on relativity? (http://www.amazon.com/Six-Not-So-Easy-Pieces-Einstein%C2%92s-Relativity/dp/0465025269) I think it conveys well the meaning of spacetime. It turns out that transformations in 3-space and 1-time, which in Newtonian physics are treated as independent of each other, cannot really be independent – transformations affect both space and time (which leads to empirically observed phenomena such as time dilation). Spacetime is the mathematical structure that provides the (theoretically and empirically) correct transformation groups.

TM 07.28.14 at 6:13 pm

re the OP, I’m intrigued by the description of economics a a formal system based on axioms. Is this more than just a metaphor? If economics is really axiomatic, shouldn’t there have been a lot of effort gone into exploring the consequences of individual axioms and formulating alternative axiomatic systems (in analogy to non-Euclidian geometry)? I don’t ever hear economic debates framed in those terms – the reference in 8 is obviously new to me but has this approach had any actual influence?

J Thomas 07.28.14 at 7:10 pm

#52

Thank you for trying to explain, but I think I would need to improve my understanding before I can understand your explanation. Maybe this is why it would take me 4 years but Zamfir could learn it quickly.I want to try one more time.

People generally feel like they understand something when they have a picture that fits it. But a physicist understand relativity when he can do the homework problems and get the right answer. This is a very different thing.

So as a simple example, it’s easy to think of us as living on the surface of a giant sphere, the earth. But if you change the math around just a little bit, you could have us living on the *inside* surface of a giant sphere. All of the outside universe shrinks inside of that sphere, distances shrink more and more, until at the center there is a point missing which is perhaps infinitely far away. The sun is little ball of energy that revolves around the inside of the sphere, and since light does not travel in straight lines, when the sun gets too far away from our part of the sphere surface its light is lost to us.

All the math can work out to do that, and get the same results we get assuming we are on the outside of the sphere. We don’t do it that way because it’s more intuitive for us to do it the way we do, but the two are equivalent. They are basicly the same theory and the same picture, but they don’t seem the same.

Similarly, there are various ways to look at special relativity. Some of them make more sense than others. Physicists settled on one that doesn’t make much sense and is hard to wrap your mind around. I speculate that they did it because they enjoyed mystification and it made them look special to understand things that appeared to make no sense.

General relativity has much harder homework problems because it solves harder problems. But the fundamental ideas are not much more complicated than SR. I will look at SR.

They wanted to think of time as another dimension. To do that, it helps if you can measure all the dimensions in the same units. And you can. You can measure time as the time it takes light to go a unit distance. Then time is a distance. Or you can measure distance as the distance that light travels in a unit time. Choose one.

Once you do that, you can use the pythagorean theorem. Total distance squared is the sum of the distances in different right-angle dimensions, squared. But right away there was a problem because they had minkowski distance instead of euclidean distance.

T^2 = x^2 + y^2 + z^2 – t^2

They said that no matter how the x,y,z,t changed, T would be constant. Here’s what it means:

Say you make a flash of light and 3 seconds later you make another flash of light. Somebody 1000 feet away who knows precisely the time and the distance can subtract the time^2 for the second flash from the distance^2 and they will get 9 = 3^2. No matter how long the distance and the time, the time difference between the two flashes will be the same! That is the minkowski distance.

Well, but we can do it in a more intuitive way.

t^2 = x^2 + y^2 + z^2 + T^2

The total distance the light has traveled from our origin, is the square root of the space distance squared plus the proper time distance squared. Now it’s all euclidean. It’s the same formula, just rearranged.

Similarly with momentum.

4-momentum = [energy, momentum-x, momentum-y, momentum-z]

and -mass^2 = -energy^2 + momentum-x^2 + momentum-y^2 + momentum-y^2

And when you adjust the momentum and energy because your own velocity is different, the mass^2 term is constant! What a surprise! And you can graph it as a hyperbolic rotation.

But switch the terms around.

energy^2 = mass^2 + momentum-x^2 + momentum-y^2 + momentum-y^2

Now it’s all pythagorean. There’s nothing mysterious going on at all. The rest mass (rest energy) is of course constant, and when you change your estimate of velocity you change the momentum and the energy, and there’s no rotation at all much less a hyperbolic one.

If you do the homework problems you’ll get the same result either way. One way it is very hard to grock, and the other way it’s easy. But for physics it doesn’t matter whether you have a clear picture how it works provided you can get the right answers. Right answers are easy for SR and hard for GR. But if you want to “understand” it, you could easily take four years to do that the minkowski way.

Robert 07.28.14 at 8:18 pm

Read Debreu’s Theory of Value, available somewhere on-line, to see economics developed on axioms, in the style of Bourbaki.

John Quiggin 07.28.14 at 8:46 pm

@Chris I’ve always found myself in agreement Brian Barry on anything of his that I’ve read, so it’s unsurprising I share his reaction to Nozick.

I’ve never thought of reading Nozick as a

reductioon Marxist/feminist assumptions. If I get time, I’ll look at the references you suggest.Mdc 07.28.14 at 9:05 pm

Lobachevski’s book is filled with beautiful, elegant, a priori proofs. Just sayin’ .

peter 07.28.14 at 10:12 pm

Bad Jim #27:

Flat-earth thinking is not confined to religious believers. Most of us rational, scientifically-trained westerners still refer to sunrise and sunset, despite knowing for half a millennium that it is the earth doing the relative setting and rising respectively, not the sun.

Thornton Hall 07.28.14 at 10:28 pm

Axiom: there is a price at which markets clear.

David Margolies 07.28.14 at 10:37 pm

Chris @43 “Hence Jerry Cohen’s well-known essay `Marxism and Contemporary Political Philosophy, or: Why Nozick Exercises some Marxists more than he does any Egalitarian Liberals`.” That sounds interesting, I thought, so I tried to find an online copy but they all seem to be behind a pay wall, then I looked at books by Cohen in Amazon, but (1) most did not show the contents, so I have no idea if the essay was included, and (2) cost US$100 or so (above my touch). (I do note Cohen wrote a book called ‘If you are an egalitarian, why are you rich?’. Now I know.)

Is there a way to read the essay without access to a University library or spending a lot of money?

Collin Street 07.28.14 at 10:50 pm

> Thus dw is treated exactly like another spacial dimension in the measurement of space-time, but it is defined as dw = i.c.dt, where i is the square root of -1.

… timelike dimensions are imaginary? Clever.

Neil Levy 07.29.14 at 2:31 am

John Quiggin: ” Rights aren’t a side constraint for Nozick”.

Nozick: “In contrast to incorporating rights into the end state to be achieved, one might place them as side constraints upon the actions to be done: don’t violate constraints C”.

“The side-constraint view forbids you to violate these moral constraints in the pursuit of your goals”

And so on. This is central to Nozick’s view, not something I just made up.

This is just the wrong way to attack Nozick, unless you want to take issue with deontology (which, incidentally, is fine with me). Someone who believes in rights thinks that rights trump other considerations. That’s what deontology is. Your beef is probably with the rights that Nozick defines, not the existence of rights. At least, that’s the right way to understand the dispute between liberal deontologists like Rawls and someone like Nozick. Your options are (a) say that Nozick has misidentified what rights we have or (b) reject the notion of rights (perhaps just economic rights).

John Quiggin 07.29.14 at 6:54 am

@Neil You’re missing my point. I reject Nozick’s use of the term “side constraints”

If the constraints bind in such a way as to preclude any collective action to improve the end state, they aren’t

sideconstraints. A decision can’t satisfy the constraints, unless it has the unanimous consent of everyone whose rights are affected. And given that everything is encompassed by property rights, there is no scope for anything else. So, it doesn’t matter what the desired end state might be, everything is determined by the choices of those with the relevant property rights.John Quiggin 07.29.14 at 9:43 am

Chris @43 The Cohen essay clarifies a lot for me. I long ago rejected the Marxist idea of exploitation for the reasons Cohen sets out (no relation to any concept of distributive justice except on the fragile assumption that the workers and the poor are the same people, no proper relation to autonomy), but I’d never linked that to Nozick and self-ownership (I focused more on the “just starting point + just processes formulation”, which I found, and still find, nonsensical as a justification for a radical policy change). I can now see why Marxists took Nozick seriously, though it doesn’t make me much more inclined to do so.

David @ 70 I could only get this in the volume Self-Ownership, Freedom, and Equality which I borrowed from my Uni library. The paywall seems solid otherwise.

Neil Levy 07.29.14 at 10:30 am

I think you’re using side-constraints in a different way to Nozick. For him, it’s equivalent to what Dworkin calls ‘trumps’. Having a right is a trump in the game.

It’s just clearly false that for Nozick everything is encompassed by property rights. It is to the point – and I think what you really want to say – that too much is encompassed by property rights. Btw, there is a persistent rumour in philosophy that Nozick didn’t believe what he wrote in ASU. Rather, he was frustrated by the low standard of argument by libertarians, and wanted to see whether it was possible to defend a consistent libertarianism. He certainly never bothered defending ASU from attack after its publication.

Neil Levy 07.29.14 at 11:24 am

Here’s an example from Nozick where he has consequences doing the heavy lifting. Animals, he says, don’t have a right not to be tortured. But we shouldn’t torture them, because the consequences – making ourselves inured to cruelty – would be bad.

John Quiggin 07.29.14 at 11:42 am

@75 Can you give an example of collective action to promote good consequences that isn’t precluded by some property right, assuming the owner wishes to exercise it.

@76 So, does Nozick say that animal cruelty laws are OK (as applied to animals that are the property of the person concerned). That is, does his concern with bad consequences trump the rights of the animal owner? Or is this just a personal recommendation, with no actual force.

More generally, I don’t think the trump analogy is quite right here. In general, trumps can only be played on specific limited occasions (for example, in bridge only if you are on lead, or a trump has been led, or you can’t follow suit on a non-trump lead). My claim is that for Nozick, rights are trumps that can be played in every trick, so there is no value in holding any card that isn’t a trump.

Sandwichman 07.29.14 at 3:24 pm

The Crisis of Democratic Theory: Scientific Naturalism and the Problem of Value

Edward A. Purcell, Jr.

Publication Year: 2014

Chapter 4: Non-Euclideanism: Logic & Metaphor

Sandwichman 07.29.14 at 3:35 pm

“publication year” obviously refers to the electronic edition.

Billikin 07.29.14 at 10:23 pm

Neil Levy: “Here’s an example from Nozick where he has consequences doing the heavy lifting. Animals, he says, don’t have a right not to be tortured. But we shouldn’t torture them, because the consequences – making ourselves inured to cruelty – would be bad.”

So I guess it’s all right for a sadistic sociopath to torture animals, because he is already inured to cruelty?

Sasha Clarkson 07.29.14 at 11:06 pm

Mdc @67

“Lobachevski’s book is filled with beautiful, elegant, a priori proofs. Just sayin’ .”You are quite correct! :)

BUT Lobachevsky’s aim was not to deduce that his new geometry was true in the real world: it was to show that axioms such that the sum of the angles of a triangle was

lessthan two right angles led to a consistent geometry with no contradictions. ie, true or not, it was at leastpossible. He then devoted a considerable effort to determine, via astronomical observations, whether the real universe was measurably non Euclidean. In his 1840 book he concluded“In triangles whose sides are attainable for our measurement, the sum of the three angles is not indeed different from two right angles by the hundredth part of a second”So, like a good scientist, he was concerned with the evidence as well as the theory.So, is economics

WissenschaftorHerrschaft? The answer depends upon who does it. In hisGeneral Theory, Keynes was basically describing partial differential equations and their possible solutions verbally – not unlike what Newton was doing in much ofPrincipia. It was a flexible approach to analysis of the problem, rather than an over precise but inaccurate “complete” solution: which is why the approach, with iterated refinements, is still fruitful today.Another scientific approach to economics was in Benoit Mandelbrot’s (and Richard Hudson’s) book,

The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward. Firstly, it is a really fascinating introduction to the theory of fractal geometry. Secondly, by comparing theory and real world data, the authors send an Exocet into the models and practices taught by business schools and used by investment firms. The authors are particularly scathing about those who pretend to mathematical precision, but plug in estimated, (or imagined), data into their models.Mandelbrot and Hudson do not create a new edifice out of the ashes of the old, but nobody reading the book and viewing the evidence presented can doubt that this is desirable. In his introduction, Hudson is suitably modest:

“This volume will not make you richer … but it may prevent you from getting poorer.”ZM 07.30.14 at 4:20 am

J Thomas, and TM

Thank you for help with understanding the concept of spacetime.

Billikin,

“spacetime was a way of representing positions in space and time”

I think of it as likely being representational (like I do with Euclid’s geometry) – but as I understand it the physicists’ shared cosmology holds it to have a truth value about the real nature of time – which is that there is no time only spacetime (which I still can’t work out the meaning of).

“Newton believed in absolute space. . . other natural philosophers who thought that space did not exist, only distance” “As for the idea that time is unmeasurable, I don’t know what you mean by that.”

Newton distinguished between absolute real time which is unmeasurable (I presume because it is transient) and human relative time which is measured through space-based devices such as sun-dials and clocks and so forth. With Einstein absolute time is no longer in the physicists’ cosmology and relative time becomes spacetime.

J Thomas,

“They wanted to think of time as another dimension. To do that, it helps if you can measure all the dimensions in the same units. And you can. You can measure time as the time it takes light to go a unit distance. Then time is a distance”

I did ask the Professor this – if I could just say space-time referred not to space or time but just to movement of bodies and distance measured between them – he said I wouldn’t be giving an accurate representation of the concept of spacetime if I did that.

Thank you for your sums, I will copy them down to try to read one day when I have more time.

TM,

Thanks for the reference, I hadn’t heard of that one.

Neil Levy

“Here’s an example from Nozick where he has consequences doing the heavy lifting. Animals, he says, don’t have a right not to be tortured.”

Well I don’t think you can claim there is not a moral absolute against torturing poor animals. Anyhow, it is certainly not the case in all legal systems. In Scandinavia animals, for example the beaver, had rights. Under the laws of Haco, foster-son of Athelstane, the beavers right to a home and rights as an inhabitant were important – and if anyone killed a beaver they would be fined. Bears and wolves were named as outlaws, but even bears had a right to a trial if they did anyone wrong, and it was thought bears had a fair enough understanding of Danish for this to work. Civil tribunals would also make decrees telling rats and mice and insects what they were meant to do in the land.

Palgrave 1832 p. cxlii

ZM 07.30.14 at 4:31 am

Oops – thank you Billikin, too – sorry that was a typo

engels 07.30.14 at 4:32 am

I think you’re using side-constraints in a different way to Nozick. For him, it’s equivalent to what Dworkin calls ‘trumps’.Is this right? I thought Nozick’s (‘side-constraints’) was stronger- no right can be disregarded (except to prevent moral armageddon)- whereas the ‘trumps’ metaphor allows one right (a low card) to be over-ridden be a another one higher up the food chain (a picture card). But I’m very rusty on this…

engels 07.30.14 at 5:13 am

there is a persistent rumour in philosophy that Nozick didn’t believe what he wrote in ASUPerhaps bolstered by this?

‘ Anarchy, State and Rent Control’

http://www.j-bradford-delong.net/movable_type/2003_archives/001281.html

Billikin 07.30.14 at 5:26 am

@ZM

J Thomas can correct me, but by the time that we get to the concept of Minkowski spacetime, time is another dimension in addition to the dimensions of space, except that it is in units of the square root of -1 (imaginary units). Perhaps that was the difference that the professor was referring to. Distance in spacetime is quite different from spatial distance. Spacetime is not like space with an additional space-like dimension called time, even though you can draw graphs like that for some purposes. I don’t think that you can get much of an idea from the physics prof saying, “That’s not it,” and “That’s not it, either.” I am pretty sure that what the prof thought that you said and what J Thomas said are not the same thing.

ZM 07.30.14 at 5:52 am

Billikin,

Do you think it is in imaginary units because from present being (= zero), you have past (positive because it has happened) and future (negative because it is yet to happen) ? Or did it just turn into imaginary units from necessity in fitting all the equations together nicely?

I would like to know what spacetime means for physicists’ cosmology (which even if not most prevalent is probably most dominant from the high modern era onwards and also impacted the wider cultural milieu) – I read about non-modern-western cosmologies and they often had time which was divided into solar years and lunar months (and people might argue as to what lunar month it was and only when certain seasonal events happened which happened in particular lunar months would the argument be resolved) and important seasonal events and so forth. Even the cosmology of ancient Greece had different sorts of times – Chronos, Kairos, the Houris etc.

With Newton the dominant epistemology in the West disallowed personified concepts of time like Father Time from being taken seriously any longer … and so you had two… absolute (abstract), and relative (measured)

By Einstein’s time the dominate epistemology seems to have moved to disallowing the absolute … and so you had one… relative… and so you had none . . . spacetime replaced time

But it seems to me that this epistemological shift is related to the idea of spacetime replacing space and time – because space and time can only be understood in and of themselves only as abstract conceptual fields in which being exists/takes place – with the dominance of relativity you lose both and gain spacetime (which seems to me to be some sort of measurement based idea – but I was told I was not on the right track… so my ideas can’t really proceed any further until I find the right track, which I hope might not take such a long time as four years, because the related cosmology and epistemology and ontology issues are more interesting to me than the actual concept of spacetime – but I don’t want to misrepresent the concept even if I never learn all the sums for it).

engels 07.30.14 at 5:53 am

I thought John’s originals complaint was that Nozick doesn’t consider the consequences of his theory (eg, as Brian Barry has pointed out, letting the needy starve to death, etc), not that consequences play no role within it (they do, as Neil says). Actually, iirc Nozick did sort of do the first- in the chapter where he claims libertarianism is a ‘framework for utopia’ – but it was rather pathetic iimho (albeit marvelously well-written).

engels 07.30.14 at 6:26 am

Last comment and I’ll quit trolling this thread:

Why Nozick Exercises some Marxists…Highly unscientific, but a search of the Monthly Review (US Marxist journal) website for Nozick gets one (1) hit, which is an obituary of Cohen. International Socialism (ournal of UK Marxist party) gets 1. Searching the Marxists Internet Archive gets 4 hits (Rawls gets 20). New Left Review is 47 : 124 (but some of those are articles by Cohen about Nozick). So it seems like there must have been quite a lot of Marxists who, like Barry, never lost a lot of sleep over Nozick…

John Quiggin 07.30.14 at 6:31 am

I Googled Nozick on animal cruelty and found this

So, I think I am right in saying that his

a prioriposition rules out both animal cruelty laws and any action that violates rights to prevent human suffering, however severe it may be. However, he is willing to contemplate limited violations of rights to prevent “excruciating” human suffering, and minimal violations to prevent similar animal suffering. From his example, he might be willing, for example, to threaten a modest fine to deter someone from torturing thousand of animals for entertainment.Still, my criticism of Nozick’s use of the term “side constraints” is unaffected. He doesn’t say that the constraints leave room for consideration of consequences, as they would if they were side constraints on optimization. He effectively admits that the constraints fully determine the allowable scope of social rules, which means they aren’t side constraints. However, he is willing to consider ad hoc adjustments to his theory when the consequences are too appalling to contemplate. ACAICT, he offers no basis for doing so, and his argument against taxation (any taking of income, however small, is slavery) is just as applicable to the concessions he makes here.

engels 07.30.14 at 6:58 am

He doesn’t say that the constraints leave room for consideration of consequences, as they would if they were side constraints on optimization.Why do you think the term ‘side constraint’ must imply this?

J Thomas 07.30.14 at 8:19 am

I would like to know what spacetime means for physicists’ cosmologyRelativity was probably the first point at which physicists decided that it didn’t have to make sense. If you can get the right answer then that’s all that’s really important. And yet they did try hard to make sense of it.

The old way, you had completely separate space and time. You could measure space. You chose some interval of unit length, and it was arbitrary what your unit was. Yards or meters, it didn’t really matter, choose one. And then you had three “axes”, and you could arbitrarily choose any three provided they were all perpendicular to each other. Suppose you chose one set and somebody else chose another. You could transform measurements from one to the other easily when you knew how, it would amount to a rotation about some axis. You could rotate in two dimensions by considering one axis to be the “real” one and the other to be “imaginary” with square root of minus one. Easy mathematical rules to do the rotation. When you rotate the length stays the same, but how that length is distributed between the two axes changes.

The easy and good way to rotate in three dimensions is with quaternions. You get a special fourth dimension which is not like the first three. It becomes the “real” one and the three space dimensions turn into three “imaginary” ones you can label i j k. Again the total length does not change, but the distribution among the three space dimensions does change. Usually you would set the fourth dimension to zero at the start and finish.

So it’s arbitrary what you choose for your three axes, you get equivalent results whatever you choose, and you can translate back and forth among whatever choices seem useful.

In the old way, time was independent of all that. Time proceeded forward inexorably, at the same rate for everybody everywhere, completely independent of space.

They believed in something that was later called “galilean relativity”. It’s arbitrary what unit distance you choose. It’s arbitrary which axes you choose to measure by. It’s arbitrary where you set the origin. And it’s arbitrary how fast you have the origin move, provided the speed and direction of movement are constant. If you have two ways to measure, and with one of them the origin is moving relative to the other, all your physics experiments will get the same results with both. If there is a difference it will be because of some outside force which affects them different because of the movement.

What changed all that was electromagnetism. Here’s the key history:

1. Michael Faraday was self-educated and he didn’t care much about math. He thought in pictures. He studied electricity and magnetism and he drew what he saw.

2. Various people tried to put Faraday’s insights into mathematical form. They kind of succeeded. Maxwell combined Faraday’s work with other things to get a consistent system which appeared to describe everything about electricity and magnetism traveling through empty space. He predicted that they travel at a constant speed, which turned out to be lightspeed. By his theory it made sense that light was the result of a vibrating electric charge, and it traveled at lightspeed.

3. Maxwell originally assumed that electricity and magnetism had their effects instantaneously everywhere. The math was simpler that way, his results are still widely taught that way, and usually the results are tolerably accurate. But he deduced that there was a delay. When you try to account for the delay the math gets messy and peculiar, and it’s easier to ignore the problems. And Maxwell’s equations are not consistent with galilean relativity. Faraday did all his work relative to his lab bench, he didn’t care about galilean relativity. Maxwell used Faraday’s results. Electromagnetism as defined by Maxwell works fine for one coordinate system traveling at one velocity. If you try to transform the results into a different system with a different velocity they turn weird. Maxwell assumed that light has a constant speed, and that speed is the same constant for everybody no matter how fast they are moving. If you measure the speed of a light beam, and somebody else measures the speed of the same light beam and they are traveling at half lightspeed, they will measure the same velocity that you do.

4. The Michaelson-Morley experiment appeared to show that Maxwell’s equations were true. They measured the same light when the earth was traveling in opposite directions, and they got the same lightspeed. It looked like arithmetic was broken.

5. The new approach said that time was not completely independent of space. It was another dimension, kind of like the other dimensions but different. When you measure things with an origin that has a velocity relative to another coordinate system, you are doing a kind of rotation between the space dimensions and the time dimension. Time and space will be distorted, just enough so that both ways the same light can be measured and get the same lightspeed. If you perform the simple lorentz transform between two coordinate systems, it all works. You will get the right answer on homework problems. And as usual, no one coordinate system is the *right* one, they are all equivalent and we can convert from one to another and get the right answers. To make that work we have to give up some ideas. Time is not something that just happens to everybody at the same rate. Various things can happen that look like paradoxes. But they aren’t paradoxes, they just happen. They only conflict with our previous assumptions.

6. If space-time was a system where you could do rotations and keep the total distance constant, it would fit quaternion math. Time would be the fourth quaternion dimension. But it doesn’t work that way. Total distance is not conserved with the rotations people chose to use. They looked for a way to make the lorentz transform to be a rotation, and they found it fit Minkowski space which is weird and hard to understand. The pictures are hard to follow. Some of the math is not easy, it turns out that when you change velocity (particularly when you change direction) you get peculiar results that take somewhat-complicated math. Velocity is not a simple obvious concept with special relativity, it kind of goes against the grain of the system. It isn’t easy to follow the details. It isn’t intuitive. It isn’t that hard to do the homework, but getting a clear picture of it is very hard because it does not map well to how our brains work.

7. Nearly a hundred years after relativity was announced, people found an easier way to think about it. The new way is sometimes called “euclidean relativity” but there’s a lot of weird stuff that gets the same name so that isn’t an adequate search phrase. The new way, you start with a different way to measure velocity. When time was completely independent of space, it made sense to measure velocity as distance divided by time. But when time is just another dimension, it makes more sense for velocity to be space-distance divided by total distance. With a few other changes, you get a system which gives you the same answers to the homework problems but which is much easier to follow. Probably within 80 to 100 years it will be mostly taught this way.

John Quiggin 07.30.14 at 8:26 am

“Why do you think the term ‘side constraint’ must imply this?”

I’m a decision theorist, so I do optimization problems for a living. That’s the way the term is used in the linguistic community in which originated.

But it’s also, I think the ordinary English interpretation. If I said that my aim was to get from A to B as fast possible, subject to the “side constraints” that I should

(i) use a given road from A to B; and

(ii) travel at exactly 60 km/h throughout the journey

I would, I think, be rightly regarded as silly. Given that the constraints exactly determine my course of action, I would do the same thing if my objective were to travel as slowly as possible, or to use as little fuel as possible, or to maximize human wellbeing.

A genuine example of a side constraint on the minimum time problem would be that I should obey all relevant traffic laws.

engels 07.30.14 at 8:43 am

Thanks, I didn’t know that ‘side constraint’ was a term in decision theory. I’ve only ever heard it used by Nozick (who as others have said, just means by it a constraint, a non-overidable limitation on what agents can do). Come to think of it, I’ve no idea why he uses that term- perhaps others do? (This is, as I’m sure you realise, at best an argument against his choice of terminology rather than his view of justice.)

John Quiggin 07.30.14 at 9:22 am

Yes, but slippery use of terminology is a sign of dishonest argument. Using terms like “side constraint” or “trump” suggests that his theory of justice is concerned with consequences, but that rights take precedence. In fact, his theory gives such an expansive role to property rights that there is no scope at all for concern about consequences, except insofar as Nozick (now in the role of philosopher-king) decides to grant ad hoc exemptions.

engels 07.30.14 at 9:32 am

Sorry, looking back I think I misunderstood your original point. I thought you were objecting to the term ‘side constraints’ being used for hard rather than a soft boundaries on a choice-set whereas I understand now you are objecting to it being used for a condition-set that fully determines the choice.

But in this case I don’t really understand your objection. Nozick doesn’t think that rights fully determine what an agent must do in a given situation [normally] and he expects them to leave room for consideration of consequences by the agent. It seems to me Nozick’s usage of the term is parallel to your ‘obey all relevant traffic laws’ rather than the example you gave above it.

John Quiggin 07.30.14 at 9:45 am

The problem now is that he is shifting from political philosophy to individual ethics without acknowledging it. His position is roughly, “I, Nozick, think you shouldn’t torture kittens (or humans), but I will defend to the death your right to do so, as long as you own the kittens (or humans)*”. But once the second part of the argument is granted, Nozick’s advice on individual ethics is entirely orthogonal.

That would be fine if he wrote two separate books. As it is, he wants to defend kitten/human-torture as a right, while pretending that his argument has a way of stopping this happening.

* Except for the magic let-out clause where I, Nozick, get to change the rules if I really don’t like the consequences.

engels 07.30.14 at 9:46 am

Using terms like “side constraint” or “trump” suggests that his theory of justice is concerned with consequencesBut they’re not ‘side constraints’ on justice, they’re side constraints on action. Agents are free to consider consequences in deciding what to do (rights constrain the choices they have).

John Quiggin 07.30.14 at 10:10 am

As I said, this is a confusion between political philosophy where justice is an issue, and individual ethics where it isn’t (at least, not for Nozick). Agents can consider what they like, but (according to Nozick) this isn’t any concern of anybody else, as long as they are within their rights. Nozick’s advice to others on how they should think about consequences is precisely as relevant as would be his suggestions on how they should decorate their homes.

engels 07.30.14 at 10:44 am

That would be fine if he wrote two separate books. As it is, he wants to defend kitten/human-torture as a right, while pretending that his argument has a way of stopping this happening.You’re right, Nozick doesn’t think, for example, that it’s good or okay for poor people to be left to starve in the streets, but he thinks that if society left them to do so, they wouldn’t have suffered any injustice. Demanding assistance from others who were unwilling to provide it would be treating those others as slaves. As I recall he does say libertarianish things in ASU (philanthrophy, etc) about why this shouldn’t happen, so he didn’t need to write two books, but whether it’s attractive or convincing is another matter (I didn’t think it was).

I’m not sure the problem you’ve raised is unique to Nozick though. A liberal might agree for example, that it’s a bad thing for someone to be without companionship, say, but forcing anyone to provide it to her as a matter of right would not be permissible. Instead, liberals would probably focus on creating conditions which would minimise the chances of this situation occurring (they’d argue).

John Quiggin 07.30.14 at 11:24 am

“Instead, liberals would probably focus on creating conditions which would minimise the chances of this situation occurring (they’d argue).”

Sure. But Nozick doesn’t have this option. The rights are what they are, and can’t be adjusted to improve the chances of good outcomes.

The liberal example is a genuine case of side constraints. Liberals would like to promote companionship and can do so by funding programs that (they hope) will encourage this, but they are constrained to respect freedom of association.

Billikin 07.30.14 at 11:27 am

J Thomas @92

Great explanation. Thanks very much.

Billikin 07.30.14 at 12:16 pm

@ZM

I think that any modern cosmologist has to take spacetime into account.

Let me try to add one thing. Suppose that we have only one dimension of space and one of time, with spacetime distance equal to the square root of the square of space-distance minus the square of time-distance. Time is measured in imaginary units. From the origin, where both space and time equal zero, let us draw a line at 45 degrees, so that for each point, (s,t), on the line, s = t. (s is the space coordinate, t is the time coordinate.) The distance between each point on the line and the origin is s^2 – t^2 = 0. Let us also draw a line at -45 degrees, so that for each point, (s,t), on the line, s = -t. The distance between each point on this line and the origin is also zero. Now we have two lines such that the distance between two points on either line is 0. In terms of spacetime, they are all the same point. Even though on the graph they are two lines.

Now, the space and time distances are related by the speed of light. Suppose that we have a photon traveling through space from the origin. Its path in terms of our graph is just the two lines we have drawn. I. e., the photon does not move in spacetime. We might speak of these two lines as a “light V”. When we have more dimensions of space, we do speak of a light cone.

What does this have to do with cosmology? Well, let us make our origin the Big Bang. The light cone of the Big Bang is at zero spacetime distance from the Big Bang. In terms of spacetime, it is the location of the Big Bang. Since to us, light appears to move in space, a single point in spacetime is to us many points in space and time. So for us the Big Bang did not just happen. It is happening.

Billikin 07.30.14 at 12:47 pm

Correction. Too early in the morning, I guess. The “light V” constructed with negative time is not anything like the light cone. Only the line with t >= 0 is concerned with the light cone when we add more space dimensions. Not that we can’t think of light going backward in time, but that’s another matter.

J Thomas 07.30.14 at 5:50 pm

Suppose that we have only one dimension of space and one of time, with spacetime distance equal to the square root of the square of space-distance minus the square of time-distance. Time is measured in imaginary units. From the origin, where both space and time equal zero, let us draw a line at 45 degrees, so that for each point, (s,t), on the line, s = t. (s is the space coordinate, t is the time coordinate.) The distance between each point on the line and the origin is s^2 – t^2 = 0. Let us also draw a line at -45 degrees, so that for each point, (s,t), on the line, s = -t. The distance between each point on this line and the origin is also zero. Now we have two lines such that the distance between two points on either line is 0. In terms of spacetime, they are all the same point. Even though on the graph they are two lines.I don’t want to go on too long about this stuff, and yet I feel such a temptation.

What you say is not wrong. It gets the right answers. But imagine this other way to look at it….

Euclidean distance is not meaningless in this situation. square root of time^2 + space-distance^2 really does mean something.

But in relativity, minkowski distance is preserved.

So if you are 3 light-years from the origin and you make a great big red laser pulse toward the origin, and then 3 seconds later you make a great big green laser pulse the same direction, when the light arrives at the origin the green one will be 3 seconds later than the red one. The difference is preserved. If you start them both at the same time they will arrive at the same time. Minkowski distance relative to the origin is preserved.

To me that’s what it means. I don’t find it useful to say that minkowski distance is the only distance and that things which have the same minkowski distance are at exactly the same time, although it isn’t wrong to think of it that way.

If you DO say that things that have minkowski distance = 0 are at the same time, then you can construct your light cone that way. Flatten out your cone so that your time dimension has everything on that cone on the T axis. You will need two different graphs then, because the upper lightcone doesn’t belong on the same graph as the lower lightcone. That will get you something interesting.

engels 07.31.14 at 2:06 am

The liberal example is a genuine case of side constraints. Liberals would like to promote [X] and can do so by funding programs… but they are constrained to respect freedom of association.It sounds like your stipulating that a genuine ‘side constraint’ must be a constraint on policy or law perhaps, rather than on agents’ freedom of action (which is how Nozick means it) So the US constitution is constraint on law perhaps, but the law itself is not a constraint on what citizens may do. I don’t think that’s persuasive, even as terminological quibble.

Billikin 07.31.14 at 2:09 am

Thanks, J Thomas. :)

I agree that Euclidean distance is still meaningful and that there is more than one way to look at all this. But if I were trying to do cosmology in terms of Minkowski spacetime, this is how I would start to think about it. By coincidence, I think that Aquinas would grok the idea of eternal creation.

Lee A. Arnold 07.31.14 at 5:49 pm

@ George Berger #38 — I think you are right. Perhaps there are also two notions of related words: “judgment” seems to have its oldest meaning from outside statements, outside logic, but then over there it becomes a type of statement among many other types of statements, and afterward it (judgment) is more like the status (position?) of “true” or “false” in a proposition. Just reading Crisis of the European Sciences right now, and it is interesting how much he was able to follow the change in the meaning of prescientific ideas. The discussion of how Galileo must have felt and grasped his own method, as opposed to how we see Galileo’s method now, is precise and practical, though written in 1936. Needs an addendum describing the even odder idealization of the lifeworld by the continuing mathematization of method, even to simulations of choosing/choice, in the era of the electronic computational revolution.

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