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.

The Types of Propositional Knowledge

This subject is important for economic methodology.

In essence, there are arguably three types of proposition, as follows:

(1) analytic a priori propositions;

(2) synthetic a posteriori propositions
These are further divided into two forms:

(i) ontologically necessary, synthetic a posteriori propositions;
(ii) ontologically contingent, synthetic a posteriori propositions;

(3) metaphysical propositions.

The first two categories are taken directly from epistemology in modern analytic philosophy, and the subcategories of (2) follow the work of Saul Kripke (Kripke 1980).

The third category – metaphysical propositions – is inspired by the ideas of Karl Popper and Bertrand Russell.

Let us take category (1) first. Analytic a priori propositions are those like “all bachelors are unmarried”: they are true if and only if they are true solely by virtue of the meanings of terms used (understood as having their standard meanings and applied consistently). An analytic proposition is known a priori: or without appeal to experience. In epistemic terms, it has necessary truth.

Synthetic a posteriori propositions – or category (2) – are those propositions that are not analytic, and are known a posteriori (or by experience, empirical evidence and inductive arguments).

These come in two forms, as follows:

(i) necessary synthetic a posteriori propositions
These are ontologically necessary in that they have either physical or metaphysical necessity. Epistemologically, however, we cannot know with apodictic truth that they are really ontologically necessary.

(ii) contingent synthetic a posteriori
Such statements are not ontologically necessary and are contingent, in that they might have been false.

Category 3 – metaphysical propositions – is inspired partly by Karl Popper’s idea of an unfalsifiable proposition and Bertrand Russell’s teapot thought experiment, though not identical with either of these.

A metaphysical proposition would be one that it is synthetic in that it is not analytic, and that asserts the real ontological existence of something but not verifiable or falsifiable a posteriori. That is, it would not be verifiable by any means to anyone else except the person who asserts it, e.g., if someone claimed that there was an invisible, incorporeal, undetectable unicorn in his garden, then this would be a “metaphysical proposition.” Furthermore, when pressed, the person would say that the unicorn does not even appear to him in any normal sensory way (say, by vision, hearing, touch, smell), but he knows it exists by some “special,” non-sensory intuition, revelation or supernatural insight.

The person asserting a metaphysical proposition claims some special epistemological access to “knowing” that it is true that defies the standard a priori or a posteriori categories. One could think up any number of mystical, irrational and obviously ridiculous propositions that would belong to this category. But one could also point to certain religious or supernaturalist ideas that are real examples of such metaphysical propositions.

In theory, any proposition could be classified into one of these categories.

But there are also these important types of proposition relevant to economics:

(1) Counterfactuals
The epistemological status of counterfactual propositions is not straightforward. Any given counterfactual might be either (1) analytic a priori when an abstract statement, or (2) synthetic a posteriori when an empirical statement.

(2) Laws of nature
Laws of nature can be interpreted as synthetic a posteriori propositions. On the traditional “regularity” theory of laws of nature, they contingent synthetic a posteriori.

On a necessitarian interpretation, they are necessary synthetic a posteriori propositions.

(3) Ceteris paribus laws
These could be either (1) analytic a priori when purely abstract or (2) synthetic a posteriori when asserted as true of reality.

BIBLIOGRAPHY
Kripke, Saul A. 1980. Naming and Necessity (rev. edn.). Blackwell, Oxford.

Deduction, Necessary Truth and the Real World

Consider this categorical syllogism:

Major premise: All bachelors are unmarried.

Minor premise: John is a bachelor

Conclusion: Therefore John is unmarried.

If valid and sound, the conclusion has necessary truth.

But that necessary truth is arguably de dicto necessity: a necessity that is a property of the argument being an analytic a priori system, where “John” is merely a hypothetical person who is a bachelor by definition. It follows that even the conclusion must be understood as analytic a priori.

But once we assert “John is a bachelor” of a real and specific person in the world, suddenly something important happens: the minor premise “John is a bachelor” becomes synthetic a posteriori, and can only be proved a posteriori, or by experience, empirical evidence and inductive arguments. The truth of the minor premise therefore becomes contingent, not necessary. It can never have apodictic truth, because there must always be some small doubt about its truth: for example, if John says he is unmarried, then he might be lying or delusional (e.g., perhaps he is mentally ill). If public records say John is unmarried, they may be in error or fraudulent. If John’s friends say he is unmarried, then they may also be mistaken or taken in by John’s lies, and so on.

There is no way to obtain absolute and apodictic truth in propositions known a posteriori.

The consequence of this is that the deduction above only has necessary truth when it is strictly understood as an analytic a priori argument and where the logical necessity is de dicto necessity.

When asserted of a real person, the minor premise and the argument can never be proved in the sense of being absolutely true, because we cannot have apodictic truth about a synthetic a posteriori proposition (the minor premise).

The belief that the syllogism has necessary and absolute truth about any concrete real world person is an illusion that arises by merely assuming the world conforms exactly to the assumptions and requirements of analytic a priori argument: we are using words to abolish uncertainty and effectively imposing an unempirical argument on the real world that can only be known a posteriori. In short, we are conflating (1) the analytic a priori with (2) the synthetic a posteriori, when they are strictly separate.

It has become fashionable in modern analytic philosophy to admit the existence of a second type of necessity: de re necessity. Here it is conceived that the possession of a property y by a certain thing x is logically necessity for it to be identified as a certain kind or type x (a type of essentialist argument).

For example, water is necessarily H₂O: for a thing to be the substance we call water, it must be by necessity have the property of being physically H₂O.

But one can wonder whether this new view that there are necessary a posteriori truths and metaphysical/ontological necessity has gone too far.

Consider the proposition:

Statement 1: water is necessarily H₂O.

Conceived as an analytic a priori statement, it has necessary truth.

But let us consider this statement:

Statement 2: This specific real world sample of water is necessarily H₂O.

Here we face the skeptical challenge and Hume’s problem of induction: how can you be absolutely certain that what you are looking at is water at all? You may have made some error. It might be something that looks like water but is not physically H₂O. Even a scientific analysis of the substance that seems to show that it is chemically H₂O could in theory be mistaken or fraudulent. Or a more elaborate sceptical challenge would be: how can you be absolutely certain that anything you have seen now or in the past that you call water really is H₂O and not some elaborate trick by Descartes’ demon?

Statement 2 above asserted of a real world thing must simply abolish uncertainty by begging the question and assuming all epistemological problems and challenges can be countered, in much the same way that the original syllogism above when asserted as absolutely and necessarily true of any concrete real world person simply abolishes uncertainty and renders the argument analytic a priori.

One could argue, then, that modern metaphysical (essentialist) necessity remains a property of analytic a priori systems.

Mises Fails Philosophy of Mathematics 101

My post below makes a broad point about the intellectual bankruptcy of aprioristic praxeology on the basis of Mises’s misunderstanding of modern epistemology and the philosophy of mathematics.

The evidence for Mises’s misunderstanding of philosophy of mathematics is here in Human Action:

“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)

“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).

First, Mises’s belief that aprioristic reasoning can deliver new, informative knowledge of the real world fails because it is all dependent on the untenable idea of Kantian synthetic a priori knowledge.

Kant’s belief in the synthetic a priori is false, and we know this now given the empirical evidence in support of non-Euclidean geometry: this damns Kant’s claim that Euclidean geometry – the geometry of his day – was synthetic a priori (Salmon 2010: 395). In addition, despite Gödel’s incompleteness theorems and the failure of Bertrand Russell’s strict logicist program, the consensus today is that most of classical mathematics can nevertheless be derived from pure logic and set theory (Schwartz 2012: 19), just as Russell thought,* and it is arguably just analytic a priori knowledge (and even arithmetic might be conceptually divided into (1) analytic a priori pure arithmetic and (2) synthetic a posteriori applied arithmetic [see Musgrave 1993: 240]).

Furthermore, as I have already shown, the human action axiom cannot be considered to be a synthetic a priori statement.

But the real issue raised by Mises here is the epistemological status of geometry, or, more precisely, Euclidean geometry.

Mises has failed to distinguish between geometry in its role as (1) a pure mathematical theory, and as (2) applied geometry (for the distinction, see Salmon 2010: 395). Mises’s statements are ignorant and wrong, because he conflates these two distinct forms of geometry. The inability to separate geometry into these senses – pure geometry versus applied geometry – leads to all sorts of philosophical disasters, amongst them Platonic mystical belief in the eternal realm of the forms and aprioristic Rationalism (the derivation of these things from Euclidean geometry is described in Salmon 2010: 393).

Rudolf Carnap explains the difference pure geometry and applied (physical) geometry:

“It is necessary to distinguish between pure or mathematical geometry and physical geometry. The statements of pure geometry hold logically, but they deal only with abstract structures and say nothing about physical space. Physical geometry describes the structure of physical space; it is a part of physics. The validity of its statements is to be established empirically—as it has to be in any other part of physics—after rules for measuring the magnitudes involved, especially length, have been stated. (In Kantian terminology, mathematical geometry holds indeed a priori, as Kant asserted, but only because it is analytic. Physical geometry is indeed synthetic; but it is based on experience and hence does not hold a priori. In neither of the two branches of science which are called ‘geometry’ do synthetic judgements a priori occur. Thus Kant’s doctrine must be abandoned).” (Carnap 1958: vi).

When Euclidean geometry is considered as a pure mathematical theory, it is nothing but analytic a priori knowledge, and asserts nothing of the world, since it is tautologous and non-informative.

But, when Euclidean geometry is applied to the world, it is judged as making synthetic a posteriori statements (Musgrave 1993: 236; Ward 2006: 25), which can only be verified or falsified by experience or empirical evidence (or, in the jargon of philosophy, can be known as true only a posteriori).

That is to say, applied Euclidean geometrical statements can be refuted empirically, and, indeed, Euclidean geometry – when asserted as a universally true theory of space – is now known to be a false theory (Putnam 1975: 46; Hausman 1994: 386; Musgrave 2006: 329). Non-Euclidean geometry is now understood to be a better theory of reality. When confined to its role as a pure mathematical theory, Euclidean geometry is true but vacuous. That is to say, modern apriorist Rationalists can defend the necessary, a priori truth of Euclidean geometry (as in Katz 1998: 49–50), but only as a pure mathematical theory that is vacuous, non-informative and tautologous. It tells us no necessary truth about reality (Salmon 2010: 395).

But isn’t Euclidean geometry still a useful empirical theory in certain ways? Yes, but this does not save Mises. Euclidean geometry is useful only because it is an approximation of reality and only at certain levels of space (Ward 2006: 25). But it is still false when judged as a universal theory of space.

Even on the most generous estimate, all you could argue is that Euclidean geometry is true only in a highly limited domain: the relatively small, macroscopic spaces and distances humans normally deal with in everyday life. But, once we move beyond this world, Euclidean geometry is false.

And even this qualification does not save the Misesian and Austrian apriorists, because we can only know that geometry is true in its limited domain a posteriori, that is, by empirical evidence.

As soon as Euclidean geometry as pure mathematics is used beyond its tautologous form, it becomes a system making synthetic a posteriori statements, not Kant’s imaginary synthetic a priori.

Since synthetic a priori propositions do not exist, it follows from this that, if Mises thinks that the axioms of praxeology are analytic a priori, then praxeology would indeed be a tautological system that is non-informative, and asserts nothing necessarily and apodictically true about the real world. The only viable route left for modern Misesian praxeologists is to accept the empirical nature of the human action axiom (and other axioms) and admit that derived praxeological theorems are empirical.

That is to say, as soon as praxeology is taken as a system that asserts something about the real world of human economic life (and is not simply asserted as a non-informative, tautologous and vacuous system), it must be judged, like applied geometry, as making synthetic a posteriori statements, which – contrary to Mises’s bizarre assertions cited above (Mises 2008: 32) – can certainly be refuted by experience and empirical evidence.

Like Kant, Mises’s project is damned, as is traditional Rationalist epistemology in general, as has been noted by the Popperian philosopher Alan Musgrave:

“The invention of non-Euclidean geometries deprived rationalism of its paradigm. It also suggested to empiricists a new way to deal with mathematics: distinguish pure mathematics from applied mathematics, locate the latter in the synthetic a posteriori compartment of Kant’s box, and the former in the analytic a priori compartment of Kant’s box. One attempt to do the last, logicism, is generally admitted to have failed. Another attempt, if-thenism, is still hotly debated among philosophers. On the other hand, the logical empiricist view of applied mathematics has met with pretty wide acceptance. The rationalist dream, ‘certain knowledge of the objects of experience by means of pure thinking’, is shattered even though the nature of pure mathematics remains problematic indeed.” (Musgrave 1993: 245–246).

Note
* Successors of logicism include (1) the formalism of David Hilbert; (2) conditionalism or “if-thenism” (a term coined by Hilary Putnam), which is a deductivist version of formalism (see Musgrave 1977); and (3) various forms of Intuitionism.


BIBLIOGRAPHY
Carnap, Rudolf. 1958. “Introduction,” in Hans Reichenbach, The Philosophy of Space and Time (trans. Maria Reichenbach and John Freund). Dover, York.

Elugardo, R. 2010. “Analytic/Synthetic, Necessary/Contingent, and a priori/a posterori: Distinction,” in Alex Barber and Robert J Stainton (eds.), Concise Encyclopedia of Philosophy of Language and Linguistics. Elsevier, Oxford. 10–19.

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.

Katz, Jerrold J. 1998. Realistic Rationalism. MIT Press, Cambridge, Mass.

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

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

Musgrave, Alan. 1993. Common Sense, Science and Scepticism: Historical Introduction to the Theory of Knowledge. Cambridge University Press, Cambridge.

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.

Reichenbach, Hans. 1958. The Philosophy of Space and Time (trans. Maria Reichenbach and John Freund). Dover, York.

Salmon, W. C. 2010. “Geometry,” in Jonathan Dancy, Ernest Sosa, and Matthias Steup (eds.), A Companion to Epistemology (2nd edn.). Wiley-Blackwell, Chichester, UK and Malden, MA. 393–395.

Schwartz, Stephen P. 2012. A Brief History of Analytic Philosophy: From Russell to Rawls. Wiley-Blackwell, Chichester, UK.

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