The Philosophic Validation of Inductive Inference

The Philosophic Validation of Inductive Inference
by Ed Thompson

What is the main unresolved philosophical issue that your philosophy has not dealt with?
A technical one, which I’d like to formulate if I don’t die too soon, but it’s a hard job: the problem of induction. Aristotle provided some leads, but there’s been no full presentation of the subject.
Ayn Rand’s answer to the questioner above [Mayhew (Ed.), 2005, p. 177] indicates an avenue for further philosophical investigation; something akin to an untapped philosophical wellspring, or uncharted philosophical territory. When I had first read Rand’s answer to this question, I became inspired to fill in this void – only to find (upon my preparatory research) that this very job had already been accomplished, by Wallace Matson, just over 2 decades ago [Den Uyl & Rasmussen (Ed.), 1984, p. 26]!

This essay is meant to provide a background to the problem of induction, to critically analyze the solution to this problem (the philosophic validation of induction, as laid out by Matson), to offer another example analogy to show that the self-same reasoning holds, and to tie together the 2 essentials of proper induction – so that any potential argument can be evaluated against this new and refined standard for it. I will begin at the beginning -- by outlining the 2 possible senses of induction.

Induction by Simple Enumeration

The philosophic “problem of induction” was first outlined by Hume (Hume, 1739, p. 93): “We have no other notion of cause and effect, but that of certain objects, which have been always conjoin’d together, and which in all past instances have been found inseparable.” Hume’s error is to consider induction as a simple method of counting, or enumeration, of various phenomena that are (or have been) temporally conjoined. For Hume, nothing joined 2 phenomena; except for a brute, temporal association.

This error of Hume’s can be explained by 2 other failures – thinking errors – of which Hume never transcended:

1. A failure to discover and validate (acknowledge) Rand’s 3 axioms: existence exists, existence is identity, and consciousness is identification.
2. A failure to discover and validate (acknowledge) that human consciousness is inherently an active process.

If Hume had not failed to acknowledge the axioms above, then he would at once recognize a corollary of the first 2 of the 3: the law of identity applied to actions (i.e. the law of causality). In short, if things exist primarily (independently of consciousness) and things are what they are (and not other things), then it follows that all things will have a certain capacity for action and change – and will never be able to exceed or violate this certain capacity. In Rand’s words (Rand, 1961, p. 151): “The nature of an action is caused and determined by the nature of the entities that act; a thing cannot act in contradiction to its nature.”

To put the epistemic importance of this aspect of reality into an illuminative analogy then: if you knew that water boiled at 100 degrees C (at 1 atm of pressure), and then someone handed you a pot of water to boil, but it didn’t boil until 101 degrees C – then you may safely conclude that the water is not pure, and begin a test for contaminants (e.g. sodium). The reason that contamination is a safe conclusion here, is that water, being itself, cannot ever exceed or violate its capacity for action and change (which involves certain boiling parameters). A new entity (or a subtraction of a pre-existing one) is what ultimately explains all noted ‘irregular’ actions in our fundamentally uniform reality.

While this ‘boiling water’ example can be, itself, already taken as a philosophic validation of induction, to quit here would be an insult to Matson, and besides, I’m not about to let Hume off the hook just yet! The second error of Hume’s – which is what ultimately allowed for the first – is to hold the premise that the mind of man is but a passive, perceptual organ of awareness. This is eloquently evidenced in the following quote (Hume, 1739, p. 1):

All the perceptions of the human mind resolve themselves into two distinct kinds, which I shall call IMPRESSIONS and IDEAS. The difference betwixt these consists in the degrees of force and liveliness, with which they strike upon the mind, and make their way into our thoughts or consciousness.

And later in the same manuscript, Hume incontrovertibly galvanizes this position with the following clear and distinct statement (p. 103): “Thus all probable reasoning is nothing but a species of sensation.” Indeed, it was this wrongly held premise (that the mind is only passive and only perceptual) that allowed Hume to go on in the same manuscript to make the following valid, but absurd, conclusion regarding the reasoning capacity of animals (p. 176): “Next to the ridicule of denying an evident truth, is that of taking much pains to defend it; and no truth appears to me more evident, than that beasts are endow’d with thought and reason as well as men.”

Adopting this Humean “animal epistemology” then, as an illuminative example – for the animals (who are “stuck” in a purely perceptual world), induction WOULD BE ultimately unjustifiable! But humans are capable of another level of awareness. We are capable of conceptual awareness – of regarding things as “units” with a similarity, and abstracting them away from a background of different things, things which fail to possess the given integrating attribute (conceptual common denominator) in ANY degree.

Now that we’ve seen how to err in making inference/generalization, let’s see how to get it right.

Induction by Mechanistic Understanding (of property attribution)

In his philosophic validation of induction, Matson utilized the hypothetical, yet counterfactual, existence of an impossible chemical compound: helium sulfide. He starts with a primitive description of sulfur [Den Uyl & Rasmussen (Ed.), 1984, p. 25] as “a yellow powdery substance that burns with an acrid odor and kills fleas.” And, on the same page, he shows how this description evolved and culminated into a mature and scientific definition: “Sulphur can now be defined as ‘Element No. 16.’

Now, noting this precise and accurate definition of sulfur, Matson conveys how it “embeds sulphur in an elegant conceptual schematism which is such that from it the various previously noted properties of sulfur can be deductively derived.” And it is this crucial ability to deductively derive (in retrospect) the noted properties of something, which differentiates what I call ‘induction by mechanistic understanding’ from Hume’s ‘induction by simple enumeration.’

Matson’s goal – and its achievement! -- is outlined on the following page (p. 26): “The attainability of truth that is at once factual and necessary paves the way to the proof of the ‘validity of scientific induction’ …” Matson asks us if it’s possible to conceive a certain change in the course of nature – one where “sulphur, which is Element No. 16, should continue to be sulphur but cease to be Element No. 16, i.e., cease to exhibit the behavior that the theory assigns to Element No. 16.” Matson’s answer to this hypothetical: “To do so would involve a contradiction.”

As to the potential criticism expressed in the following form: but isn’t it conceivable that there is a time when element no. 16 ‘changes’ its behavior, and begins to combine with helium to produce helium sulfide?, Matson replies that “the purported conceivability of this mishap presupposes an untenable distinction between what a thing is and what it does … sulphur cannot remain Element No. 16 (which is, among other things, the having of exactly six electrons in the valence shell) and combine with Element No. 2 (which is the having of no valence shell at all), chemical combination being the sharing of valence electrons.”

What is it that makes Matson so sure that sulfur won’t ever chemically combine with helium? How can he generalize to all instances – past, present, and future – as to the feasibility of the instantiation: helium sulfide? In short, it is his mechanistic understanding of chemical combination. One of the properties of elements is their variable capacity for chemical combination – the essential mechanic of chemical combination is the sharing of valence electrons. To posit a chemical combination without such sharing, would be to posit an entity that exceeds or violates its capacity for action and change.

Another Example Analogy: Getting to Venus (from the Morning & Evening Star[s])

In an effort to repeat “Matsonian” rules of proper induction, here is an amended 4-step argument from a past contribution of mine.

I. Logical assumptions
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Material objects = that which have spatio-temporal continuity (existence exists)

Perception = direct pickup—by an organism—of the contrasts or variances (and therefore, of the invariances) in that organism’s environment

Knowledge (conceptual) = contextually-sufficient discernment of one existent from others (i.e. “getting the reference right”)
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II. Agent’s background perceptual experience …
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-Particular object #1 = Morning Star (to a first observer; merely a bare particular)
-Particular object #2 = Evening Star (to a first observer; merely a bare particular)
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III. Rational agent’s use of the conceptual faculty …
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The conscious identification that the particular object #1 (Morning Star), a celestial body that is perceived in space and time at: [insert one half of Venus' orbit here] -- is identifiable with the particular object #2 (Evening Star), a celestial body that can be perceived in space and time at: [insert the other half of Venus' orbit here].

This identification, this veridical generalization (from 2 particulars to one general thing), entails because one, and only one, object (celestial, or otherwise) may occupy a particular space at a particular time. There are 2 possible explanations for the celestial body that corresponds to one half of the full orbit of Venus, and the celestial body that corresponds to the other half of the orbit …

Potential explanation #1: At the point where the celestial body is at the end of one half of the orbit, and proceeds into the other half – its identity changes. In moving out of one half of the orbit, and into the other – in that millimeter of space that separates the 2 halves – the whole planet instantly changes into another planet.

Potential explanation #2: At the point where the celestial body is at the end of one half of the orbit, and proceeds into the other half – its identity holds. Only one object, celestial or otherwise, can occupy the same space at the same time. (i.e. it is impossible for the Morning Star and the Evening Star to NOT BE the same object—due to axiomatic limitation of what can be true of existence).
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IV. Conclusive discernment
The 2 different and distinct perceptual instances of seeing stars (Morning and Evening) can now be conceptualized as different views of the same kind of thing (indeed, the same EXACT thing). It is not possible that this empirical finding is false.
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Essential Requirements for Proper (Mechanistic Understanding) Induction

1. Acknowledgment of the axioms and the viewing of data with a corresponding integration with the axioms (i.e. allowing them to delimit conceptual plausibility).

-In the case of helium sulfide, it was necessary to view existence as identity so as not to bifurcate what a thing is – from what it does.

-As part of a thing’s identity is the exact space that it occupies, along with the fact of the conservation of matter (existence exists), in the case of the planet Venus then, it was necessary to view the 2 particular and distinct perceptual experiences in light of the fact that things don’t turn into completely different things via simple location change.

2. A withholding of confident generalization until enough facts have been integrated so that you can deduce noted properties from the relations of fundamental particularities.

-In the case of helium sulfide, it was necessary to discover and validate the mechanics of chemical combination, so that alternative events (in the future) could be discredited a priori (via deduction from known limitation).

- In the case of the planet Venus, it was necessary to discover and validate the mechanics of planetary orbit, and to gather enough data on the half-orbits of the “2” celestial bodies to rule out, conclusively, the possibility of a “planet switch” at a given point in time and space (a point where we couldn’t continue tracking Venus along its orbit, for instance).
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Reference:
Den Uyl, D. J. & Rasmussen D. B., eds. (1984) The Philosophic Thought of Ayn
             Rand. Urbana: University of Illinois Press
Hume, D. (1739) A Treatise of Human Nature: Being an Attempt to Introduce the
            Experimental Method of Reasoning into Moral Subjects. London: John Noon
Mayhew, R. (2005) Ayn Rand Answers: The Best of Her Q & A. New York, NY:
            New American Library
Rand, A. (1961) For the New Intellectual. New York, NY: New American Library

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