Deductive reasoning is the tautological reasoning from basic principles to specific conclusions. Aristotle’s famous syllogism
Socrates is a man.
All men are mortal.
Therefore, Socrates is mortal.
is an example of deductive reasoning. The general form of deductive reasoning has been given the name modus ponens. It goes like this:
P is true
If P is true, then Q is true
Therefore Q is true
Inductive reasoning, on the other hand, is a statement about likelihood. The parallel example in inductive reasoning might be
Most adult men are more than 26 inches tall.
Socrates was an adult man.
Therefore, Socrates was probably more than 26 inches tall.
Inductive reasoning does not provide metaphysical certitude. It only provides confidence. If you take a position of extreme skepticism, one in which you demand metaphysical certitude, it will be very confining. Without inductive reasoning we couldn’t cross the street, eat breakfast, or go to sleep at night without being in terror for our lives. We use inductive reasoning all of the time because we must.
David Hume addressed inductive reasoning in his 1748 work, An Inquiry Concerning Human Understanding. In essence, in my views on this subject I follow Hume and he advocated a position of what might be called “practical skepticism”:
It seems to me, that the only objects of the abstract science or of demonstration are quantity and number, and that all attempts to extend this more perfect species of knowledge beyond these bounds are mere sophistry and illusion. As the component parts of quantity and number are entirely similar, their relations become intricate and involved; and nothing can be more curious, as well as useful, than to trace, by a variety of mediums, their equality or inequality, through their different appearances. But as all other ideas are clearly distinct and different from each other, we can never advance farther, by our utmost scrutiny, than to observe this diversity, and, by an obvious reflection, pronounce one thing not to be another. Or if there be any difficulty in these decisions, it proceeds entirely from the undeterminate meaning of words, which is corrected by juster definitions. That the square of the hypothenuse is equal to the squares of the other two sides, cannot be known, let the terms be ever so exactly defined, without a train of reasoning and enquiry. But to convince us of this proposition, that where there is no property, there can be no injustice, it is only necessary to define the terms, and explain injustice to be a violation of property. This proposition is, indeed, nothing but a more imperfect definition. It is the same case with all those pretended syllogistical reasonings, which may be found in every other branch of learning, except the sciences of quantity and number; and these may safely, I think, be pronounced the only proper objects of knowledge and demonstration.
All other enquiries of men regard only matter of fact and existence; and these are evidently incapable of demonstration. Whatever is may not be. No negation of a fact can involve a contradiction. The non-existence of any being, without exception, is as clear and distinct an idea as its existence. The proposition, which affirms it not to be, however false, is no less conceivable and intelligible, than that which affirms it to be. The case is different with the sciences, properly so called. Every proposition, which is not true, is there confused and unintelligible. That the cube root of 64 is equal to the half of 10, is a false proposition, and can never be distinctly conceived. But that Caesar, or the angel Gabriel, or any being never existed, may be a false proposition, but still is perfectly conceivable, and implies no contradiction.
The existence, therefore, of any being can only be proved by arguments from its cause or its effect; and these arguments are founded entirely on experience. If we reason a priori, anything may appear able to produce anything. The falling of a pebble may, for aught we know, extinguish the sun; or the wish of a man control the planets in their orbits. It is only experience, which teaches us the nature and bounds of cause and effect, and enables us to infer the existence of one object from that of another.[4] Such is the foundation of moral reasoning, which forms the greater part of human knowledge, and is the source of all human action and behaviour.
Mathematics is deductive in nature; it does not require inductive reasoning. Very nearly all other human knowledge requires induction. Inductive reasoning is not unscientific; it is the very basis of science. We derive inferences about the future from observing the past. That’s as true of our everyday interactions as it is true of the actions of nuclear particles. The primary difference is the level of confidence and in practical terms we must give some level of confidence to our inductive conclusions based on past events. We really have no other choice.
How do you stand on the excluded middle?
Am I guilty of that here? If so, please explain.
Guilty of what? I’m only asking your opinion of the validity of the law of excluded middle. Or rather, if you see anything problematic in its employment.
I was confused.
Well, Russell saw a distinction between the excluded middle and non-contradiction. I also think there’s some value to characterizing some things as just plain “unknown”.
Sure. That’s one avenue some philosophers and mathematicians take. My take on it is that it, excluded middle, can lead us into thickets. It’s not that the law is “false” or “invalid”, but its employment can mislead us. Let me quote something for you to give you some idea of where I’m coming from. This is from Wittgenstein’s Philosophical Investigations, para. 352 [He’s continuing his discussion of mental “experience”]:
I’d argue that in addition to “unknown” that when the subject is humans the answer often encompasses both X and not X.
Is John Doe cruel or kind? Yes.
Sometimes John is cruel and sometimes he’s kind. Or cruel here and kind over there. Cruel now, kind later. Cruel, but believes he’s being kind. Inadvertently kind while intending to be cruel. Cruel but with a cruelty modified somewhat by kindness. Blurring intention and effect? Sure, because it’s inevitable.
Shouldn’t we set aside considerations of emotion (or even humans) altogether when talking reason? You can, but excluding emotion from considerations of the real world (which, frustratingly, does include humans) is like excluding gravity from physics. Every perception, every action, every interaction, every plan, every theory that involves humans involves billions of little pools of quicksand waiting to gum up the workings of reason.
The biggest mistakes I’ve made in my life involve wrongly supposing that humans (including myself) can be understood using logic.
Riffing on the Wittgenstein quote, the picture is never in perfect accord with reality. The territory is not the map.
However, that is not to say that all pictures are equally in accord with reality. Provability and unprovability are two of the yardsticks that could be used to measure that accord.
Michael, I think I’d chalk your example up to “limitations of language”. We cannot truthfully say whether John Doe is cruel or kind. We can say within the limits of our perceptions that he acted cruelly or kindly in a specific instance.
We can observe John’s actions and draw a conclusion as to how to categorize them. That’s the backward-looking thing you’re talking about. But if we want to predict his actions going forward we would also have to make some reasonable guesses about his motivation. If we don’t know why he acted a particular way in January, we will not have very useful information as to how he will act in July.
January 1: John hits his cat. We don’t know why. We just know he hit his cat. So: will he hit his cat in July?
Did he hit his cat because he’s mentally ill? Did he hit his cat because he’s a sadist? Was he a fundamentally moral person who in a terrible lapse hit his cat and then felt terrible remorse and decide to change his life? Did he hit his cat because he saw a lime disease-carrying tick and wanted to knock it away? Was the cat on fire?
If you don’t know why he did it, you cannot assume that on July 1 he’ll hit his cat again. Or refrain from hitting his cat.
Six billion people each with their own (often obscure) motives and reasoning is why we cannot predict real world events outside of the realm of physics. People are not rational, and that irrationality, compounded in multiple dimensions, complicates the job of attempting to predict any behavior involving humans. Which is why everything from psychology to economics fails — and will likely always fail — to predict the future with any degree of accuracy.
There’s a huge gap between “completely unpredictable” and “completed determined”. We can say with pretty fair confidence that John won’t start wearing his cat as a hat. Why? Because most people aren’t insane. Either you’re erring in the direction of extreme skepticism which I would presume is an intellectual pose because living with such skepticism is impossible or you, too, believe that there are lots of things about people, individually and corporately, that are pretty darned predictable.
We won’t suddenly start eating sand instead of ice cream or start breathing molten lava instead of air.
“It’s long,†said the Knight, “but it’s very, very beautiful. Everybody that hears me sing it – either it brings tears into their eyes or else–â€
“Or else what?†said Alice, for the Knight made a sudden pause.
“Or else it doesn’t, you know.â€
No, of course most of what most people do is within certain parameters. But in terms of predicting future events which rely on humans – most stuff outside of physics – we have the problem of individuals, both large and small in terms of their influence, being significantly unpredictable.
The battle of Missionary Ridge, Civil War. Could we have a month before, a week before, or ten minutes before, predicted that Union soldiers and junior officers, without orders from their generals, would decide to charge that ridge against long odds and actually win? Not a chance. Not even if we’d known everything about every soldier involved. People do weird stuff sometimes. In all likelihood a couple of men just said, “Fuck it, I’m going up there.”
Zoom out and you can look at a match-up between the two sides in the war and predict that the North would win. In theory. If you could also predict that the British and French would stay out of the war and that Little Mac would lose the election, and numerous other events. None of which was clearly predictable at the time. Grant could have had liver failure. Sherman could have failed to take Atlanta. Lee could have not split his forces. But a million people whose names we don’t know, could also have made different decisions that brought about different results.
The only way to predict the future is to deny free will and random chance. I’ve often said that my life turned on a split-second pivot where I happened to look up and happened to see a girl through a window. My action at that moment was completely atypical. Completely out of character. I had never in my life done anything like it before.
Because we met we wrote books. Because we wrote books (these are actual cases, not inventions,) some kids grew up and joined the military and shot people, and others went off to study human rights and others became scientists.
Millions of similar moments occur every day, and because of them events slide this way or that. Jonas Salk found a polio vaccine. Was it predictable that someone would? Sure. Just like it’s predictable that we’d some day figure out the cause of black plague. But not so predictable you’d want to bet a dollar on the outcome. Certainly not if you had to guess the year or month. Men and women great and small matter, and they have free will, and they are afflicted or empowered by random chance. The results will always be unpredictable.
Plenty of stuff within physics is not deterministically predictable either, as evidenced by the classic 3-body gravitational problem. But some of those computationally intractable systems can be “meta-predicted,” if you will, through the relatively recent mathematics of chaos- or complexity theory and bottom-up modeling approaches. So we are not completely at sea when deterministic prediction fails.
We can predict _that_ thunderstorms will occur over a given area and time, for example, even if we cannot say exactly where or when.
The mathematical surfaces of strange attractors (search the Lorenz Attractor for an example) have an interesting property: they tend to map well-defined sets of permissible solutions to a given set of dynamical equations, even as they render mathematically impossible the prediction of where/when any specific solution will be on those defined surfaces at a given future moment.
Fortunately, although deterministic prediction is out, it is often possible to say with confidence what will NOT happen/work/be stable (any and all solutions that do NOT lie on the strange attractor’s surface), which is often valuable information in its own right. Get the rough equations and parameters right for a given situation, and you can develop profound insight, if not automatic answers.
This is, IMHO, one reason why a lot of politics is intuitively negative.
We humans get around this mathematical limit by carrying around several sets of (varyingly coherent) predictors based prior experience and ideological cant, applying them opportunistically in the short term, and simply switching predictive hats as dictated by changes in the local situation.
This flexibility eliminates the need for one-size-fits-all deterministic prediction, if not the desire for its coherence. After all, what better way to get ahead in life is there than knowing what is really going on?
(It also, by the way, confounds our political adversaries.)
One safe prediction is that we will continue to use this (half-) baked-in cognitive method (which can itself be understood in systemic terms), even as we continue to clamor for ever more deterministic predictions with which to operate our lives. Another is that, if we don’t operate with enough societal design margin to handle the inevitable errors, the system will crash and reset once it is forced too far from the attractor. Balance is key.
@ Michael
“Shouldn’t we set aside considerations of emotion (or even humans) altogether when talking reason? You can, but excluding emotion from considerations of the real world (which, frustratingly, does include humans) is like excluding gravity from physics. ”
You know, Michael, Hume agreed with that:
A Treatise of Human Nature, Sect. iii. Of the Influencing Motives of the Will
It is our passions, our emotions, that supply impetus to our lives. Reason can only help us to shape the means to realize our passion-created ends. Reason has no other office in the realm of human action.
Then there’s hypothetico-deduction. Make a tentative assumption to explain a phenomenon, deduce empirical implications, the more novel and unexpected the better, then test those implications to either lend support to the conjecture, or falsify it. Then, if the conjecture is supported, to refine the hypothesis and devise new tests; or if falsified, to modify or discard the hypothesis in light of the new evidence.
Or you are not conditioning correctly in your probabilistic reasoning. If you corrected for that the uncertainty you are describing might diminish significantly. For example,
Prob(John is cruel),
is not the same as,
Prob(John is cruel|He is dealing with an animal).
In this case, you are lacking data and not approaching the issue in a proper way.