The Probability of a Proposition

I would like to arm my readers with the ability to quickly recognize invalid inferences. Inference will be explored below but first I want to say a few words about how careful thinking is the best medicine for of our times. My working position is that we cannot deal with the problems of the day with the same thinking that created them and that the pollutions, extinctions and other abuses of our environment reflect states of cultural or inner consciousness that are equally ill.

Advertising and PR find endless ways to twist the human heart and mind into painful contortions from which they can force people to act to relieve the psychic pressure – to buy this or that. We fill our heads with non-stop lying images. These fields started as information rich attempts to persuade potential buyers by sharing the virtues of the products in question. Does that seem incredible? Take a look at this typical ad from the age that saw the birth of advertising.

searsjuanita1911It was not long before the ad men (and they were men for the most part) discovered it was much more effective to bypass the reasoning mind and directly manipulating the hopes and fears we all entertain around death, sex, status and social insecurities. This was much more effective. One thing led to another until today we are literally awash in invalid inferences.

When Subaru says its car is love and fills its commercial messages with images of young couples in non-polluted, idyllic nature scenes or warm family relations the logic involved runs something like this:

You feel bad, as you should because you do not own our car.
Here is an example of people happy with their lives because they have love in them.
You need to own our car if you want to have love in your life.

Or a politician’s campaign:

You feel bad, as you should since I am not in office.
Here’s an example of what the guy in office does wrong.
You need to vote for me if you want to feel better about your self, your country and your future.

Everywhere the first move is to create dissatisfaction, a lack of contentment with what you already experience in the real world. It is business 101 – create the need and sell it. This is why so much of what you see and hear is surreal, animated; camera tricks being used to create worlds impossible to realize in reality. They maximize the contrast with your daily experience of people, nature, emotions and social interactions. If you have a TV watch it without the sound on for a few hours. Watch with your B.S. detector well fed, rested and ready for action. What’s real?

By the way, thinking about doing the little experiment and actually doing it with the laboratory of your own nervous system are two very different things. The whole point is to reclaim the ability to have experiences for your self and not be satisfied with the canned goods being offered. Learning is by doing so the whole body-mind is involved. Living vicariously is a trap, unworthy of the opportunity we receive with one more precious day to be alive.

If you dismiss these concerns about the medium being the message with the line they taught you – ‘Oh, I know it is not real, just an entertaining fantasy’ – then you are naive about how the world really works. The for-profit companies creating these fantasies would not continue to invest billions of dollars if the product did not induce people to act as those companies desire. Reams of unpopular research over decades supports the claim that these techniques successfully manipulate public behavior.

There are a number of reasons you might want to consider developing cognitive Aikido for dealing with these things. For one, as the slow grind of social collapse continues under the weight of diminishing energy resources and increasing pollutions, fewer and fewer of us will be found in the inner circle of winners where the consumer paradise is rumored to be found. Not that the number of images of people supposedly enjoying that tin-foil paradise will lessen, far from it. Put bluntly, it is just going to drive you crazy if you believe on some level your happiness depends on purchases you cannot afford. Another good argument for learning effective counter-measures is that peace of mind and contentment strengthen the immune system. In a world where antibiotics and healthcare systems increasingly fail to deliver it could be having inner contentment  is our most practical avenue to a long and healthy life, at least for those of us outside of the charmed circle. The final reason I will ask you to consider is simply what affect your life will have on others. Everywhere in hyper-capitalism’s twilight people are over-worked and under-appreciated. Simple common courtesy is not common, the happy-to-be-alive radiance once seen on people’s faces has all but disappeared and the crushing burden of our secular guilt due to our ongoing participation in ecocide have cast a darkness over the developed world which no one fully escapes. Use this cognitive Aikido to fight back and not only will you become less susceptible to those who would manipulate your most intimate being, but you just might become the glimmer of light that those around you need to get through their day without becoming monsters.

Without further ado on to another excerpt from my project.

Non-Bayesian statistics and probability has mostly been a study of how chance and randomness affect events. In this approach it makes sense to talk about the probability that event X will occur but it does not make sense to talk about the probability of a proposition. Bayesian thought is nothing less than a reconsideration of these fundamental definitions. It finds that probability encompasses statistics once it is given a proper theoretical foundation. This new foundation builds on the use of probability as a guide to reasoning under uncertain evidence. It is easy to spell out the differences by quickly reviewing the basics of logic. Here we come to the heart of the matter of this Bayesian conceptual revolution. Logic as expressed in the predicate calculus is highly technical. This presentation is only as technical as needed to share a sense of the conceptual coherence this alternative view of probability provides.

Here are the classic formations of proper deductive logic side by side with a typical application. These diagrams follow the standard logical presentation in which a line separates the premises of the argument from the conclusion; the line represents “therefore”.

Logic1These illustrate the extent to which proper deductive conclusions can be drawn. Each alternative not listed leads to logical fallacies if the scope of logic remains deductive. A is referred to as the antecedent, B as the consequence. Each can be assigned what is referred to as a truth value. In deductive logic the only truth values allowed are true and false and so we talk of valid and invalid arguments. If one attempts to reason that B is true therefore A is true one commits the logical fallacy of affirming the consequence. For example if Bob did not study then he fails the test – he failed the test – therefore Bob did not study. It is easy to see that this incorrectly removes all the other reasons for which Bob may not have passed the test; he simply couldn’t understand the material, was too ill to attend class on the day of the test, etc.

If one tries to reason by drawing a conclusion from A being false therefore B is false one commits the logical fallacy of denying the antecedent. Staying with Bob such invalid reasoning runs along these lines; if Bob studied then he will pass the test – he did not study – therefore he did not pass the test. Again it is easy to see that this does not take into account all the other possible reasons Bob might have been able to pass the test; he had already learned the material, cheated, got lucky, etc.

Here is the rub. These very fallacies are often the only form of reasoning available for considering questions in the real world. We humans confront them multiple times a day. A weaker form of syllogism is possible if one extends the scope of the possible truth values from only true and false being allowed so that they are able to take on a range of probabilities. Now instead of logical fallacies it becomes a question of correctly reasoning about uncertainties, inductive logic. We say an inductive argument is weak or strong.

Logic2Notice that these are entirely logical connections. The relationship illustrated in the weaker syllogisms is not in the direction of cause and effect; it does not assert that because there are clouds there will be rain, after all many times in the past it has been cloudy but has not rained. Instead the direction is one of logic; it asserts that if there is rain then there must also be clouds. If it is 9 am and one is trying to decide to take an umbrella or not the state of the sky and past experience are the evidence one has on which to form a conclusion. You form a prediction, one of many you will attempt throughout the day. To make the prediction you weigh the evidence, you inductively consider just how cloudy is it, how dark are the clouds, what way is the wind blowing, and what did they forecast on the news last night?

This extension to plausible inference was examined by G. Polya in ‘Mathematics and Plausible Reasoning’ (1954) particularly volume two subtitled appropriately ‘Patterns of Plausible Inference.’ Here the weak syllogisms are taken one more step where they are shown to explain other typical characteristics of inferences. We all seem to intuitively understand “the verification of certain consequences strengthens our belief more and that of others strengthens it less” (Polya pg. 6). We also operate as if further substantiating evidence increases plausibility though sometimes the new evidence affects the strength of weakness of our conclusions considerably and sometimes only slightly.

Logic3There are many more forms of logical patterns in both inductive and deductive logic. There are patterns for dealing with propositions that are incompatible with each other and patterns for adding the quantifiers “some” and “all” to the propositions.  These few provide sufficient illustration for our purposes. It is reassuring that the extension of logic by using plausibility agrees with our common sense notions but is there anything more substantial to bring in their defense? Indeed there is. The physicist Richard Cox was able to derive the laws of probability from a set of postulates that justifies the logical interpretation of probability. He does so using Boolean algebra. Regular algebra deals with quantities; Boolean algebra deals with propositions. Boolean algebra defines operators on which today’s computers rely, for example, the logical operations indicated by AND, OR, NOT. In “The Algebra of Probable Inference” (Cox 1961) Cox derives probability theory from an extension of Boolean algebra and in so doing proves it is the only theory of inductive reasoning that maintains logical consistency. It is said that Cox returned probability theory to its original 18th century roots as formalized by Laplace. He does this by proving probability theory to be the axioms of logic when logic deals with uncertainty. In the 1950s this approach was considered too subjective to be used in science and engineering so the alternative foundation of probability theory in the frequentist school was developed. Cox’s brilliant achievement was to show that the original logical foundation was in fact the most coherent. The Cox Theorem has provided a rigorous mathematical mapping of inductive logic to probability theory. It is a fundamental intellectual achievement.

One, I might add, that I believe deserves to be shepherded through the coming societal upheavals.

Oh, and Subaru is not love, it is a car. One of an estimated 900 million that are currently running around on our planet, eating our future alive. They are saying there will be over two billion light vehicles on the road by 2050. Really? Inference is how we are able to think about the future. Right now there is no more important ethical and practical question to be asking. Like it or not the ecological evidence is overwhelmingly telling us the coming generations will suffer under some catastrophic tipping point or another. That is the most probable outcome. Business as usual will not continue and whatever comes next will be cleaning up or avoiding the toxic results of our actions for centuries. Time to wake up and smell the burnt toast, anyone noticed any strange weather here in the U.S. of late? Two billion cars by 2050 is, to put it as politely as I can, crazy talk.

The data matters, that the prior convictions are reasonable matters, that we understand the best we can do is sketch a probability curve of what is most likely matters. It is the truth of the strength of human knowledge. Epistemologically these three curves will meld and mold each other into a most probable outcome, the result of our careful reasoning. Carrying the weight of our best understanding we are ethically obligated to act as if it is the truth, even though our result is also a curve and will meet new data and evolve through another cycle.

The point of all this is this: the data that has been gathered in the last few years concerning the severity of the ecological crises has exceed what was expected by most of our models, sometimes considerably. Some of the weather events outside your door were not expected for another decade or more. The models are being recalibrated but it should be common knowledge that in the conservative IPCC reports of 2007 the worst scenarios are the ones the historic data matched. It should be common knowledge that the same historic trend lines matching the worst scenarios modeled is also the case for the Limits to Growth studies. All of these are saying that what we are doing now is almost certainly stealing our ease at the cost of massive suffering by people just like us who happen to be born in the future instead of now. I cannot help but wonder, might those future beings be us in some way, paying the piper as cause and effect work their way down the deep time centuries of DNA time? However that may be the here and now is real, precious and threatened.

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