Monday, February 1, 2010

Exploring issues of causality

It is a remarkable fact that in many debates, religious as well as political, issues of cause and causality arise yet the debaters have little conception of what these terms mean. In this blog I want to explore issues of causality and how they can best be argued and assessed.

Much general confusion inheres in conflating efficient causality and regular conditionality – which is what “necessary and sufficient conditions” are really all about. (cf. Mario Bunge, Causality and Modern Science, pp. 33-34, 1979). The other part of the problem resides in extrapolating conditions peculiar to general traits for scientific laws into human domains.

I want to focus on the first of these for now.

The criteria of necessary and sufficient conditions was actually invoked originally by Galileo to replace the concept of efficient cause (ibid., p. 33). In this regard, it was recognized from early on that "efficient causation" was often too limited or narrow a concept to be practical or workable. As for “necessary and sufficient conditions” - they are really a statement of regular conditionality that exposes no real criteria for causal efficacy.

Nonetheless, in many venues they are about the best we can hope for in approaching a feasible discussion of causes. For example, Robert Baum, in his textbook, LOGIC, p. 469-70, correctly observes that n-s conditions are practical replacements (in logic) for causes. In other words, instead of saying or asserting "x caused y", one stipulates that a, b are necessary conditions for x to exist at all, and c,d are sufficient conditions for y to have been the sole effect of cause x.

Baum’s reasoning is clear (ibid.): because “cause” (generic) can be interpreted as proximate or remote, or even as the “goal or aim of an action” and is therefore too open-ended, ambiguous and construed in too many different ways. Thus, “cause” is too embedded in most people’s minds with only one of several meanings, leaving most causality discussions unproductive and confused. If my “cause” and your ‘cause” in a given argument diverge, then we will not get very far.

Because of this one uses the more neutral term “condition” and specifies necessary and sufficient ones. The latter terms are specifically meaningful in the context of determining causal conditions, and hence, causes. If one eschews them, then one concedes he is incapable of logical argument incorporating the most basic affiliation with cause or causation.

Given this, let's explore further the concept of conditionalness or conditionality. The goal is to see if or how we can drive n-s conditions toward a firmer basis, say of causal efficacy. Generally four characteristics are assigned for efficient causality: conditionalness, existential succession, uniqueness and constancy. The first, conditionalness is a generic trait of scientific law.

Thus, for example, applying conditionalness to the occurrence of large solar flares, I know I must include such factors as: steepness of the magnetic gradient in the active region, rate of proper motion of sunspots in the active region, magnetic class of said spots, magnetic flux, and helicity of the magnetic field. Each of the above allows a degree of determinacy in the prediction, once I make the measurements.

For example, the magnetic gradient: grad B = [+B_n - (-B_n)] / x

where the numerator denotes the difference in the normal components of the magnetic field (between opposite polarities of the active region) as measured by vector magnetograph and the denominator the scale separation between them. If I calculate grad B = 0.1 Gauss/km, then I know a flare is 96% probable within 24 hrs. In the case of existential succession, in the physical case of the solar flare I know that when the magnetic gradient spikes or steepens to 0.1 Gauss/km a flare is imminent to 96% probability – in 24 hrs.

Unlike conditionalness, the attribute of uniqueness (or high level determinacy such that a one-to-one onto mapping occurs between C(cause) and E (effect)) is absent from certain kinds of law – such as statistical regularities peculiar to statistical mechanics (e.g. the Maxwell-Boltzmann distribution function) or the empirical- statistical correlations that show how sunspot morphology is related to the frequency of certain classes of flares.

It is also absent from those quantum phenomena (including the spontaneous inception of the cosmos) which are governed by quantum logic, not binary classical logic. This is why it is futile to get into arguments with people who merely use classical either-or logic and haven't been exposed to quantum logic. See also my previous blog on this issue:

One example I gave therein was in a claimant who asserted: "No primary cause can be physical". The trouble is, that this assumption is based on a classical system of logic that is binary and uses binary {1,0} or (yes, no) operators. Thus, since a careless person- perhaps attempting to execute a "proof" of a creator, will assert all physical entities must be caused, he will make the classical error of applying this to the cosmos' origin.

But what if instead of classical mechanics and its deterministic provisions, quantum mechanics is incorporated, say at the level of quantum gravity? Can the proposition still hold? No, since we saw the binary{0,1}-valued observables may be regarded as encoding propositions about properties of the state of the system. Thus a self-adjoint operator P with spectrum contained in the two-point set {0,1} must be a projection; i.e., P^2 = P. Such operators are in one-to-one correspondence with the closed subspaces of H, the Hilbert space. But they are not in such correspondence with classical operators that one might assign to classical causality conditions!

Anyway, we move on. Uniqueness is a characteristic, but not an exclusive trait of causation. When one avers “uniqueness of causation” one really means “the rigidity of causation” as opposed to say plasticity which would be associated with human processes, influences, choices and outcomes. For example, plasticity was at work in the 2000 presidential election, embedded in the (disjunctive) plurality of proximate causes of why Al Gore lost Florida to Bush, and hence the presidency in the electoral vote count (though he did win the popular vote across the U.S. by 500,000). . Among these causes: i) 200,000 Dem voters bailed and voted Repub (bear in mind in the final count Bush only won by 537 votes), ii) Nader garnered nearly 50,000 votes - and they were claimed "taken from Dems" - though this has never been proven, and iii) more than 58,000 African -Americans were disenfranchised as documented by Greg Palast in the first chapter of his book, The Best Democracy Money Can Buy.

The distinguishing aspect of plasticity in causality is that a given outcome (say the potential election of Gore in 2000) could be attained by a whole range of alternative means. (E.g. Gore could have won in 2000 if Nader had not run, OR if Gore had fought hard enough for the purged votes to be reinstated, OR if he had fought for the 3,100+ butterfly ballot votes to be reinstated in Palm Beach County, OR if he had demanded all the votes in every county be counted- which the Miami Herald later showed would have won it for him). Note that the key aspect here is that the alternatives are not mutually exclusive.

If only “necessary and sufficient conditions” are to be regarded as antecedents in a casual connection then a simple causation is implied (which lies at the heart of regular conditionality):

If C, then (and only then) E

Again, this is justifiably applied in the context of totally deterministic – and “rigidly causal” examples such as occur in the scientific realm (Newton’s 2nd law: F= ma) but NOT human dynamics or processes. For the latter, the imposition of linear causal chains to describe events and outcomes is defective ontologically since it crafts an artificial line of development in a whole stream of causes (e.g. disjunctive plurality of causes).

As Bunge observes (p. 132) this amounts to a fabrication that may prove useful in terms of description or conveying complex information, say about the 2000 election, but it falls way short in arriving at the efficient causation we seek. The gist of all the preceding is that it is facile, naïve and utterly preposterous to over-extrapolate the“necessary and sufficient conditions” to human affairs and events. That will remain the case until such time the human agents and actors are at least as predictable as the particle of a gas are, say, in terms of their velocities in the Maxwell-Boltzmann distribution.

The Problem of employing False Conditionality- Hence False Causation:

While the whole preceding section may appear to be a rarefied discussion, it actually has significant practical application: namely in ferreting out false causation arguments. Most of these, in fact, mistake a false conditionality for an efficient causation. Some examples from the past are really extreme, but I will point out just one - the classic used by mathematician Leonhard Euler on the French atheist Denis Diderot (who also, alas was innumerate).

Anyway, the story goes like this: on being informed of a new "proof for God's existence" Diderot expressed a desire to hear it, from Euler. Euler then walked toward him and announced (without cracking even a slight grin):

"Sir, (a + b)^n/ n = x, hence God exists! Reply!"

The poor Diderot, lost in any abstract math, was so stunned - the story goes- that he nearly lost his mind and senses and had to leave Paris.

However, had he even basic training in logic and the nuances of causation, he could have easily peered calmly at Euler, and informed him: "Sir, the so-called proof is nothing but nonsense that has nothing to do with the entity you are trying to prove. You have merely given a mathematical equation, nothing more - and hence, a false conditionalness which you mistake for efficient causation!"

Of course, any number of other examples can be substituted for Euler's false conditionality. For example, "God is two-dimensional in time" - proves efficient causation. Or "God is the uncaused cause", when in fact all that's being done is to insert a noun which hasn't even been vetted for the bare necessary and sufficient conditions for it to exist.

The point is that most such arguments fall because while they invoke some form of efficient causation, they don't use or deliver it. They deliver a fraud masquerading as it, which we recognize as a false conditionalness. Worse, asserting "God is a first cause" is actually and technically unprovable within an axiomatic system based on cause! (Of course, one may eschew such a system - but then he loses the ability to argue from or about "cause"!) This is directly from application of Gödel's Incompleteness theorems.

In this case the set of causal elements in the axiomatic system, call the set: Z ={C1, C2, C3,........Cn) has ONE element which is uncaused. It matters not whether it is C1 or any other. The point is, the proof of its existence can't be rendered from within the axiomatic system that uses the set Z for a causal argument. Thus, one will inevitably find at least one contradiction, and this contradiction means the system is incomplete, so the set must be also.

Look at it this way: say Z = C1 is equivalent to saying C1 is "the first cause of all Z". But if: Z = C1 were provable-in-the-system, we have a contradiction: for if it were provable in-the-system, then it would not be unprovable-in-the-system, so that "Z= C1 is unprovable-in-the-system" would be false. Again, it can't be provable in the system since C1 is an element from a presumed CAUSAL set. So, Z = C1 is unprovable-in-the-system is not provable-in-the-system (Z), but unprovable-in-the-system (Z). Technically, one would require a "meta-set" such that Z' = Z + k', the uncaused element- with Z purged of it. However, it can be shown that invoking such a meta-set leads to an infinite regression.

This shows why - before one interjects false conditionality- he or she had first better be sure Kurt Gödel isn't looking over his shoulder!

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