The Difference between a priori and a posteriori Probability

Imagine a pure thought experiment: an abstract, logical world where everything is true by definition.

In this world, we have a fair dice. The pure mathematical a priori probability of rolling a 6 on this dice is 1/6. That probability has necessary truth – but limited only to the abstract fair game of dice one is imagining. The analytic a priori propositions that express the imaginary world and probability in question do have necessary truth – but limited to this abstract analytic a priori system. This is the epistemological nature of a priori probabilities.

But what happens when we step into the real world? As soon as we move to the real world and take any given real world dice, we cannot have apodictic certainty that the dice is not loaded and that the probability 1/6 really applies with necessary truth.

Why? Because of (1) the epistemological problems with how we know a posteriori knowledge and (2) Hume’s problem of induction. No matter how much evidence you have that the dice is fair, there is still a tiny possibility you are mistaken. This still holds even if – for good measure – the empirical relative frequency approach to show the probabilities of the outcomes when throwing the dice is used and this shows the dice is fair.

In short, the belief that the probability that any given dice will roll a 6 is 1/6 has become an a posteriori probability and contingent, not necessarily true.

Most people just take the abstract analytic a priori model first sketched and impose it on the real world, forgetting that this is an epistemological mistake. The difference between

(1) abstract a priori truth and

(2) contingent, empirical a posteriori truth is real.

It applies even to probability.

More on this issue here.

Walter Block’s An Austrian Critique of Mainstream Economics: A Critique on Epistemology

This is a talk by Walter Block on Austrian economics and its disagreements with neoclassical economics, given at the Mises Institute in Auburn, Alabama, the US, on 21 July, 2015.



I want to focus on epistemological issues here.

Let us review the epistemological problems here one by one:

(1) the Austrians badly misunderstand the philosophy and epistemology of the logical positivists.

For Austrians like Block the expression “logical positivism” is simply an ignorant term of abuse for all empiricists whom they regard as their opponents. However, there are (to my knowledge) virtually no logical positivists today, and strict logical positivist philosophy is not what is used by empiricist modern opponents of Austrian praxeology. In fact, logical positivism had had its day and had been largely abandoned by the 1950s. Modern moderate empiricism is not logical positivism.

The central element of logical positivist philosophy was the verifiability criterion for meaningfulness: the view that if a statement could (1) not be categorised as a true analytic a priori statement and (2) was not a synthetic a posteriori statement that could be verified, then it was a meaningless metaphysical proposition. This idea of course has very serious problems and proved the Achilles’ heal of logical positivism, and one of the many reasons for its rejection in mainstream analytic philosophy. Even the leading British logical positivist A. J. Ayer admitted that the core of logical positivism was wrong and it was badly flawed as a complete, coherent philosophy.

But moderate empiricists in mainstream analytic philosophy today are not logical positivists and do not accept the verifiability criterion, facts which Austrians seem ignorant of. These embarrassing philosophical errors are also committed by the Austrian Hans-Hermann Hoppe.

(2) If (1) isn’t bad enough, Block conflates logical positivism with Popper’s falsificationist principle. Popper thought that all the empirical propositions of science must pass the test of not being falsified: as long as a current scientific theory has not been falsified, then a rational person should accept it, but it must still be subject to testing in the future so that continued acceptance of a theory must depend on it continuing to pass the falsifiability test.

But that Popperian epistemological principle of falsificationism is not logical positivism, which was instead concerned with the verifiability of empirical propositions as a test of their meaningfulness.

Worse still, Block seems (if I am not mistaken) to imply that modern empiricists and the older logical positivists never accepted the necessary truth of analytic or pure mathematical statements, yet again the same mistake made by Hans-Hermann Hoppe. For the real logical positivist perspective on epistemology, see here.

(3) Block fails to mention or make explicit that the epistemological basis of Mises’ praxeology is Kantian synthetic a priori knowledge: the idea that there are statements both empirical (synthetic or non-analytic) and necessarily true of the real world. Kantian synthetic a priori knowledge, however, cannot be accepted as real nor defended anymore, and all alleged synthetic a priori statements can be re-interpreted as either analytic statements or (2) empirical statements (= synthetic a posteriori). As Block notes, even mainstream neoclassicals reject Mises’ praxeology because even they cannot accept such a flawed and unconvincing epistemological basis to economic science.

Yet, as Block notes, the Austrian school itself is divided over the very epistemological foundations of economics: there are Austrians who follow Hayek in rejecting praxeology and apriorism and who embrace a moderate empiricist method. Thus the Austrian school cannot even agree itself on whether praxeology is right or wrong.

(4) in Block’s argument about the exchange of a pen for a tie, he has not proved anything with necessary truth, for the simple reason that the person taking the tie might actually be mentally ill and have no opinion about the pen or the value of the tie at all, or alternatively he might be lying and hate the pen and like his tie more but be merely pretending to like it. The assumption that the person must by necessity value the pen more than the tie is sloppy logic and plainly untrue.

(5) Block’s assertion that there is a necessary tendency for profits to fall to zero in Mises’ evenly rotating economy would be necessarily true, but only as an analytic a priori statement asserted of a purely imaginary world or abstract model. The point is: it would not be an empirical statement, and so its necessary truth is a property of its analyticity. The only way one could maintain the necessary truth of something empirical (or synthetic) is to defend Kantian synthetic a priori knowledge. But, as we have seen above, the Austrian epistemology of Mises based on Kantian synthetic a priori knowledge cannot be seriously sustained or defended and this is why Austrian attempts to assert necessary truths of the real world fail time and again.

(6) Block also appears to be arguing that there is a necessary tendency for profit rates to be equalised in capitalism. This is untrue, and requires assuming certain assumptions about the real world that are not true, such as an unrealistic degree of competition across markets, no significant market power, no or minimal barriers to new entry, no strong patent rights giving certain companies a great advantage unavailable to competitors, no aggressive use of capacity utilisation as a barrier to entry, and no significant, persistent differences in profit mark-ups in different sectors and industries.

To what extent there is a tendency for profits to be equalised in real world capitalism is nothing but an empirical question.

(7) So too regarding the idea that minimal wage laws always cause unemployment when this is asserted as a necessary truth, it remains nothing but an analytic a priori statement asserted of a purely imaginary world or abstract model. The question whether any particular minimal wage law tends to cause unemployment in the real world is an empirical question.

Further Reading
“Why Should we reject the Existence of Synthetic a priori Knowledge?,” May 23, 2014.

“Hoppe’s Caricature of Empiricism,” September 10, 2013.

“Hoppe on Euclidean Geometry,” September 11, 2013.

“Hoppe on Euclidean Geometry, Part 2,” September 14, 2013.

“Hayek on Mises’ Apriorism,” May 23, 2011.

“Mises versus Ayer on Analytic Propositions and a priori Reasoning,” March 16, 2014.

“Kirzner on Hayek on Prices,” May 22, 2013.

“Does the Market Tend to Drive Profits to Zero?,” January 11, 2014.

“Sraffian Long-Run Equilibrium Prices of Production and Post Keynesianism,” April 11, 2015.

“Epistemology in Modern Analytic Philosophy: A Review,” September 17, 2013.

The Two Epistemological Ways to Interpret the Labour Theory of Value

The labour theory of value can be expressed as the following proposition:

“The labour theory of value (LTV) is an economic theory of value that states that the economic value of a good or service is determined by the total amount of socially necessary labour required to produce it.”
https://en.wikipedia.org/wiki/Labour_economics#Labour_theory_of_value

There are two ways in which, epistemologically speaking, we could interpret this proposition, as follows:

(1) as a synthetic a posteriori proposition (= an empirical proposition), or

(2) as an analytic a priori proposition.

If we interpret it as (1) an empirical proposition, then the LTV is not necessarily true, but contingent and known as true only a posteriori by experience, empirical evidence, and inductive argument. As a matter of historical fact, Marx took the LTV from Ricardo, who in turn took it from Adam Smith, and these men seem to have taken it as an empirical statement.

But now any Marxist who defends the LTV as an empirical proposition faces the demand to prove by experience, empirical evidence, and inductive argument that such a type of value really exists. They have to show us how abstract socially necessary labour time (SNLT) can be actually and meaningfully defined as a real measure of heterogeneous labour. They have to show how to calculate the abstract socially necessary labour time (SNLT) unit values of commodities. They need to show how these SNLT values map onto, or correspond to, the “natural” or “true” exchange values or prices of commodities, and identify real world prices that are direct examples of such SNLT values.

Alternatively, if we interpret the LTV as (2) an analytic a priori proposition, then the LTV is necessarily true and known a priori (not by any empirical evidence), but strictly speaking as a proposition it is a mere definition or tautologous statement. It is an analytic statement like:

(1) all bachelors are unmarried.

Even if there were actually no bachelors in the world, this proposition would still be necessarily true, but it is a mere analytic truth, that is, a mere definition or tautologous statement.

Experience teaches us of course that there are things in the world that are men who are not married, and so can be classified as unmarried men or bachelors.

But we make a deep mistake if we do not scrutinise analytic statements carefully to see if they are coherent, consistent, meaningful and useful, and – above all – whether they actually refer to things that have real existence and empirical relevance. The analytic proposition “all bachelors are unmarried” fulfils these criteria. It is a coherent and useful analytic proposition that can be used to classify objects in the real world into a class.

But we could for example propose the following analytic statements:

(1) all unicorns have horns.

(2) All dragons are able to fly and breathe fire.

It is obvious that the real world does not contain unicorns or dragons (at least we have no rational reason to think so). But these are still valid and true analytic propositions because there are worlds of human fiction where these things are imagined to exist, e.g., the dragons in the Lord of the Rings novels and films. Now an imaginary world is analogous to a highly artificial model that does not explain or relate to anything in the real world.

The propositions above about dragons and unicorns are only useful and relevant as analytic statements referring to a purely imaginary or hypothetical world in our minds – say, the world of human fiction or fantasy writing.

If the Marxists wish to interpret the LTV as analytic a priori proposition, then they could defend it as a merely empirically-empty and tautologous definitional statement. But they would still face the tremendous hurdle of proving that their analytic definitions are something more than analytic statements referring to a purely imaginary or hypothetical world in our minds, on a par with “All dragons are able to fly and breathe fire.”

That is to say, they still face the same severe empirical challenges that they would face if they choose to interpret the LTV empirically.

If Marxists cannot do this, and they retreat to a defence of the LTV as an analytic truth, it seems to me the only sensible way to treat the LTV is as a purely imaginary or hypothetical, useless proposition that adds nothing to economic knowledge. It has no explanatory power in the analysis of a real world economy. As a postulated phenomenon, it cannot be found in the real world and has no discernible causal power as a factor in a real world economy, unlike real higher-level emergent properties like the general state of expectations or aggregate demand.

And, finally, what would even be the point of asserting the LTV as some analytic concept? It would be nothing but a pointless and worthless idea, with no explanatory or causal power, tacked on to real economic science, which is at least a body of empirical truths and defensible, empirically-tested theories.

The LTV is, quite simply, on a par with the Austrian and neoclassical concept of the “natural rate of interest” or Milton Friedman’s “natural rate of unemployment”: we are dealing with concepts only conceivable in wholly higher-level abstract models that are so unrealistic and so remote from, and so irrelevant to, the real world that they are nothing but fictions.

Are all Facts Theory-Laden?

If we define “fact” as a synthetic a posteriori proposition, then it would appear that nearly all facts are to some extent “theory-laden,”* but that does not vindicate apriorism or Kant’s synthetic a priori knowledge, nor does it discredit the moderate form of empiricism that is rightly at the heart of modern methodology and epistemology in the natural and social sciences.

When we interpret some data or fact in the natural and social sciences ordinarily we will clearly pre-suppose a number of theories when we make interpretations of the facts.

But the standard theories we presuppose in either the natural sciences and social sciences have already been justified empirically, by experience, inductive argument and inference to the best explanation (which is just another non-deductive, or inductive form of reasoning) by long debates and arguments in philosophy or in the natural and social sciences too.

At the most basic level, there are all sorts of theories we do have about the world in which we exist and we make when we do natural and social sciences (including economics), such as the following:

(1) the real existence of other human minds;

(2) the real existence of an external world of matter and energy that is the causal origin of our sensory data (= an indirect realist ontology);

(3) that the past had real existence (and is not some figment of our imagination);

(4) the existence of a set of physical and chemical laws that have been discovered by the natural sciences that account for the order and nature of the universe;

(5) the view that our earth is about 4.54 billion years old;

(6) the view that all livings things on our earth are the product of a Darwinian process of evolution by natural selection (and, if one wants to be technical, also by (i) sexual selection and (ii) artificial selection by humans);

(7) the human mind is the product of the physical activity of the brain, and so on.

And of course we can keep listing such theories too as we move from natural science to the social sciences. (And note I use the word “theory” in the sense of a hypothesis that has been confirmed or justified by evidence.)

Theories (1) to (3) belong to the philosophical sub-disciplines we call ontology and epistemology. The theory that other human minds really exist and that an external world exists can only be justified empirically by inductive argument by analogy and inference to the best explanation. There are no a priori or deductive arguments that can establish the necessary truth of these ideas. In fact, you cannot prove they are necessarily true at all: they are synthetic a posteriori propositions whose truth is extremely probable at best, and we know this only by experience, induction or inference to the best explanation.

Exactly the same thing can be said of propositions (4) to (7): these are empirical propositions of the natural sciences that are synthetic a posteriori: their truth is extremely probable at best and is confirmed by experience, induction or inference to the best explanation.

We could continue listing “prior” theories that a social scientist like an economist assumes when interpreting some data or facts, but we would also find that these too are nothing but empirical propositions whose truth can be believed because we have good empirical evidence to do so. We will also encounter useful concepts that are formulated to categorise and classify objects and phenomena in the world which are analytic a priori (or true by definition because we define them in such-and-such a way). While this does presuppose a further type of “theory” when looking at data or facts, the ultimate test of whether a system of analytic classifications and definitions is useful and appropriate is how well it can classify and describe the world, so the actual justification for its use is not divorced from empiricism.

At some point of course we will start to encounter bad and false empirical theories or assumptions in some disciplines, such as in neoclassical economics. But even here the only way to know if a theory about the real world is true or false is by experience, induction or inference to the best explanation. You are not going to do it by armchair apriorism.

So what is the substantive point here?

Mises claimed that the German Historical School and the logical positivist empiricists of his time thought that they could take facts without recourse to any theory. Perhaps they did. They were wrong, and modern empiricism has since moved on.

And clearly heterodox economists of the non-neoclassical Institutionalist and Post Keynesian schools seem to accept that facts are theory-laden too (e.g., see Hodgson 1999: 146; Lawson 1997: 295).

But the lazy comment that all facts are “theory-laden” is still used by apriorists like Austrian economists to attack modern empiricism in their attempts to vindicate the intellectually bankrupt method called Mises’ praxeology.

It is an absurd exercise in vain, for the admission that “all facts are theory-laden” does not vindicate epistemological apriorism in either the natural or social sciences and not in economics either, and does not refute a more moderate version of empiricism that accepts that we do indeed have many prior theories but that they are also justified empirically.

The “all facts are theory-laden” mantra does not discredit the modern empirical method. Nor does it refute the observation that we have no good reason to think that all of our knowledge of the real world is anything but empirical and justified empirically: we have no good reason to think epistemological apriorism is a viable or necessary method in our study of the world in all of its complexity, from the natural world to the complex world of human societies.

Any given datum or fact may indeed presuppose a long list of prior theories or propositions. But we will find that these theories or propositions are themselves also empirical and have been justified too by some other social or natural scientist or philosopher who asked the question “how do we know such-and-such is true” and justified its truth convincingly a posteriori by experience, induction or inference to the best explanation.

Note
* The only possible exception I can think of is Descartes’s cogito ergo sum (or cogito) argument, but on closer inspection probably many would argue that it is not free from a prior theory/assumption that there is an “I” that must be understood as a discrete conscious entity and perceiving subject that perceives objects of perception.

On a related point if the cogito argument is reformulated to conclude that some perceptions, sensations or thinking exist or are occurring, then it might possibly be considered an ontologically and epistemologically necessary a posteriori truth (but there are also arguments against this), and even if it were it takes you nowhere epistemologically: it is a dead end and cannot be used as a secure foundation for apriorism, nor to deduce any necessary truth in the natural and social sciences.

BIBLIOGRAPHY
Hodgson, Geoffrey M. 1999. Economics and Utopia: Why the Learning Economy is not the End of History. Routledge, London and New York.

Lawson, Tony. 1997. Economics and Reality. Routledge, London and New York.

Mises and Empiricism

Israel Kirzner relates an anecdote about Mises in his book Ludwig von Mises: The Man and his Economics (2001).

Kirzner once asked Mises how any individual person can know that other people really are “purposeful” in the sense of the human action axiom (Kirzner 2001: 88).

Kirzner relates that Mises’s answer surprised him greatly: Mises replied in effect that we know the existence of other human agents by observation (Kirzner 2001: 88).

Kirzner proceeds to use this answer to argue that Mises was not really the extreme apriorist that he is normally held to be (Kirzner 2001: 89).

However, Mises’s answer (if he really meant it) suggests another conclusion: Mises was just a confused and inconsistent thinker.

Elsewhere in his body of work, Mises regards the epistemological status of the human action axiom as synthetic a priori and a type of Kantian category prior to experience, as we can see here:

“… it is expedient to establish the fact that the starting point of all praxeological and economic reasoning, the category of human action, is proof against any criticisms and objections. No appeal to any historical or empirical considerations whatever can discover any fault in the proposition that men purposefully aim at certain chosen ends. No talk about irrationality, the unfathomable depths of the human soul, the spontaneity of the phenomena of life, automatisms, reflexes, and tropisms, can invalidate the statement that man makes use of his reason for the realization of wishes and desires. From the unshakable foundation of the category of human action praxeology and economics proceed step by step by means of discursive reasoning. Precisely defining assumptions and conditions, they construct a system of concepts and draw all the inferences implied by logically unassailable ratiocination. With regard to the results thus obtained only two attitudes are possible; either one can unmask logical errors in the chain of the deductions which produced these results, or one must acknowledge their correctness and validity.” (Mises 2008: 67).

“The human mind is not a tabula rasa on which the external events write their own history. It is equipped with a set of tools for grasping reality. Man acquired these tools, i.e., the logical structure of his mind, in the course of his evolution from an amoeba to his present state. But these tools are logically prior to any experience.

Man is not only an animal totally subject to the stimuli unavoidably determining the circumstances of his life. He is also an acting being. And the category of action is logically antecedent to any concrete act.

The fact that man does not have the creative power to imagine categories at variance with the fundamental logical relations and with the principles of causality and teleology enjoins upon us what may be called methodological apriorism.

Everybody in his daily behavior again and again bears witness to the immutability and universality of the categories of thought and action. He who addresses fellow men, who wants to inform and convince them, who asks questions and answers other people's questions, can proceed in this way only because he can appeal to something common to all men--namely, the logical structure of human reason. The idea that A could at the same time be non-A or that to prefer A to B could at the same time be to prefer B to A is simply inconceivable and absurd to a human mind. We are not in the position to comprehend any kind of prelogical or metalogical thinking. We cannot think of a world without causality and teleogy.” (Mises 2008: 35).

As I have argued here, this Misesian epistemology is entirely unconvincing.

One needs empirical evidence to determine what even constitutes a conscious and voluntary human act as defined in the action axiom.

In fact, the “action” as conceived by the human action axiom is to be strictly limited to:

(1) the conscious behaviour of humans;

(2) to exclude unconscious and involuntary behaviour, and

(3) (presumably) to non-mentally-ill human beings.

But Mises requires empirical evidence to demonstrate what these things even are and how to identify them.

To give an example: take sleep-walking. We observe human beings who perform complex physical tasks such as walking and (in extreme cases) driving motor vehicles while in a state of sleep. Such people cannot remember the experiences. Yet sleepwalkers’ eyes are open: presumably the visual system (retinas, optic nerve, visual cortices, etc.) is functioning and presumably the visual cortices show brain activity that is correlated with visual perception.

Are sleep-walkers engaged in action with a purpose? The Misesian might counter: no, because sleep-walkers are not conscious. But how on earth do we know that sleep-walkers are not conscious? Can we know it a priori?

We cannot do so, and need empirical evidence. For example, it could be that being in a sleepwalking state is like being in a dream state and involves some level of consciousness, but that most sleep-walkers simply forget the experience when they wake up. Would they then be engaged in action with a purpose?

However, it seems that most sleep-walking does not occur in REM sleep (when most people dream) but in the deepest, slow-wave sleep in which dreams are rare (Seager 1999: 34), so the idea that most sleepwalkers are genuinely unconscious is possible and probable. But, as noted above, it is empirical evidence and inductive argument that yields this type of a posteriori knowledge about sleep-walking, not a priori reasoning.

But it is far worse than this, for, as Kirzner noticed and Mises appears to have conceded, you need empirical evidence and inductive argument by analogy to make the case that other human minds even exist (Kirzner 2001: 88 even states that it is observation that convinces us to reject solipsism).

These insights are enough to damn the alleged synthetic a priori status of action axiom.

That Mises spent his life defending the Kantian synthetic a priori status of the action axiom but then casually and privately admitted to Kirzner that observation (a kind of empirical evidence) is needed to know that other purposeful human minds even exist only shows what a third rate philosopher and thinker Mises really was.

BIBLIOGRAPHY
Armstrong, D. M. 1963. “Is Introspective Knowledge Incorrigible?,” The Philosophical Review 72.4: 417–432.

Kirzner, Israel M. 2001. Ludwig von Mises: The Man and his Economics. ISI Books, Wilmington, Del.

Mises, L. 2008. Human Action: A Treatise on Economics. The Scholar’s Edition. Mises Institute, Auburn, Ala.

Seager, William. 1999. Theories of Consciousness: An Introduction and Assessment. Routledge, London and New York.

Why Mises’s Praxeological Theories are not Necessarily True of the Real World

Take as an example some Austrian who says: it is a praxeological and necessary truth about the real world that, if human beings by their actions drive a monetary market interest rate below the equilibrium rate, then this must necessarily result in excess capital investment causing an Austrian business cycle (ABC). I stress that this is more a “vulgar” Austrian view, and the actual Austrian economists could present more sophisticated defence of their theories.

But such a “vulgar” Austrian statement as above has no necessary truth about the real world.

Why? The reason is that it is contingent on many factors, which range from basic epistemological ones (such as number (1) below) to social, institutional and economic ones, as follows:

(1) the very existence of other acting human minds in the first place. No philosopher has succeeded in proving a priori that other minds exist: the best you can do is an inductive argument from analogy, which only has probabilistic truth at best;

(2) the existence of economies with money;

(3) the existence of economies with loans made in money terms;

(4) the existence of economies with loans made in money and with interest made in money terms;

(5) the truth of loanable funds theory as determined by time preference, which is highly doubtful given that monetary interest rates are better explained by liquidity preference.

(6) the truth of the view that demand for credit will equal some alleged stock of loanable funds, and this can be reduced to a simple and reliable function of interest rates determining the quantity of credit demanded as plotted on a demand curve for loanable funds, when the demand for credit is highly complex and contingent on many factors well beyond interest rates, such as, for example, expectations and uncertainty;

(7) in Mises’s early business cycle theory (ABCT) and the classic ABCT of Hayek the existence of a unique Wicksellian natural rate of interest: something whose probability is close to zero given the empirical evidence that real world economies do not and cannot obtain a general equilibrium state;

(8) The early Hayekian versions of the Austrian business cycle theory assume an economy starting from a general equilibrium state and returning towards one, which is something whose probability is again close to zero given that real world economies do not and cannot obtain general equilibrium states.

And this list is far from exhaustive.

The intellectual fraud of the “necessary” truth of Austrian praxeological theories can be demonstrated quite clearly, since a similar list of contingently true requirements could be provided for any praxeological theory of any kind.

Epistemology in Modern Analytic Philosophy: A Review

There are three fundamental epistemological categories with respect to propositions and knowledge in modern analytic philosophy:

(1) the “analytic” versus “synthetic” distinction
This is a distinction involving the semantic form of propositions. A sentence is analytic if and only if it is true solely by virtue of the meanings of terms used (Elugardo 1997: 13). Every sentence that is not analytic is synthetic;

(2) the notion of “necessity” versus “contingency”
This relates to the nature of truth and can be understood in (i) a metaphysical/ontological sense or (ii) a conceptual/verbal sense (or de dicto). A logically necessary truth in sense (ii) is not metaphysically necessary, but true only by virtue of the definitions of terms used;

(3) the a priori versus a posteriori distinction
This involves how a proposition is epistemologically known to be true or false. An a priori truth is known without appeal to experience, and an a posteriori truth is known by appeal to experience or empirical evidence.

With regard to analyticity, it is also possible to distinguish three types of analytic sentence, as follows:

(1) an explicit analyticity, such as “Bachelors are bachelors.” These can also be called “identity propositions” or “truths of logic”;

(2) an implicit analyticity, where the sentence is true by definition, e.g., “Bachelors are male.” Here we have a predicative proposition in which the predicate asserts something of a subject already containing that idea implicitly; and

(3) another type of analyticity where propositions are true in virtue of the meanings of the words used, but not true by definition: “Nothing is both red and green all over” or “whatever is coloured is extended.”

Types (1) and (2) describe what is called “Frege analyticity” (Boghossian 1997) in the following senses:

“A sentence is analytic if and only if either (i) it is a logical truth, or (ii) it can be converted into a logical truth by substitution of synonymous expressions, salve veritate, and formally valid inferences.” (Elugardo 1997: 15).

All “Frege analytic” truths are known a priori.

But type (3) above describes a kind of analyticity that is wider in sense than (1) or (2), and the epistemological status of (3) was once held to be synthetic a priori (Elugardo 1997: 15). Today many would say it is analytic a priori, but a type that Boghossian (2008: 203) calls “Carnap analyticity” (after the logical positivist Rudolf Carnap).

In 1951, Quine (1951) attacked the analytic–synthetic distinction. Elugardo (1997: 15) argues that Quine admitted the existence of “Frege analytic” truths in sense (1), but thought that even these logical truths are open to revision. But Quine also argued that Frege analyticity in sense (2) is untenable. Quine’s rejection of this type of analytic statement is derived from his unwillingness to accept any definition of “synonymy” that is circular (in that it relies in turn on the concept of “analyticity” for its definition), and because of his verbal behaviourism.

But Quine’s attack on Frege analyticity is controversial. Many modern analytic philosophers think Quine did not succeed in his arguments, and that analyticity does indeed exist (Grice and Strawson 1956; Putnam 1962 and 1975; Quinton 1967; Glock 1996 and 2003; Nimtz 2003). Nor it is surprising that modern Rationalists support the existence of Frege analyticity (Katz 1967; Chomsky 1988).

Quine also argued against the logical positivist view that verification of a single synthetic proposition is possible by empirical evidence and without the need for verifying other sentences. For Quine, every synthetic proposition relies on and presupposes a number of other sentences, a view which lead to Quine’s confirmation holism and the Quine-Duhem thesis.

Thus knowledge is an interconnected “web of belief,” and those beliefs at the core are only the most difficult to give up, while those at the periphery are easy to give up. Nevertheless, all beliefs are capable in principle of being given up and none immune to revision (Elugardo 1997: 14). Philosophers have continued to debate this view too.

Such were the main controversies in analytic philosophy on epistemology until the 1970s. Until the 1970s, most analytic philosophers thought that all necessary truths are a priori and all contingent truths are a posteriori. Then Saul Kripke argued that the three concepts above are distinct, and that there are actually “necessary a posteriori” truths, such as, for example, the statement that “water is truly H₂O.”

Kripke introduced a revolution in analytic metaphysics and epistemology, and he also argued that scientifically true identities are necessary a posteriori truths (Elugardo 1997: 12).

Kripke also contended that there is such a thing as “contingent a priori” truth, but the existence of this type of truth is still disputed.

Links
“The Return of Metaphysics into Analytic Philosophy,” August 29, 2013.

“Epistemology and Kinds of Knowledge,” July 25, 2013.

“Schwartz’s A Brief History of Analytic Philosophy: from Russell to Rawls: Chapter 3,” August 25, 2013.

“Quine and the Analytic–Synthetic Distinction,” August 24, 2013.

“Schwartz’s A Brief History of Analytic Philosophy: from Russell to Rawls: Chapter 2,” August 23, 2013.

“Schwartz’s A Brief History of Analytic Philosophy: From Russell to Rawls: Chapter 1,” August 22, 2013.

BIBLIOGRAPHY
Boghossian, Paul. 1996. “Analyticity Reconsidered,” Nous 30: 360–391.

Boghossian, Paul. 1997. “Analyticity,” in B. Hale and C. Wright (eds.), A Companion to the Philosophy of Language. Basil Blackwell, Oxford. 331–368.

Boghossian, Paul. 2008. “Analyticity Reconsidered,” in Paul A. Boghossian, Content and Justification: Philosophical Papers. Clarendon Press, Oxford. 195–224.

Chomsky, Noam. 1988. Language and Problems of Knowledge: The Managua Lectures. MIT Press, Cambridge, Mass. and London.

Elugardo, R. 1997. “Analytic/Synthetic, Necessary/Contingent, and a priori/a posteriori: Distinction,” in Peter V. Lamarque (ed.), Concise Encyclopedia of Philosophy of Language. Pergamon, New York. 10–19.

Frege, Gottlob. 1986. The Foundations of Arithmetic (2nd rev. edn.). Basil Blackwell, Oxford.

Glock, Hans-Johann. 1996. “Necessity and Normativity,” in Hans Sluga and David G. Stern (eds.). The Cambridge Companion to Wittgenstein. Cambridge University Press, Cambridge and New York. 198–225.

Glock, Hans-Johann. 2003. Quine and Davidson on Language, Thought and Reality. Cambridge University Press, Cambridge.

Grice, H. P. and P. F. Strawson. 1956. “In Defence of a Dogma,” Philosophical Review 65: 141–158.

Horwich, Paul. 1992. “Chomsky versus Quine on the Analytic-Synthetic Distinction,” Proceedings of the Aristotelian Society n.s. 92: 95–108.

Katz, Jerrold J. 1967. “Some Remarks on Quine on Analyticity,” Journal of Philosophy 64: 36–52.

Katz, Jerrold J. 2010. “Analyticity,” in Jonathan Dancy, Ernest Sosa and Matthias Steup (eds.), A Companion to Epistemology (2nd edn.). Blackwell, Malden, MA and Oxford. 224–230.

Nimtz, C. 2003. “Analytic Truths – Still Harmless After All These Years?,” in H. J. Glock, K. Gluer, and G. Keil (eds.), Fifty Years of Quine’s ‘Two Dogmas’. Rodopi, Amsterdam and New York. 91–118.

Pap, Arthur. 1958. Semantics and Necessary Truth: An Inquiry into the Foundations of Analytic Philosophy. Yale University Press, New Haven.

Popper, Karl. 1957. “Philosophy of Science: A Personal Report,” in C. A. Mace (ed.), British Philosophy in the Mid-Century: A Cambridge Symposium. Macmillan, New York. 155–191.

Putnam, H. 1962. “The Analytic and the Synthetic,” Minnesota Studies in the Philosophy of Science 3: 358–397.

Putnam, Hilary. 1975. “The Analytic and the Synthetic,” Hilary Putnam, Mind, Language, and Reality. Cambridge University Press, Cambridge. 33–69.

Quine, Willard Van Orman. 1951. “Two Dogmas of Empiricism,” Philosophical Review 60: 20–43.

Quine, Willard Van Orman. 1960. Word and Object. M.I.T. Press, Massachusetts.

Quine, Willard Van Orman. 1981. “Two Dogmas of Empiricism,” in From a Logical Point of View. Harvard University Press, Cambridge, MA. 20–46.

Quine, Willard Van Orman. 1991. “Two Dogmas in Retrospect,” Canadian Journal of Philosophy 21.3: 265–274.

Quinton, Anthony. 1963–1964. “The ‘a priori’ and the Analytic,” Proceedings of the Aristotelian Society n.s. 64: 31–54.

Quinton, Anthony. 1967. “The ‘a priori’ and the Analytic,” in P. F. Strawson (ed.), Philosophical Logic. Oxford University Press, Oxford. 107–128.

Watkins, J. W. N. 1957. “Between Analytic and Empirical,” Philosophy 32.121: 112–131.

Robert Murphy gets Mises’s Epistemology Wrong

Over at his blog, Robert Murphy is involved in a new Methodenstreit, and selectively quotes a passage from Mises that demonstrates that Murphy himself does not properly understand Mises’s epistemology:

Robert Murphy, “Mises on A Priori Reasoning,” Free Advice, 12 September.

That is underscored by this comment of his later in the post:

“I was going to be snotty about it, but that would be unfair since many Misesians thought Mises was making synthetic a priori propositions. But, look at literally the sentence right before the one you quoted. Mises wrote:

‘This theorem is a tautology, its deduction results in an analytic judgment. Nonetheless nobody would contend that geometry in general and the theorem of Pythagoras in particular do not enlarge our knowledge.’

So Mises is here saying that the Pythagorean theorem is an analytic a priori statement.”
http://consultingbyrpm.com/blog/2013/09/mises-on-a-priori-reasoning.html#comment-73618

First, let us imagine (for the sake of argument) that Mises was really saying that praxeology and Euclidean geometry are analytic a priori. What are the consequences of that?

As analytic a priori systems, neither praxeology nor Euclidean geometry can provide us with any necessarily true knowledge of the real world known a priori. The instant either is asserted as true of the real world, both become synthetic a posteriori and must be judged true or false empirically.

But, if that were true, this has destroyed praxeology as the system imagined by Mises as providing necessarily true knowledge of the real world known a priori:

“Praxeology is a theoretical and systematic, not a historical, science. Its scope is human action as such, irrespective of all environmental, accidental, and individual circumstances of the concrete acts. Its cognition is purely formal and general without reference to the material content and the particular features of the actual case. It aims at knowledge valid for all instances in which the conditions exactly correspond to those implied in its assumptions and inferences. Its statements and propositions are not derived from experience. They are, like those of logic and mathematics, a priori. They are not subject to verification and falsification on the ground of experience and facts. They are both logically and temporally antecedent to any comprehension of historical facts. They are a necessary requirement of any intellectual grasp of historical events” (Mises 2008: 32).

Mises is saying here that praxeology is not just an analytic a priori system. First, he is saying that it is not open to verification and falsification on the grounds of experience (or a posteriori), but can be known a priori. Secondly, it also provides necessarily true knowledge of the real world that cannot be refuted by empirical evidence (“It aims at knowledge valid for all instances in which the conditions exactly correspond to those implied in its assumptions and inferences”).

The only way it can do this is if the theorems of praxeology are synthetic a priori.

Murphy has badly misinterpreted Mises. If Mises really thought that praxeology was merely analytic a priori, then the Mises quote I have just cited above makes no sense. Mises’s epistemology would be hopelessly contradictory and self-refuting.

Secondly, let us return to the original passage Murphy quotes in his post.

But let us quote it in its entirety and with full context:

“Aprioristic reasoning is purely conceptual and deductive. It cannot produce anything else but tautologies and analytic judgments. All its implications are logically derived from the premises and were already contained in them. Hence, according to a popular objection, it cannot add anything to our knowledge.

All geometrical theorems are already implied in the axioms. The concept of a rectangular triangle already implies the theorem of Pythagoras. This theorem is a tautology, its deduction results in an analytic judgment. Nonetheless nobody would contend that geometry in general and the theorem of Pythagoras in particular do not enlarge our knowledge. Cognition from purely deductive reasoning is also creative and opens for our mind access to previously barred spheres. The significant task of aprioristic reasoning is on the one hand to bring into relief all that is implied in the categories, concepts, and premises and, on the other hand, to show what they do not imply. It is its vocation to render manifest and obvious what was hidden and unknown before.

In the concept of money all the theorems of monetary theory are already implied. The quantity theory does not add to our knowledge anything which is not virtually contained in the concept of money. It transforms, develops, and unfolds; it only analyzes and is therefore tautological like the theorem of Pythagoras in relation to the concept of the rectangular triangle. However, nobody would deny the cognitive value of the quantity theory. To a mind not enlightened by economic reasoning it remains unknown. A long line of abortive attempts to solve the problems concerned shows that it was certainly not easy to attain the present state of knowledge.

It is not a deficiency of the system of aprioristic science that it does not convey to us full cognition of reality. Its concepts and theorems are mental tools opening the approach to a complete grasp of reality; they are, to be sure, not in themselves already the totality of factual knowledge about all things. Theory and the comprehension of living and changing reality are not in opposition to one another. Without theory, the general aprioristic science of human action, there is no comprehension of the reality of human action.

The relation between reason and experience has long been one of the fundamental philosophical problems. Like all other problems of the critique of knowledge, philosophers have approached it only with reference to the natural sciences. They have ignored the sciences of human action. Their contributions have been useless for praxeology.

It is customary in the treatment of the epistemological problems of economics to adopt one of the solutions suggested for the natural sciences. Some authors recommend Poincaré’s conventionalism. They regard the premises of economic reasoning as a matter of linguistic or postulational convention. Others prefer to acquiesce in ideas advanced by Einstein. Einstein raises the question: ‘How can mathematics, a product of human reason that does not depend on any experience, so exquisitely fit the objects of reality? Is human reason able to discover, unaided by experience through pure reasoning the features of real things?’ And his answer is: ‘As far as the theorems of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.’

However, the sciences of human action differ radically from the natural sciences. All authors eager to construct an epistemological system of the sciences of human action according to the pattern of the natural sciences err lamentably.

The real thing which is the subject matter of praxeology, human action, stems from the same source as human reasoning. Action and reason are congeneric and homogeneous; they may even be called two different aspects of the same thing. That reason has the power to make clear through pure ratiocination the essential features of action is a consequence of the fact that action is an offshoot of reason. The theorems attained by correct praxeological reasoning are not only perfectly certain and incontestable, like the correct mathematical theorems. They refer, moreover, with the full rigidity of their apodictic certainty and incontestability to the reality of action as it appears in life and history. Praxeology conveys exact and precise knowledge of real things.” (Mises 2008: 38–39).

First, it is quite clear here that Mises is rejecting the “popular objection” he refers to in paragraph 1. Mises is saying that Euclidean geometry provides real knowledge about the external world, despite being a system of tautologies derived by deduction from the axioms. He is implying that Euclidean geometry is Kantian synthetic a priori knowledge (because Mises cannot properly distinguish between (1) analytic a priori pure geometry and (2) synthetic a posteriori applied geometry).

Secondly, although it is poorly expressed, Mises appears to be thinking of synthetic a priori knowledge when he says that:

“In the concept of money all the theorems of monetary theory are already implied. The quantity theory does not add to our knowledge anything which is not virtually contained in the concept of money. It transforms, develops, and unfolds; it only analyzes and is therefore tautological like the theorem of Pythagoras in relation to the concept of the rectangular triangle. However, nobody would deny the cognitive value of the quantity theory.”

Mises cannot seriously believe that his monetary theory provides no necessary knowledge of reality, and it seems that he is referring to the synthetic character of these theories by his reference above to “the cognitive value of the quantity theory.”

Next, Mises is very clear in rejecting the analytic a priori character of praxeology when he rejects (1) Poincaré’s conventionalism and (2) Einstein’s view of mathematics as being divided into (a) pure mathematics (which is necessarily true) and (b) applied mathematics (which is only true of the real world contingently).

The final paragraph of Mises clinches my argument:

The theorems attained by correct praxeological reasoning are not only perfectly certain and incontestable, like the correct mathematical theorems. They refer, moreover, with the full rigidity of their apodictic certainty and incontestability to the reality of action as it appears in life and history. Praxeology conveys exact and precise knowledge of real things.” (Mises 2008: 39).

This entails that praxeological theorems are necessarily and absolutely true, and are known a priori, but also yield necessary knowledge of the real world. That is nothing but Kantian synthetic a priori knowledge.

And, finally, if Mises did not think that praxeological theorems were synthetic a priori, why is Mises desperate to defend the existence of synthetic a priori in The Ultimate Foundation of Economic Science: An Essay on Method (1962)?:

“The essence of logical positivism is to deny the cognitive value of a priori knowledge by pointing out that all a priori propositions are merely analytic. They do not provide new information, but are merely verbal or tautological, asserting what has already been implied in the definitions and premises. Only experience can lead to synthetic propositions. There is an obvious objection against this doctrine, viz., that this proposition that there are no synthetic a priori propositions is in itself a — as the present writer thinks, false — synthetic a priori proposition, for it can manifestly not be established by experience.

The whole controversy is, however, meaningless when applied to praxeology. It refers essentially to geometry. Its present state, especially its treatment by logical positivism, has been deeply influenced by the shock that Western philosophy received from the discovery of non-Euclidian geometries. Before Bolyai and Lobachevsky, geometry was, in the eyes of the philosophers, the paragon of perfect science; it was assumed that it provided unshakable certainty forever and for everybody. To proceed also in other branches of knowledge more geometrico was the great ideal of truth-seekers. All traditional epistemological concepts began to totter when the attempts to construct non-Euclidian geometries succeeded.

Yet praxeology is not geometry. It is the worst of all superstitions to assume that the epistemological characteristics of one branch of knowledge must necessarily be applicable to any other branch. In dealing with the epistemology of the sciences of human action, one must not take one’s cue from geometry, mechanics, or any other science.

The assumptions of Euclid were once considered as self-evidently true. Present-day epistemology looks upon them as freely chosen postulates, the starting point of a hypothetical chain of reasoning. Whatever this may mean, it has no reference at all to the problems of praxeology.” (Mises 1962: 5).

In other words, the collapse of Euclidian geometry as synthetic a priori knowledge does not apply to the synthetic a priori status of praxeology!

This, if nothing else, is breathtaking in its pig-headed unwillingness to reconsider the epistemology status of praxeology given the fall of Euclidian geometry as the paradigmatic case of synthetic a priori knowledge.

I will just end by noting that part of the problem we face in interpreting Mises is that Mises hismelf was not always clear, and was probably confused about basic epistemological concepts, as his critic Hans Albert has noted:

“Mises gives a Kantian answer to the question of how the a priori character of praxeological knowledge and its apodictic certainty is to be explained. This knowledge apparently can be reduced to the logical structure of the human mind which is supposed to be the basis for thought and action. ... On the one hand he seems to suggest that he is introducing with his principle of action a synthetic a priori proposition, as he ascribes informational content to the principle. On the other hand, he declares the question of whether the respective propositions are synthetic or analytic to be purely verbal and therefore uninteresting. This seems to show that he was not aware of the connection between analyticity and informational vacuity. He permanently compares his allegedly a priori knowledge with logical and mathematical knowledge and gives such a description of the respective propositions and their mode of derivation that one comes to suspect them to be analytic. He confounds the analytical character of propositions with the logical character of the relationships between propositions in a deduction. But the fact that particular propositions are deducible from particular sets of premises does not render them analytic. For instance, in physics propositions from geometry get an empirical interpretation, and, interpreted in this way, they are synthetic. But propositions which are the result of the ‘logical unfolding’ of certain concepts contain no information. They are analytic not because they are derived, but because they follow from definitions which do not carry information themselves. When Mises tells us that the concept of money already implies all theorems of the theory of money, the alleged certainty of the basis of this derivation does not help him to establish a nonvacuous economic theory. The theory of money as he envisages it here would be without informational content and could not be used to explain anything.” (Albert 1999: 131–132).

BIBLIOGRAPHY
Albert, H. 1999. Between Social Science, Religion and Politics: Essays in Critical Rationalism. Rodopi, Amsterdam.

Mises, Ludwig von. 1962. The Ultimate Foundation of Economic Science: An Essay on Method. Van Nostrand, Princeton, N.J.

Mises, L. von. 2008. Human Action: A Treatise on Economics. The Scholar’s Edition. Mises Institute, Auburn, Ala.

The Laws of Thought

The Laws of Thought (or Laws of Logic) are fundamental to good argument, and are often violated or misunderstood, and a fascinating question is: what is their epistemological status?

The Laws of Thought can be set out as follows:

(1) the Law of Identity
This can be stated simply as the idea that any entity x is identical with itself (or x = x). With respect to propositions, it means that, if a proposition p is true, then it is true (or p → p).

A violation of the Law of Identity is the informal logical fallacy of equivocation: changing the meaning of terms in an argument or using the same term in different senses.

(2) Law of Noncontradiction
This can be stated as the idea that one cannot assert as true a proposition p and its negation at the same time (or p ∧ ¬p is false). Such a statement is self-contradictory. That is to say, the proposition p and its negation (¬p) asserted as true at the same time are mutually exclusive.

The source of the Law of Noncontradiction is Aristotle’s Metaphysics, although he gives three versions of the law, in (1) an ontological, (2) psychological and (3) logical sense.

(3) the Law of Excluded Middle
This states that every meaningful proposition is either true or false. There is no third option. Put another way, either the proposition p is true or its negation (¬p) is true. Symbolically, this means that p ∨ ¬p must be true.

It is also generally believed that laws (1) and (3) are tautologies.

There are of course many other tautologies important for deductive logic, such as De Morgan’s theorems, but the laws of thought remain fundamental.

But, as noted above, what is their epistemological status? Are they simply analytic a priori? And even if we can interpret them in that sense when considered only as pure tautologies, could they also be given an empirical synthetic a posteriori status when asserted as true of the real world? (just as pure geometry and applied geometry each have a different epistemological status.)

For it seems that the law of identity also expresses, or is bound up with, a deep metaphysical truth about existence: existence and identity are closely related concepts, as was stressed by Gottlob Frege and Quine (Scruton 1994: 143).

Indeed, Bertrand Russell gave the laws of logic an ontological interpretation:

(1) law of identity: ‘whatever is, is.’

(2) the law of contradiction: ‘nothing can both be and not be.’

(3) the law of excluded middle: ‘everything must either be or not be.’

Russell thought that these were “self evident logical principles,” but the possibility that the law of excluded middle may not apply to certain quantum mechanical phenomena (Quine 1986: 86–87) should alert us to the idea that the laws of thought are ultimately empirical statements derived from human experience of the macroscopic world. (And this does not falsify the law of excluded middle with respect to the macroscopic world at all, but confines or limits it as a truth to that domain.)

That is to say, surely it is not unreasonable to assert that “every thing that exists is identical with itself” is, in the end, an empirical observation of the fundamental nature of the world of human experience. Of course, we cannot even conceive of how it could be false, but then human beings most probably could not conceive of the counter-intuitive truths of quantum mechanics until the 20th century.

Even in the realm of the laws of thought, when these laws are asserted as truths of the real world, they arguably must be considered empirical.

Links
“Law of Thought,” Wikipedia
http://en.wikipedia.org/wiki/Three_classical_laws_of_thought#Aristotle

“Law of Noncontradiction,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_noncontradiction

“Law of Identity,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_identity

“Law of Excluded Middle,” Wikipedia
http://en.wikipedia.org/wiki/Law_of_Excluded_Middle

BIBLIOGRAPHY
Scruton, R. 1994. Modern Philosophy: An Introduction and Survey. Penguin Books, London.

Quine, W. V. 1986. Philosophy of Logic (2nd edn.). Harvard University Press, Cambridge, Mass.

Bob Murphy All At Sea on Geometry and Economic Epistemology

A beautiful illustration of the continuing errors of Austrians who support Misesian praxeology can be seen in Robert Murphy’s comments in this video on geometry, and in his debate with David Friedman.*



Robert Murphy, like Mises, cannot properly distinguish between (1) pure geometry and (2) applied geometry (on which, see Salmon 1967: 38). When Euclidean geometry is considered as a pure mathematical theory, it can be regarded as analytic a priori knowledge, and asserts nothing necessarily true of the external, real world, since it is tautologous and non-informative. (An alternative view derived from the theory called “conditionalism” or “if-thenism” holds that pure geometry is merely a set of conditional statements from axioms to theorems, derivable by logic, and asserting nothing about the real world [Musgrave 1977: 109–110], but this is just as devastating to Misesians.)

When Euclidean geometry is applied to the world, it is judged as making synthetic a posteriori statements (Ward 2006: 25), which can only be verified or falsified by experience or empirical evidence. That means that applied Euclidean geometrical statements can be refuted empirically, and we know that Euclidean geometry – understood as a universally true theory of space – is a false theory (Putnam 1975: 46; Hausman 1994: 386; Musgrave 2006: 329).

Murphy’s confusion is also confirmed in these remarks below.



The fact that the refutation of Euclidean geometry understood as an empirical theory leaves pure geometry untouched does not help Murphy, because pure geometry per se says nothing necessarily true about the real-world universe, and is an elegant but non-informative system.

Albert Einstein was expressing this idea in the following remarks about mathematics in an address called “Geometry and Experience” on 27 January 1921 at the Prussian Academy of Sciences:

“One reason why mathematics enjoys special esteem ... is that its laws are absolutely certain and indisputable, while those of all other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts. In spite of this, the investigator in another department of science would not need to envy the mathematician if the laws of mathematics referred to objects of our mere imagination, and not to objects of reality. For it cannot occasion surprise that different persons should arrive at the same logical conclusions when they have already agreed upon the fundamental laws (axioms), as well as the methods by which other laws are to be deduced therefrom. But there is another reason for the high repute of mathematics, in that it is mathematics which affords the exact natural sciences a certain measure of security, to which without mathematics they could not attain. At this point an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things. In my opinion the answer to this question is, briefly, this:- As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
http://www-history.mcs.st-and.ac.uk/Extras/Einstein_geometry.html

If we were to pursue this analysis further as applied to economic methodology, it would follow that praxeology – if it is conceived as deduced from analytic a priori axioms – is also an empty, tautologous, and vacuous theory that says nothing necessarily true of the real world. And the instant any Austrian asserts that praxeology is making real assertions about the world, it must be judged as synthetic a posteriori, and so is to be verified or falsified by experience or empirical evidence.

What Murphy fails to mention is that the only way to sustain his whole praxeological program is to defend the truth of Kant’s synthetic a priori knowledge, which, as we have seen from the last post, is a category of knowledge that must be judged as non-existent.

Note
* Murphy also conflates (1) the logical positivists’ verifiability criterion for meaningfulness with (2) Popper’s falsifiability criterion for scientific knowledge, but this is an issue I will not bother to pursue here.

BIBLIOGRAPHY
Hausman, Daniel M. 1994. “If Economics Isn’t Science, What Is It?,” in Daniel M. Hausman (ed.), The Philosophy of Economics: An Anthology (2nd edn.). Cambridge University Press, Cambridge. 376–394.

Musgrave, Alan. 1977. “Logicism Revisited,” British Journal for the Philosophy of Science 28: 99–127.

Musgrave, Alan. 2006. “Responses,” in Colin Cheyne and John Worrall (eds.), Rationality and Reality: Conversations with Alan Musgrave. Springer, Dordrecht. 293–334.

Putnam, Hilary. 1975. “The Analytic and the Synthetic,” in Hilary Putnam, Mind, Language and Reality. Philosophical Papers. Volume 2. Cambridge University Press, Cambridge. 33–69.

Salmon, Wesley C. 1967. The Foundations of Scientific Inference. University of Pittsburgh Press, Pittsburgh.

Ward, Andrew. 2006. Kant: The Three Critiques. Polity, Cambridge.

Quine and the Analytic–Synthetic Distinction

I am taking a quick detour through analytic philosophy and epistemology at the moment, as a type of prolegomena to economic methodology.

In 1951, Willard Van Orman Quine (1908–2000) published the now famous paper “Two Dogmas of Empiricism” (1951; reprinted in Quine 1981), in which he argued that the conventional idea of analyticity (or the analytic nature of a proposition) cannot be defended, and that the distinction between analytic and synthetic truths is not clear cut.

“Two Dogmas of Empiricism” is often said to be one of the most important papers in analytic philosophy of the late 20th century, though Quine continued to develop his epistemological views later in life, so that he modified or shifted the arguments used in “Two Dogmas” (Creath 2004: 47).

In “Two Dogmas of Empiricism,” Quine examines the intensional definitions or meanings given to the concepts of “analyticity” and “synonymy.”

Quine complains that the process of definition necessary for understanding “analytic truth” rests on the concept of “synonymy,” and that affirming or establishing that these two linguistic forms are proper synonyms is “far from clear” (Quine 1951: 25). Moreover, Quine asserts that appeals to “synonymy” supposedly fall back on “analyticity,” so that we have a circular argument.

Quine therefore argues that all attempts to define “analyticity” fall back on intensional terms in a way that is viciously circular, and that intensional definitions do “not hold the key” to the concepts of synonymy and analyticity (Quine 1951: 27). Ultimately, intensional terms like “analyticity” must be defended in extensional terms, or, that is to say, in terms of their reference to verbal behaviour (Glock 1996: 204).

Quine therefore concluded that the standard ideas of analyticity and analytic truth were indefensible, and so the analytic and synthetic distinction unclear.

Many responses to Quine were made (Grice and Strawson 1956; Putnam 1962; Quinton 1967; Glock 1996; Nimtz 2003; Gutting 2009: 11–30).

Glock argues that, although the process by which “analyticity” is defined is circular, it is nevertheless not a vicious form of circularity (Glock 1996: 204; Glock 2003: 75). Quine’s demand that an intensional concept like “analyticity” needs to be reduced to extensional ones is unreasonable and unnecessary (Glock 2003: 75).

We can consider the following proposition:

(1) All bachelors are unmarried.

It is not possible to deny the truth of this proposition without simply redefining one of the words, and the definition of “analyticity” in terms of synonymy is not unjustified if intensional meanings can be sustained without being reduced to extensional verbal behaviour.

Quine’s complaints, then, about the circularity involved in defining “analyticity” cannot be sound, nor are they sufficient to overthrow the definition of analyticity in terms of synonymy.

Quine himself later denied that his major criticism of the concept of “analyticity” in “Two Dogmas of Empiricism” was simply that attempts to define it are circular (indeed Glock 2003: 77 contends that Quine dropped the “circularity” charge as early as 1953), and other philosophers seem to accept this, and instead claim that Quine’s actual fundamental complaint was that the term of “analyticity” must be analysed in a behavioural sense.

So with Quine’s behaviourism very much the relevant background theory, Quine’s objection appears to be that neither “analyticity” nor “synonymy” can be reduced to verbal behaviour or behavioural criteria (Gibson 1996: 99; Creath 2004: 49; Gutting 2009: 21; Hylton 2006: 183). This view was confirmed when critics charged that Quine’s standard for the definitions of these terms was impossibly high, and Quine responded by saying precisely that he wished “no more, after all, than a rough characterization in terms of dispositions to verbal behavior” (Quine 1960: 207).

So it is clear that Quine wants a behaviourist semantics (Gibson 1996: 99). Quine also redefined analytic sentences to mean those that all people in a community of speakers learn are true by learning the meanings of the words involved (Gibson 1996: 100). But, Quine argued, neither this behaviourist semantical definition nor a “popular” or ordinary language notion of analyticity (Elugardo 1997: 15) can provide a strict scientific clarification that can defend the intensional semantic one that justifies the necessary verbal truth of analytic propositions (Gibson 1996: 100).

In essence, Quine’s attack on analyticity is to be understood in the logical positivist tradition of the verification principle: how is the term of analyticity to be related to the empirical verbal behaviour of human beings as judged by a methodological behaviourism? (Creath 2004: 49). The paradox, as Creath points out, is that:

“Quine is pushing against Carnap the very demands that Carnap had pushed against the metaphysicians” (Creath 2004: 49).

But Quine’s whole attempt to reject strict analytic truth would seem to collapse once we recognise that (1) the verification principle cannot be accepted, and (2) the whole behaviourist project is unsound (Gutting 2009: 21; Burgess 2004: 51–52).

Ultimately, then, Quine’s attempt to reject the analytic versus synthetic distinction is a failure.

These conclusions are broadly in line with the arguments of Quine’s critics, who find that analytic truths do exist, but they are, as in conventional empiricist epistemology, trivial or non-informative (Putnam 1962; Nimtz 2003).

For example, Putnam argued that there is indeed an analytic versus synthetic distinction but that it is ultimately a trivial one (Putnam 1962: 361).

BIBLIOGRAPHY
Burgess, John P. 2004. “Quine, Analyticity and Philosophy of Mathematics,” The Philosophical Quarterly 54.214: 38–55.

Creath, Richard. 1990. Dear Carnap, dear Van: The Quine-Carnap Correspondence and Related Work. University of California Press, Berkeley, CA and London.

Creath, Richard. 2004. “Quine on the Intelligibility and Relevance of Analyticity,” in Roger F. Gibson, (ed.). The Cambridge Companion to Quine. Cambridge University Press, Cambridge, UK and New York. 47–64.

Elugardo, R. 1997. “Analytic/Synthetic, Necessary/Contingent, and a priori/a posterori: Distinction,” in Peter V. Lamarque (ed.), Concise Encyclopedia of Philosophy of Language. Pergamon, New York. 10–19.

Gibson, Roger F. 1996. “Quine’s Behaviorism,” in William O’Donohue and Richard F. Kitchener (eds.), The Philosophy of Psychology. Sage, London. 96–107.

Glock, Hans-Johann. 1996. “Necessity and Normativity,” in Hans Sluga and David G. Stern (eds.). The Cambridge Companion to Wittgenstein. Cambridge University Press, Cambridge and New York. 198–225.

Glock, Hans-Johann. 2003. Quine and Davidson on Language, Thought and Reality. Cambridge University Press, Cambridge.

Grice, H. P. and P. F. Strawson. 1956. “In Defence of a Dogma,” Philosophical Review 65: 141–158.

Gutting, Gary. 2009. What Philosophers Know: Case Studies in Recent Analytic Philosophy. Cambridge University Press, Cambridge.

Hylton, P. 2006. “W. V. Quine (1908–2000),” in A. P. Martinich and David Sosa (eds.), A Companion to Analytic Philosophy. Blackwell, Malden, Mass. and Oxford. 181–204.

Nimtz, C. 2003. “Analytic Truths – Still Harmless After All These Years?,” in H. J. Glock, K. Gluer, and G. Keil (eds.), Fifty Years of Quine’s ‘Two Dogmas’. Rodopi, Amsterdam and New York. 91–118.

Putnam, Hilary. 1962. “The Analytic and the Synthetic,” Minnesota Studies in the Philosophy of Science 3: 358–397.

Putnam, Hilary. 1975. “The Analytic and the Synthetic,” in Hilary Putnam, Mind, Language and Reality. Philosophical Papers. Volume 2. Cambridge University Press, Cambridge. 33–69.

Quine, Willard Van Orman. 1951. “Two Dogmas of Empiricism,” Philosophical Review 60: 20–43.

Quine, Willard Van Orman. 1960. Word and Object. M.I.T. Press, Massachusetts.

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Quine, Willard Van Orman. 1991. “Two Dogmas in Retrospect,” Canadian Journal of Philosophy 21.3: 265–274.

Quinton, Anthony. 1967. “The a priori and the analytic,” in P. F. Strawson (ed.), Philosophical Logic. Oxford University Press, Oxford. 107–128.

What is the Epistemological Status of Praxeology and the Action Axiom?

A reading of the opening chapters of Mises’s Human Action does not provide straightforward answers.

First, consider these statements:

“Praxeology is a theoretical and systematic, not a historical, science. Its scope is human action as such, irrespective of all environmental, accidental, and individual circumstances of the concrete acts. Its cognition is purely formal and general without reference to the material content and the particular features of the actual case. It aims at knowledge valid for all instances in which the conditions exactly correspond to those implied in its assumptions and inferences. Its statements and propositions are not derived from experience. They are, like those of logic and mathematics, a priori. They are not subject to verification and falsification on the ground of experience and facts. They are both logically and temporally antecedent to any comprehension of historical facts. They are a necessary requirement of any intellectual grasp of historical events” (Mises 2008: 32).

“Even the most faithful examination of a chapter of economic history, though it be the history of the most recent period of the past, is no substitute for economic thinking. Economics, like logic and mathematics, is a display of abstract reasoning. Economics can never be experimental and empirical. The economist does not need an expensive apparatus for the conduct of his studies. What he needs is the power to think clearly and to discern in the wilderness of events what is essential from what is merely accidental” (Mises 2008: 864).

“What assigns economics its peculiar and unique position in the orbit both of pure knowledge and of the practical utilization of knowledge is the fact that its particular theorems are not open to any verification or falsification on the ground of experience. Of course, a measure suggested by sound economic reasoning results in producing the effects aimed at, and a measure suggested by faulty economic reasoning fails to produce the ends sought. But such experience is always still historical experience, i.e., the experience of complex phenomena. It can never, as has been pointed out, prove or disprove any particular theorem. The application of spurious economic theorems results in undesired consequences. But these effects never have that undisputable power of conviction which the experimental facts in the field of the natural sciences provide. The ultimate yardstick of an economic theorem’s correctness or incorrectness is solely reason unaided by experience” (Mises 1949: 858).

So here we are told that the “theorems” of praxeology “are not open to any verification or falsification on the ground of experience.” The “statements and propositions” of praxeology are “not derived from experience.” If this means that the deductions that constitute praxeological theories are true a priori, then Mises is saying that praxeology knowledge has necessary, a priori truth.

But, in addition to being valid and sound, a deductive argument could only have absolute certainty if its axioms and premises are all necessarily true.

But Mises admits that praxeology uses synthetic a posteriori premises and assumptions in its arguments:

“Man … can never be absolutely certain that his inquiries were not misled and that what he considers as certain truth is not error. All that man can do is to submit all his theories again and again to the most critical reexamination. This means for the economist to trace back all theorems to their unquestionable and certain ultimate basis, the category of human action, and to test by the most careful scrutiny all assumptions and inferences leading from this basis to the theorem under examination. It cannot be contended that this procedure is a guarantee against error. But it is undoubtedly the most effective method of avoiding error” (Mises 2008: 68).

“Every theorem of praxeology is deduced by logical reasoning from the category of action. It partakes of the apodictic certainty provided by logical reasoning that starts from an a priori category. Into the chain of praxeological reasoning the praxeologist introduces certain assumptions concerning the conditions of the environment in which an action takes place. Then he tries to find out how these special conditions affect the result to which his reasoning must lead. The question whether or not the real conditions of the external world correspond to these assumptions is to be answered by experience. But if the answer is in the affirmative, all the conclusions drawn by logically correct praxeological reasoning strictly describe what is going on in reality” (Mises 1978: 44).

The idea that every “theorem of praxeology is deduced by logical reasoning from the category of action” and thus has “apodictic certainty” could only be true if all premises – both hidden and stated – in deductions are also absolutely true (as merely analytic a priori propositions) and all arguments were valid and sound.

But that argument will not work, because Mises has admitted that praxeological reasoning requires synthetic a posteriori propositions which can never be necessarily true or free from at least some small degree of doubt about their truth. Therefore no derived deduction or theory can have true “apodictic certainty”: this is a wild fantasy of Mises.

In Human Action (Mises 2008: 65–68) and The Ultimate Foundation of Economic Science (Mises 1978 [1962]: 44), Mises has tacitly conceded that praxeology’s deductive reasoning will sometimes rely on some empirical assumptions.

Now Mises believes in categories of the human mind and that the action axiom is a category:

“the problem of the a priori is of a different character. It does not deal with the problem of how consciousness and reason have emerged. It refers to the essential and necessary character of the logical structure of the human mind.

The fundamental logical relations are not subject to proof or disproof. Every attempt to prove them must presuppose their validity. It is impossible to explain them to a being who would not possess them on his own account. Efforts to define them according to the rules of definition must fail. They are primary propositions antecedent to any nominal or real definition. They are ultimate unanalyzable categories. The human mind is utterly incapable of imagining logical categories at variance with them. No matter how they may appear to superhuman beings, they are for man inescapable and absolutely necessary. They are the indispensable prerequisite of perception, apperception, and experience.” (Mises 2008: 34).

“The human mind is not a tabula rasa on which the external events write their own history. It is equipped with a set of tools for grasping reality. Man acquired these tools, i.e., the logical structure of his mind, in the course of his evolution from an amoeba to his present state. But these tools are logically prior to any experience.

Man is not only an animal totally subject to the stimuli unavoidably determining the circumstances of his life. He is also an acting being. And the category of action is logically antecedent to any concrete act.

The fact that man does not have the creative power to imagine categories at variance with the fundamental logical relations and with the principles of causality and teleology enjoins upon us what may be called methodological apriorism.

Everybody in his daily behavior again and again bears witness to the immutability and universality of the categories of thought and action. He who addresses fellow men, who wants to inform and convince them, who asks questions and answers other people's questions, can proceed in this way only because he can appeal to something common to all men--namely, the logical structure of human reason. The idea that A could at the same time be non-A or that to prefer A to B could at the same time be to prefer B to A is simply inconceivable and absurd to a human mind. We are not in the position to comprehend any kind of prelogical or metalogical thinking. We cannot think of a world without causality and teleogy.” (Mises 2008: 35).

“Aprioristic reasoning is purely conceptual and deductive. It cannot produce anything else but tautologies and analytic judgments. All its implications are logically derived from the premises and were already contained in them. Hence, according to a popular objection, it cannot add anything to our knowledge.

All geometrical theorems are already implied in the axioms. The concept of a rectangular triangle already implies the theorem of Pythagoras. This theorem is a tautology, its deduction results in an analytic judgment. Nonetheless nobody would contend that geometry in general and the theorem of Pythagoras in particular do not enlarge our knowledge. Cognition from purely deductive reasoning is also creative and opens for our mind access to previously barred spheres. The significant task of aprioristic reasoning is on the one hand to bring into relief all that is implied in the categories, concepts, and premises and, on the other hand, to show what they do not imply. It is its vocation to render manifest and obvious what was hidden and unknown before.” (Mises 2008: 38).

“The scope of praxeology is the explication of the category of human action. All that is needed for the deduction of all praxeological theorems is knowledge of the essence of human action. It is a knowledge that is our own because we are men; no being of human descent that pathological conditions have not reduced to a merely vegetative existence lacks it. No special experience is needed in order to comprehend these theorems, and no experience, however rich, could disclose them to a being who did not know a priori what human action is. The only way to a cognition of these theorems is logical analysis of our inherent knowledge of the category of action. We must bethink ourselves and reflect upon the structure of human action. Like logic and mathematics, praxeological knowledge is in us; it does not come from without.

All the concepts and theorems of praxeology are implied in the category of human action.” (Mises 2008: 64).

“… it is expedient to establish the fact that the starting point of all praxeological and economic reasoning, the category of human action, is proof against any criticisms and objections. No appeal to any historical or empirical considerations whatever can discover any fault in the proposition that men purposefully aim at certain chosen ends. No talk about irrationality, the unfathomable depths of the human soul, the spontaneity of the phenomena of life, automatisms, reflexes, and tropisms, can invalidate the statement that man makes use of his reason for the realization of wishes and desires. From the unshakable foundation of the category of human action praxeology and economics proceed step by step by means of discursive reasoning. Precisely defining assumptions and conditions, they construct a system of concepts and draw all the inferences implied by logically unassailable ratiocination. With regard to the results thus obtained only two attitudes are possible; either one can unmask logical errors in the chain of the deductions which produced these results, or one must acknowledge their correctness and validity.” (Mises 2008: 67).

From these statements, it is clear that Mises is influenced by a Kantian or, more correctly, neo-Kantian epistemology (Lachmann 1976: 56; Rothbard 2011: 108) of the Marburg school.

The human action axiom can be stated as follows:

(1) All human action is rational.

That statement when asserted without defining “rational” is likely to provoke derision, because if by “rational” we mean consistent with the laws of logic and characterised by valid and sound deductive and inductive reasoning, then there are manifestly many examples of irrational human behaviour.

But Mises has his own idiosyncratic definition of “rational”: he means with a purpose, or end in mind.

Therefore the proposition is to be rewritten:

(1) All human action is purposeful, in the sense of having a purpose or end in mind.

But even here problems exist. What about unconscious and involuntary behaviour? What about behaviour of mentally ill human beings? What about nervous tics?

Mises is already required to carefully limit what he means by “human action”:

“Human action is purposeful behavior. Or we may say: Action is will put into operation and transformed into an agency, is aiming at ends and goals, is the ego’s meaningful response to stimuli and to the conditions of its environment, is a person’s conscious adjustment to the state of the universe that determines his life. Such paraphrases may clarify the definition given and prevent possible misinterpretations. But the definition itself is adequate and does not need complement of commentary.

Conscious or purposeful behavior is in sharp contrast to unconscious behavior, i.e., the reflexes and the involuntary responses of the body’s cells and nerves to stimuli. People are sometimes prepared to believe that the boundaries between conscious behavior and the involuntary reaction of the forces operating within man’s body are more or less indefinite. This is correct only as far as it is sometimes not easy to establish whether concrete behavior is to be considered voluntary or involuntary. But the distinction between consciousness and unconsciousness is nonetheless sharp and can be clearly determined.

The unconscious behavior of the bodily organs and cells is for the acting ego no less a datum than any other fact of the external world. Acting man must take into account all that goes on within his own body as well as other data, e.g., the weather or the attitudes of his neighbors. There is, of course, a margin within which purposeful behavior has the power to neutralize the working of bodily factors. It is feasible within certain limits to get the body under control. Man can sometimes succeed through the power of his will in overcoming sickness, in compensating for the innate or acquired insufficiency of his physical constitution, or in suppressing reflexes. As far as this is possible, the field of purposeful action is extended. If a man abstains from controlling the involuntary reaction of cells and nerve centers, although he would be in a position to do so, his behavior is from our point of view purposeful.

The field of our science is human action, not the psychological events which result in an action. It is precisely this which distinguishes the general theory of human action, praxeology, from psychology. The theme of psychology is the internal events that result or can result in a definite action. The theme of praxeology is action as such. This also settles the relation of praxeology to the psychoanalytical concept of the subconscious. Psychoanalysis too is psychology and does not investigate action but the forces and factors that impel a man toward a definite action. The psychoanalytical subconscious is a psychological and not a praxeological category. Whether an action stems from clear deliberation, or from forgotten memories and suppressed desires which from submerged regions, as it were, direct the will, does not influence the nature of the action.” (Mises 2008: 11–12).

It follows that “human action” is to be strictly limited to:

(1) the conscious behaviour of humans;

(2) to exclude unconscious and involuntary behaviour, and

(3) (presumably) to non-mentally ill human beings.

But Mises requires empirical evidence to demonstrate that all these things do not constitute voluntary behaviour with a purpose.

How does Mises know that normal functioning of the organs or blinking of the eyes is not conscious behaviour with a purpose? He might appeal to intuition and personal experience, but his critic can reply (rightly, in my view) that this is just a type of empirical evidence. And, ultimately, it is through empirically-based science that we have good grounds for understanding these things to be involuntary, or for understanding that certain mentally ill people do things with no conscious purpose in mind.

Another example is nervous tics: these are perfect examples of involuntary and compulsive behaviour with no discernible purpose or end in mind. Yet we can only know that nervous tics are involuntary neurological disorders after scientific investigation of such phenomena.

Let us now look at the proposition again:

(1) All human action is purposeful, in the sense of having a purpose or end in mind.

After these careful restrictions on the definitions of terms and the empirical evidence for excluding certain people and actions, the proposition cannot be considered as true a priori or as synthetic a priori: it is a synthetic a posteriori proposition.

It is, frankly, no surprise that the whole fairy tale of praxeology built on a neo-Kantian category or as synthetic a priori knowledge was abandoned by Murray Rothbard who regarded the axioms of praxeology as having a “broadly empirical nature” (Rothbard 2011: 65).

But once one admits that one’s starting axiom is only true a posteriori there is serious problem. Rothbard cannot then claim that all derived inferences and theories of praxeology have apodictic truth because something known a posteriori can never have absolute or apodictic truth: there must be always, even in the most convincing inductive argument, some small degree of doubt or uncertainty about the truth of the induction given the fact that the foundational axiom is not necessarily true. The further consequence that all other axioms of the system are only true a posteriori requires that the theory is indeed grounded in empirical matters of contingent fact, and that, ultimately, must be tested against reality and also describe reality.

I end with some serious questions about Mises’s competence in logic.

Hans Albert points out the following:

“Mises gives a Kantian answer to the question of how the a priori character of praxeological knowledge and its apodictic certainty is to be explained. This knowledge apparently can be reduced to the logical structure of the human mind which is supposed to be the basis for thought and action. ... On the one hand he seems to suggest that he is introducing with his principle of action a synthetic a priori proposition, as he ascribes informational content to the principle. On the other hand, he declares the question of whether the respective propositions are synthetic or analytic to be purely verbal and therefore uninteresting. This seems to show that he was not aware of the connection between analyticity and informational vacuity. He permanently compares his allegedly a priori knowledge with logical and mathematical knowledge and gives such a description of the respective propositions and their mode of derivation that one comes to suspect them to be analytic. He confounds the analytical character of propositions with the logical character of the relationships between propositions in a deduction. But the fact that particular propositions are deducible from particular sets of premises does not render them analytic. For instance, in physics propositions from geometry get an empirical interpretation, and, interpreted in this way, they are synthetic. But propositions which are the result of the ‘logical unfolding’ of certain concepts contain no information. They are analytic not because they are derived, but because they follow from definitions which do not carry information themselves. When Mises tells us that the concept of money already implies all theorems of the theory of money, the alleged certainty of the basis of this derivation does not help him to establish a nonvacuous economic theory. The theory of money as he envisages it here would be without informational content and could not be used to explain anything.” (Albert 1999: 131–132).

Finally, the human mind has been given a certain structure and way of interpreting the world and certain intuitions, which roughly correspond to Kant’s categories, but this structure is undoubtedly the product of Darwinian evolution (Albert 1999: 132), and has been adapted to the experience of an external environment to allow survival and success in that environment. Mises himself acknowledges the role of evolution in this respect (Mises 2008: 33). But our knowledge of these facts and the structure of the mind cannot consist of analytic propositions: it has been discovered by empirical science.


BIBLIOGRAPHY
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