Rand’s Law of Identitiy

In induction, rand on 21/06/2011 at 2:59 am

I’ve learned very few truly valuable things in life. I won’t list them all, and they may be repugnant or less than valuable to some, but I will list one: argument is not about winning. If you win an argument, you lose. Arguments are about getting closer, no matter how hard they are, to the truth. Of course, I choose not to go into a lengthy argument about why this is the case, simply because I’m not out to convert anyone.

That said, there are times that I see arguments that are just wrong. In these cases, I do not mean to say that their conclusions are therefore false, only that the argument is fallacious — not manifestly so, as is often the case. Some times the wrongness is hidden deep within, and only by prying carefully at the edges can we get a glimpse at where the argument runs afoul.

I will focus on the article “Debunking Popper: A Critique of Karl Popper’s Critical Rationalism,” by Nicholas Dykes. I won’t hold it against him because he is an Objectivist, since he clearly is familiar with critical rationalism (CR) far more so than most. I will say this once and only once: *critical rationalism may be false.* That said, I hope that the arguments presented in the paper, once I have addressed them, will be understood to be quite poor criticism of CR. I implore others to find better, stronger, bolder criticisms of CR in the future. That way, *if* CR is false, we may reject it and move on to something better.

This will be a several-part series, simply due to the length of the article. It would be tedious for me to write it all at once and even more tedious for others to read it.

§ 2, ¶ 1-4.

Dykes provides an adequate–perhaps even naïve–introduction to the problem of induction, yet somehow concludes that Hume was directing his problem of induction at the ‘Law of Identity,’ rather, to use the language employed by Dykes, than at the possibility of inferring the knowledge of specific identities: which identities are fixed and others fluid? Hume does not suggest that entities have no identities, merely that an infinite number of tests cannot confirm a universal law. I will address this point of confusion later. Furthermore, Dykes never explains exactly how Popper formulated the problem of induction. This distinction is of an utmost importance: many philosophers of science take the problem of induction to be a psychological problem: since we learn from experience, and past experience says nothing about future experience, our learning must be some sort of habit-forming process that successfully tracks truth through some sort of reliable method. This is taken to be the inductive method.

The problem of induction, as Popper saw it, is a logical problem, and is split into two halves: in the first, during the ‘context of discovery,’ no matter the number of singular observations of identities collected, they do not logically entail anything about universals (or for that matter unobserved singular observations of identities). True theories do not leap out of heaps of facts like Athena from Zeus’ brow. Theories are instead the imaginative creations of fallible individuals. In the second, during the ‘context of justification,’ no matter the number of finite corroborations, the theory does not become more grounded, or more certain, or more probable, simply because they have been tested in only a comparatively limited number of cases. It would be like looking through an infinitely large pile of needle-like pieces of hay in search for the one true needle, yet all the pieces of hay will, only under very specific circumstances, turn out to be hay. One cannot be certain that, even if they should through sheer luck fall upon the true needle, they are in possession of the true needle, simply because they have not tested it in every single specific circumstance.

The problem of induction a problem that’s been covered from every conceivable angle ad nauseam from both the psychological and logical ends, and most epistemologists either have put the problem aside to work on other problems (‘what, exactly, is the nature of this inductive method?’) or accepted that induction just doesn’t work. Dykes, however, asserts that “Induction does not depend for its validity on observation, but on the Law of Identity” (¶ 5) and then goes on to explain by use of quoting H.W.B. Joseph (¶ 9) that

A thing, to be at all, must be something, and can only be what it is. To assert a causal connexion between a and x implies that a acts as it does because it is what it is; because, in fact, it is a. So long therefore as it is a, it must act thus; and to assert that it may act otherwise on a subsequent occasion is to assert that what is a is something else than the a which it is declared to be.

The language is a bit arcane for my tastes, so please forgive me if I attempt to simplify what Joseph says:

In order for a thing to be it must be what it is. Asserting a causal connection between a and x implies that a acts as it does because it is a. If it is a, it must act as a; and to assert that it may act not as a is to assert that a is not a.

Dykes says that “Existence implies identity” (¶ 10). Take this as a given. What follows from that? If, for instance, all emeralds were grue (to use one of the most infamous examples), then all emeralds would be, in fact, grue. ‘Grue’ simply means that “Green before December 5th, 2015, blue after December 5th, 2015.” By saying, “It is not possible to exist without being something, and a thing can only be what it is: A is A,” (¶ 10) Dykes is missing out on the fact that universals may have identities that vary over time: Acorns grow into oak trees; eggs hatch into chickens; caterpillars turn into butterflies; children grow into adults; electrons switch immediately from ‘up spin’ to ‘down spin.’ There is change in the universe, and at times it is quite difficult to demarcate between two different identities, or learn if they are in fact an identity, while at other times the switch is drastic and unpredictable.

The possibility remains that, like oak trees and good wine, emeralds may ‘biologically’ age quite gracefully over time, or have a chemical switch triggered by some radioactive decay, thereby developing a nice blue sheen on December 5th, 2015 (or any other date for that matter). This possibility should instill a major doubt of any sort of inductive method. Once one admits that possibility, as the possibilities that the emerald may be ‘grorange,’ or ‘grack,’ or ‘grown,’ then any certainties we may have had by accumulating instances that corroborate the theory that all emeralds are green will be for naught: we have also corroborated an infinite number of unintuitive theories that may also be true. Therefore, when Dykes says “Thus to deny any connection between a thing, its actions, and their consequences, is to assert that the thing is not what it is; it is to defy the Law of Identity,” (¶ 10) I am happy to take him at his word: these counterfactuals do not defy the Law of Identity simply because the Law of Identity is a truism: if emeralds were to be grue (or any other Goodman-predicate), then emeralds would in fact be grue. However, we do not know with the limited available evidence whether or not emeralds are grue, green, grack, grown, grorange, …

Thus, I feel like a pedant to explain something some obvious to the Randian: You cannot make emeralds green by declaring that A=A.


  1. […] One of the many reasons why objectivist epistemology is silly. HT Lee Kelly. […]

  2. The “universals” you get from induction are not the same thing as universal statements.

    The fact is, when you understand induction correctly, you will see that induction doesn’t need repetition of observations at all, you only need one observation to establish inductive necessity – IF you have identified the nature of the thing correctly, then it will behave in such-and-such a way (under so-and-so circumstances) at all times. It doesn’t require any auxiliary universal hypotheses or any of that nonsense.

    Repetition establishes nothing logically, that’s true – but repetition was never the essence of induction, repetition was always just an error check. For most things, one observation is all that’s necessary (because the thing has acted thus in this instance, it will act thus in all instances). Of course it’s possible that a thing may have a nature that’s peculiarly time-dependent (like grueness) that’s revealed in the future, in that case the thing simply doesn’t have the identity you thought it did – but it has ANOTHER identity in which the time-dependent nature is included. That doesn’t mean the emerald is grue, it means it’s not an emerald but something else.

    It’s another thing, not an emerald, that’s grue, it’s another thing, not an emerald, that’s grorange, etc., the emerald is the thing that’s green.

    What may turn out to be the case is that there are no emeralds, only “emeroids” (the grorange things), etc.

    Popper’s CR in fact depends on identity: if you have a theory, and you deduce the experience-touching consequences of it, that depends on things having identities – OTHERWISE THE CONSEQUENCES WOULDN’T BE LOGICALLY NECESSARY, and modus tollens wouldn’t be a falsifying test.

    For a long time it seemed like a victory for philosophy to detach logical necessity from things, to have it free-floating, or the rules of the game, etc., etc. I was of that mind too, but I’ve come to see the subtlety of Rand’s position that logic is, “The art of non-contradictory identification” and that logical necessity is inherent in things, not just in talk about things.

    The main culprit in all this has been the notion of “Representation” that came into vogue roundabout Galileo’s time – it threw philosophy off course for a few hundred years. Direct Realism is the way out of the rut.

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