Economics and Social Justice: A Type-Token Consideration

Originally this paper was presented at the UC Davis Philosophy Undergraduate Conference in the Spring of 2016 (here). The compliment which remains with me today is from the keynote speaker, Dr. Weijers, who recommended that I expand this consideration to form the groundwork for a book as a counter-response to the prevailing theory that abstract subjects have little to no application in our practical, real-world experiences – especially metaphysics. However, this paper, if it were ever to be expanded into a book, would make two radical conclusions. First, that our purely abstracted concepts stand in much closer relation to our purely pragmatic experiences than we are willing to acknowledge. And second, if we follow the conceptual principles and criteria advocated by the modern Social Justice Warrior, they will lead us to intellectual suicide. Of which, in part, my comfort of our return to sanity is to be found in my magnum-opus-hopeful Concept, Number, and God.


Economics and Social Justice: A Type-Token Consideration [1]

“The whole situation has arisen, as we have seen, from the endeavor to describe an external world ‘explanatory’ of our various individual sensations and emotions, but a world, also not essentially dependent upon any particular sensations or upon any particular individual.” – Alfred Whitehead, An Introduction to Mathematics

One of the great misfortunes of studying multiple subjects is not, contrary to the popular beliefs of those within each subject, the internal consistency of each subject, but the greater difficulty in seeing how these subjects work inconsistently alongside each other. The thesis of my paper is that there exists a singular problem –namely, the type/token relationship problem – which not only shadows Metaphysics, Epistemology, and Philosophy of Language, but also kicked under the rug, and at the expense of great reward, in Economics, that happens to resurface as a climactic modern social problem in how we are currently conceiving the notion of Social Justice.

I will be presenting this paper in five major points: First, I’ll provide an explanation of the common skeptical hypotheses found in Metaphysics, Epistemology, and Philosophy of Language as the Skepticism concerning Causality, Skepticism concerning Induction, and the Kripkenstein argument from the impossibility of Private Language. Second, I’ll provide a brief argument why I believe each of these skeptical hypotheses could simply be reduced to a problem with establishing a type in relation to some set of finite instances of tokens. These tokens being the unique subject matter of each circumstance. Third, I’ll briefly explain that Economics, as perhaps is so with all natural and social sciences, takes full advantage of creating models and scientific hypotheses rooted in simply sweeping under the rug these philosophical problems. Fourth, I will briefly explain that one of the large problems facing our modern society, namely, racial social justice, is a resurfacing, or discontinuity, of this problem coming back out from under the rug of our economic benefits, and perhaps even all natural and social sciences. And fifth, I leave my project open-ended with a simple question, “Do our solutions concerning these problems in Metaphysics, Epistemology, and Philosophy of Language have practical, moral, and social repercussions which we are failing to take into consideration?”

Part 1 – The Skeptical Hypotheses

Metaphysical Skepticism of Cause and Effect:

Hume’s skepticism concerning Cause and Effect can only be understood in light of his strong Empiricism. This empiricistic assumption is guide for Hume in his central question of how do we bridge causes with effects. What impressions do we receive of this connection, if any, and how may we respond?


First, Hume begins by delineating two sorts of categories of knowledge: Relations of Ideas and Matters of Fact. Relations of Ideas are truths such as Geometry, Algebra, and Arithmetic. These are truths which are derived exclusively by the relationship between numbers, and, as such, they will always retain their certainty and evidence. Matters of Fact, on the other hand, are not only known in a different sort of way, but their truths, and contingency of truth, are extraordinarily different from Relations of Ideas. For example, in Matters of Fact, contraries are possible to whatever is being stated because the contrary will never imply a contradiction. Furthermore, the falsity of some proposition concerning a matter of fact, cannot be determined by an act of the mind, but only by demonstration.


This latter category of knowledge is the sort of knowledge which Hume intends to question and disrupt its securities. Matters of fact appear to depend upon the relation between cause and effect. We should then inquire to the nature, and how we obtain knowledge of cause and effect.


As a first step, Hume asserts that Cause and effect are not a priori truths for two reasons. First, a priori reasons, if they can contribute anything to illuminate the principle of Cause and Effect, are only insofar as highlighting possibility and not preference of certain cause and effect relationships. And second, experience, via sense impressions, are the only source of determinative knowledge concerning which preference an object will take in any cause and effect pair. Therefore, Hume’s quest could be highlighted by three questions:


  • What is the nature of all our reasonings concerning matter of fact?
  • What is the foundation of all our reasonings and conclusions concerning that relation?
  • What is the foundation of all conclusions from experience?

To the above, Hume will provide a negative answer: our conclusions concerning cause and effect are not based upon reason, or any process of the understanding. Past Experience can be allowed to give direct and certain information of those precise objects only, and that precise period of time, which fell under its cognizance. “But why this experience to future times, and to other objects?” (2) Does it necessarily follow that because one thing possess something that others would as well? To answer this, Hume constructs a two-part response which, in his articulation, forms our basic intuition of cause and effect:


  1. I have found that such an object has always been attended with such an effect
  2. I foresee that other objects, which are, in appearance, similar, will be attended with similar effects.


But what connects A to B or vice versa? We need some statement C to provide the “inferential glue” to the above.


The answer is through a series of negative arguments. Again, as above, Hume provides us with two sorts of reasoning: Demonstrative and Moral. Demonstrative Reasoning (ie. Relations of Ideas) is obviously not this sort of reasoning which Hume believes will provide us with statement C. The other is Moral Reasoning (ie. Matters of Fact and Existence), and, quite literally for Hume, this is the pudding where the proof lies. Whatever is our connection between two Matters of Fact, we must begin by investigating our modes of reasoning concerning Matters of Fact.


However, Hume points out a tautological similarity:


a’. “I have found, in all past instances, such sensible qualities conjoined with such secret powers.”[2]

b’. “Similar sensible qualities will always be conjoined with similar secret powers.”[2]


Hume then concludes that if we are to reason out cause and effect, then we must come to it by some other means – a means worth investigating. This principle Hume calls “Custom or Habit”, but not reasoning. Memories and Senses record pairs of events, customary conjunction is then an implied property of repetition. And this implication isn’t reasoning, it’s a sub-species of instinct. Hume’s conclusion is that what bridges two events as cause and effect is simply an instinctual bond.

Epistemological Skepticism of Induction:

First – A General Framework of Induction


In our day-to-day living, all things being equal, we collect information about the outside world, we store it in our memory, and retrieve it for later events. This could be such knowledge as “the rules of poker” or “tomorrow, your train leaves at 9am from the Oxford station,” or “it was sunny yesterday.” And, quite frankly, if this was the only task for which we use knowledge and memory, the problem of induction would never arise. The reason is because the problem of induction is the problem of taking old knowledge and attempting to extend it to other events: it is the problem of justifying our inferred, new knowledge from old knowledge.

This perhaps could be better illustrated by explaining the difference between the nature of deductive and inductive logic. In Deductive Logic, the conclusion not only necessarily follows from premises but also follow logical forms. And these logical forms, be it syllogisms or the four forms (AEIO), are not so much as concerned with the contents but concerned with the relationships between each variable. On the other hand, in Inductive Logic, we fail to have such forms or syllogisms because Inductive Logic isn’t only concerned with the relationships between propositions, but also the contents of those propositions. The reasons are two-fold. First, in Inductive Logic, the conclusion doesn’t necessarily follow from the premises (ie. The premises can be true and the conclusion false). And, second, as an extension of the first, Inductive Logic is required to justify those terms which we say make a premise more or less “probable”, or “relatively probable”, and justify how those probabilities allow us to infer from one event A to another event B.
However, to put to use an exceedingly overused example, we could ask the question, “Will the sun rise tomorrow?” Obviously, we believe the sun will rise tomorrow, but, like Descartes’ Methodological Doubt, what criteria, or reason or method, may we be said to be justified in inferring from the past to the future, or from one thing to the existence of some other thing? We are inclined to say that we “infer it from past experiences,” but, the follow-up question would be,” But are we justified in asserting past experiences as evidence in that way?”


To answer this, we need to make an important distinction. When we say past experiences of repetitions is the cause for us to believe that the future will “keep the ball rolling”, so to say, down the same grooves, it appears that there are two types of statements we can make. First, we can make the psychological statement which says, “Past circumstances, habit, and instinct give rise to our expectations.” And second, we can ask the more pressing, and philosophical, question, “Do we have any rational basis for this expectation or, as Russell pointed out, are we simply the chicken about to get is neck wrung?”


And it is in the search to answer this question, therefore justifying induction, which has led so many philosophers to posit a large range of answers.


Second – The Problem of Induction
According to Hume, the rational man was the man who could make proper use of reason. This would imply that knowledge of the strength and weaknesses of evidence was taken into consideration. But if this is to be the definition of a rational man, then it would follow that one would also be required to know the relationship between one proposition and another.


Deduction, simply enough, allows us to necessarily entail our conclusion from true premises. However, to do the same for Induction, we would be required to provide some sort of justification for probability. What sort of inferences and what sort of justification? Hume assumed that:


“[W]e can have reason to believe in the truth of any proposition concerning an empirical
matter of fact only insofar as we are able to connect the state of affairs which it describes with something that we now perceive to remember.” [3]


Hume’s argument is that one may only believe, or have reason to believe, in the existence of any thing outside the datum of our experiences, if the unobserved thing is connected to that datum in a law-like fashion. In other words, given some experience y, we can only rationally expect z if there is some law-like connection x between y and z. He believes those “reasons” of law-like fashion are cause and effect. And, therefore, that is why Hume’s project was so concerned, and ended with, his view that we have no rational basis for induction because we have no rational basis for cause and effect.


Here are the nine stages of his argument, according to A.J. Ayer:

First, “Knowledge of the relation of cause and effect is not, in any instance, attained by reasoning a priori, but arises entirely from experience.” [3]


In other words, one could deny any cause and effect instance without a contradiction. The event A, “The sun rose yesterday”, has nothing in of itself which would guarantee event B, “The sun will rise tomorrow”. There is nothing in event A that entails any other event, B or otherwise. Furthermore, experience of cause and effect are only known by a posteriori reasoning.


Second, there is no such thing as synthetic necessary connections between events.
This is simply saying that in experience there is nothing in event A which would require that event B must follow.

Third, the only ground we have to believe that event A causes event B is due to a repetition of past experiences and their conjunction via a habit of the mind.

Fourth, therefore, given the above, inference from the premise, “All hitherto observed A’s bear relation R to B’s,”[3] to the conclusion, “This A will have the relation R to some B,”[3] is not formally valid.

Fifth, to ensure the above is a valid argument, some premise p must be added, such as the following:
“that instances of which we have had no experience, must resemble those of which we have had experience, and that the course of nature continues always uniformly the same.”[3]


Sixth, but we would be required to justify this principle. We can’t appeal to the reliability of the matters of fact, for that is what we are trying to prove. And we cannot appeal to the truths of the forms of deductive logic because for each inference we can imagine it not being the case without contradiction.
Seventh, perhaps one could argue that the principle isn’t demonstrable, but probable, again, arises, “How?” (We would have to then repeat the above steps). One could appeal to the Principle of Uniformity of Nature, but that, itself, is rooted upon the principle of induction – which we are attempting to justify.
Eighth, we could attempt to by-pass the Principle of Uniformity of Nature, but, then we fall back into the same problem of induction.
Ninth, because our inferences are not formally valid, and any attempts to justify results in circularity, we ought to be logically skeptical of induction while recognizing it as something we all believe in. In other words, while we cannot justify the principle of inductive logic, we can assert the psychological necessity for us to posit such inferences.

Philosophy of Language Skepticism of Private Language

Kripkenstein, a fictional reference to Kripke’s interpretation of Wittgenstein’s problem of language, makes a particularly complicated argument which I will shorten down to the central point. Say you are asked to answer the question, “What is 55 + 10?” You may be led to provide the answer “65”. The question, of course, is “How do you know?” The obvious response would be, “By the rules of addition which governs the ‘+’, or addition, function symbol.” While this may seem like a perfectly reasonable answer, one could further ask the question, “How do you know that you didn’t use the (+) (quus) operator?” The quus operator would be defined as, “If x<70, then 55+10 is 65. If x>70 then x is 5.” The question would then be asked again, “How do you know that in calculating 55+10 you are not using the quus operator instead of the plus operator?”

Perhaps it would be best to argue by analogy via James Ross’s work in his essay entitled Immaterial Aspects of Thought.

We can begin by asking the question, “Can judgments be definite pure forms?” It would appear that they are, if we desire to make judgments about validity, inconsistency, and truth. (And any formal thinking: Conjunction, disjunction, modus ponens, etc.).
However, what, exactly, is formal thinking? Formal thinking, and likewise formal thoughts, is any “form” which can be demonstrated in a single case, though all possibilities cannot be realized by any number of components, or length of each component, or understanding of the component itself. These are all contents of the form, a formal thought is “a form of understanding”[4].

This distinction between formal thoughts and the contents of those thoughts are made quite well when Ross writes, “The fact that I cannot process every case of modus ponens, because most of them have premises too long for me to remember, sentences too long to say, or words I do not understand, is adventitious, like my not being able to do modus ponens in Portuguese. Those are features of the functors, not of the function. The function that has to be realized in every case is the one wholly realized in the single case.”[4]


The important point to make note of in this argument is that formal functions, and functions of any type for that matter, are NOT the arrays, or sets, of inputs and outputs. Formal functions are the form by which inputs become outputs. That is why Ross argues that physical processes are not the same as thinking. Why? Because no matter how many physical inputs we may observe and no matter how many physical outputs we may observe, we will never be able to derive a formal function from it.

But why can’t we derive pure functions from some set of physical inputs and outputs? It is because any physical process is impotent in determining among incompossible abstract functions. But this point appears to simply be taken at face-value because of the work already complete in Analytic Philosophy when Ross writes, “Goodman’s “grue” considerations and the plus-quus adaptations by Kripke suggest the form of my argument to show that.”[4] “That”, being the physical indeterminacy of formal functions.

However, Ross is able to open a part of Kripke’s project concerning the plus-quus problem when he writes, “Whatever the discriminable features of a physical process may be, there will always be a pair of incompatible predicates, each as empirically adequate as the other, to name a function the exhibited data or process “satisfies”. That condition holds for any finite actual “outputs,” no matter how many.”[4] This point could be easily noted in the history of physics when describing the function of a pendulum (As Thomas Kuhn points out in his book The Structure of Scientific Revolutions) in Aristotelian, Newtonian, and Einsteinian physics. Each theory is incompossible with each other theory, but they all explain the same physical process. What Ross is arguing is that there is nothing about the swinging pendulum that would tell us whether or not Aristotle, Newton, or Einstein was correct.

The problem becomes worse when we consider that pure functions cannot be exhausted and, therefore, “’All the additions’ is as incoherent as ‘all the sets.’ So ‘what’ addition is cannot be explained by ‘all the outcomes’: rather, each and every outcome is determined by what addition is. It is impossible that all cases of addition be actual, even if infinities are performed because, even if we used up all the suitable numbers, the function itself would still be repeatable, say, for the same additions, but now done in a different order. The action cannot be exhausted by its cases, however many there are.”[4]

Part II – The Type/Token Relationship Problem

I believe all three of the previous skeptical problems could be reduced, at least formally and without regard to the nuances of each particular subject, to simply a problem between abstracting some type from some set of tokens. In the skepticism of causality, the problem appears to be abstracting some form of cause/effect type from some set of cause/effect tokens. In the skepticism of induction, it appears that we are attempting to posit some future state of affairs type from some set of tokens of past events. In the Skepticism of Private Language, it appears that we are attempting to justify some abstract function type from some collection of mental state tokens or, in Ross’s case, some physical state tokens.

If we are able to abstract out the nuances of each particular subject, in much the same way we can abstract out the content of number in axiomatic systems, I believe it is perfectly reasonable to argue that the isomorphic argument could be made that the problem in each form of skepticism is the skepticism of justifying some type from some collection of tokens.

Part III – The Economic Advantages of Induction

While it is well known that these type/token problems exist in philosophy, it appears that nothing of it is heard, or it is rarely spoken of, in economics.

If we can call an Economist anything, it is that they are data-miner in the highest degree of social analysis: human market order. Lots of data comes in, large models go out, projections are made, and courses of action are proposed. But a question seems to be looming over all of this labor. If there are so many problems facing these type-token relationships, then how is economics getting off the ground?

I believe the general response, or at least the popular response, has been simply to ignore the philosophical problems just mentioned. Lots of data comes in, large models go out, projections are made, and courses of action are proposed. But these philosophical problems haven’t been swept under the rug at, generally speaking, great consequences to the economist.

Given theories of economics such as Behavioral, NeoClassical, Keynesian, Austrian Economics, or Chicago School, have given us great insight into the sociological, economical, and psychological properties of society. While arguments such as the Black Swan Theory, an economic theory advancing the argument for the unpredictability of market change, have been advocated, I would assume that such have done very little in forcing economists to take these deeper philosophical problems into consideration. But, again, why should they? It has come at very little expense to their field.

This advantage could also be expanded to include any, or all, of the natural or social sciences. One could perhaps even argue that the knowledge ‘about’ anything in natural or social science is really to a seek knowledge ‘about’ a kind of thing – which is not a range of only ‘one’ but always of ‘many’.

Part IV – The Social Problems from Type/Token Inferences

However, I don’t believe these problems are unfelt, they are simply felt in another, but related, area. It is as if we have attempted to straighten the carpet by pressing down the crease only to find the crease has simply moved to another part of the carpet.

I think the most pressing problem of type/token relationship is found hidden under the social problem of stereotypes versus individuals. On the one hand, there is something oddly wrong with arguing that some person is expected, or anticipated, to act a certain way given some social stereotype (ie. racial, sexual, religious, organizational, political, etc.). In our conception of personal responsibility, we tend to argue that it is the individual, not the expected stereotype of the individual, which is bearer of moral judgments, values, and duties. However, on the other hand, it seems pragmatically advantageous, if not perceptively or scientifically necessary, to classify our relations in stereotypes.

Or, perhaps, put another way, on the one hand we have an intuitive understanding of the problem of the type/token relationship while, on the other hand, an intuitive understanding of the advantages of establishing such relationships. But I believe the singular difference between the philosophical and economic considerations of the type/token relationship problem and the social considerations of the type/token relationship problem is that the latter seems to be pressed with moral problems which the former hasn’t been taken into much consideration because of the lack of initial moral cost.

Part V – Concluding Remarks

The thesis of my paper was that there exists a singular problem –namely, the type/token relationship problem – which shadows Metaphysics, Epistemology, and Philosophy of Language, which is kicked under the rug, and at the expense of great reward, in Economics, that happens to resurface, as a climactic modern social problem, in how we are currently conceiving the notion of Social Justice.

While I do not believe there is a simple solution, I do believe we can reasonably conclude with two questions:

First, “Do our solutions concerning these problems in Metaphysics, Epistemology, and Philosophy of Language have practical, moral, and social repercussions which we are failing to take into consideration?”

And second, “Would it be the moral philosopher’s duty to attempt to propose social solutions that incorporate proposals from metaphysicians, epistemologists, or, for lack of a better term, meta-linguists?”


[1] Inspiration of this essay goes to my tutor, Dr. Christofidou, of Worcester College, Oxford University.
[2] Causation by E. Sosa and M. Tooley
[3] Probability and Evidence by A.J. Ayer
[4] Immaterial Aspects of Thought by James Ross
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