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Isaac Newton (Bolton, Sarah K. Famous Men of S...

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It’s often said that the distinction between deductive and inductive reasoning is that one argues from the general to the specific, and that the other does so from specific to the general, but this is not correct across all forms of these sorts of reasoning.

Each can work both ways. Whoa. That’s quite an assertion, so I’ll attempt to show why here…

In deductive reasoning, the truth of an argument’s conclusion automatically follows from the truth of its supporting statements if it’s valid. Also, it’s possible for one or more of such an argument’s supporting statements to be false, and this renders it unsound even when valid. Valid but knowingly unsound arguments are not persuasive, and cannot ethically be used as though they were compelling.

Deductive arguments reorganize what we know rather than providing any new data. Deductive conclusions cannot go beyond what’s expressed or implied in their supporting statements.

Inductive reasoning, such as some of the informal sort more typically used in everyday life, can only justify conclusions as more or less probable, depending on the strength of the argument and the prior adherence of an audience to its evidence. This form of reasoning does provide new knowledge, by moving us from the known to the unknown, unstated, and not implied.

In generalizing from particular examples, I’ll show how it may be deductive and then inductive:

If I were to be on the shoreline of my local beach, and noted that the pebbles found there were worn smooth and comfortable to the touch by the actions of water and sand, and were to completely and perfectly enumerate each and every such pebble on the shore, to find them all worn smooth, an unlikely and difficult task at best, I would know with certainty that all of these pebbles were smooth and comfortable to the touch. Each and every one. The argument would then follow deductively.

If, though, I were to find one smooth pebble, and then another, and so on, and after noting from a large enough but limited sample of such stones that they are almost all smooth to the touch, though I may find a few which are not, I could conclude inductively that they are more often smooth and worn than not. The argument follows to a high degree of probability based on the size and representativeness of the sample examined, and it is an acceptable substitute for the certainty we cannot usually get in measuring things in the real world.

The things to look out for when generalizing are known as the fallacy of composition, and the hasty generalization, these errors made when we attempt to apply deductive certainty where it does not belong, the first in assuming that the whole of a population is necessarily like the parts, and the second in drawing an unfounded general conclusion on the basis of too little sample data.

Now from general to specific, classifying rather than generalizing.

If I were to get a perfect count of all sand-ground stones on this hypothetical beach, not over-counting or skipping some, and they all were worn smooth, then I could conclude certainly that any one of these stones was going to be smooth in texture just like all the others. The argument would follow deductively.

But if I were to do the more likely thing, and count a fairly sizable number of these pebbles, all showing signs of wear and smoothness, then I could argue with a good chance of being correct in saying that any one of the stones I pick up would be ground and smooth. It would then be an inductive argument.

The error to avoid committing here is the very opposite of the fallacy of composition, the fallacy of division, in which one misapplies deductive certainty by claiming that the part is necessarily like the whole.

To close out, the examples I used in this post come from a quote attributed to Sir Isaac Newton, that cranky and brilliant English guy, which goes:

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. ~ Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton (1855) by Sir David Brewster (Volume II. Ch. 27).


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Related to the theme of the previous post in this series, on the value of integrity, a second thing of great importance is a respect for facts and whatever truth that those facts bear out, whether I like it or not. Tying into this and secondary to it is a deference to reality over fantasy, while retaining the ability to enjoy fantasy when honestly presented in the form of good works of fiction and in roleplaying games.

I only become annoyed when fantasy is presented as fact, especially with the implied intent to deceive and insult the intelligence of the deceived. Ideas can be stupid, claims can be silly, absurd, mistaken or fallacious, and actions can be stupid, but it is against my philosophy to consider people to be stupid. That just doesn’t feel right to me, and it angers me sometimes to see charlatans and scam artists treat their marks as though they were idiots.

Some of the smartest people there are, and you yourself may know or know of a few, can be remarkably gullible despite their often considerable intelligence and education. Smarts are no protection from being fooled, as is often shown by some scientists falling for the conjuror’s or mentalist’s tricks of alleged psychics, intuitives and mediums.

Now, when I say facts, I refer to those collections of events, properties or those things that make statements and beliefs about them true, false, or probable to varying degrees. I do not refer to anything set in stone or incontrovertible on the basis of any authority, nothing at all that is fixed and eternal, so as well to the truth that those facts bear out.

My concept of truth is more like those of Carl Sagan or Richard Feynman, not Plato or Rene Descartes…excepting for those formal truths, abstract and only true by definition and convention, of mathematics and formal reasoning. Truths of the world itself are synthetic, not analytic as in deductive logic, and as far as anyone has demonstrated during the entire history of science. They are tentative, provisional, and not absolute or fixed nor discoverable through pure reason alone.

Without data, pure reasoning tells us nothing about the worlds together outside and inside our skulls.

It’s not a simple and false dichotomy of objective versus subjective, but a landscape between these as two extremes with varying and often uneven terrain of perspective. There is a world external to us, and our own mental, internal worlds in the same overarching reality, in which there exist both the facts we observe around us, and those objective facts pertaining to our subjective states.

Not just objectivism or subjectivism, but perspectivism sharing features of both along a continuum.

At least, this seems to me to be the best, simplest, and most economic explanation for our experiences. But let’s try to avoid being naive realists. Our experiences, crucial to how we see the world and upon which we so heavily depend for much of our knowledge, can often fool us if we too easily take what we perceive at face value.

The data we receive about either depends on both our observations and the contributions we make to those observations based on how we construe our sense data, our current mental and physical conditions, our sensory equipment and artifactual instruments, and on our bodily location in spacetime.

It is a fact, for example, that as you read this, you are experiencing yourself looking at the text on the screen of whatever device you are using to access this blog post. I could of course deny that this was the case, but my denial would not be compatible with the objective fact of your experiencing the perception of these words.

This would be true even if you did not know the language this post is written in — you would still perceive the shapes, color, and arrangement of the text, though you might not understand it without translation — or even if you were unfamiliar with whatever my culture happens to be and its customs and mores.

But why include facts, truth in some form, and reality in whatever state in the same discussion at all? Because, despite their being very different things, they are all heavily interconnected and touch on each other rather closely.

Noting that facts are what make claims and beliefs about them true, false, or probable, it’s also important to note that facts themselves are neither true nor false. They either exist, or not.

True and false are verdicts we lend to our claims, and these verdicts are born out, or not, by the facts pertaining to the claims in question. Beliefs and statements of such can be treated as hypotheses, and these hypotheses should have a meaningful, testable outcome if they are to be useful as candidates for knowledge.

It does us no good to have a “heads I win, tails you lose” approach to claims where no matter the outcome there’s no difference to the truth or falsehood of our statements.

This is one reason supernatural explanations are not used in science: they make no meaningful difference at all in their outcome.

Any data we can imagine would be compatible with the work of a supernatural agency, since supernatural entities are by definition unlimited by any natural law or process; we learn nothing about a phenomenon by labelling our ignorance God, or invisible pink unicorns, or leprechauns.

Such “explanations” are untestable and uninforming.

So as a guy with a well-known scientific bias, I reject supernatural explanations as useless, though I support looking into supernatural claims as there is most likely something interesting going on with them, provided there is data available for the seeking.

We must distinguish between supernatural explanations and claims; the former is useless and tells us nothing new, the latter is interesting and can sometimes tell us quite a bit, however ordinary the explanation turns out to be — as long as there is enough data to reach a verdict.

Sometimes there isn’t. Sometimes there’s not enough information to come to a conclusion, but that does not give us a license to throw up our hands in despair and call it inexplicable; it is merely currently unexplained, and future data may alter that.

I tend to accept a scientific consensus, but let’s be careful to distinguish it from a political one.

The former is based upon a convergence of data in multiple fields of study, often thousands or millions of lines of information, all pointing to the most likely conclusion given the current state of those lines of data, all converging on the same answer; a scientific consensus is not reached by a vote, or a poll survey, nor by an electoral process or popularity contest, and is not dependent on the political ideologies of those contributing the data.

Not so for a political consensus, and politics can often be used to subvert the process of science, though this subversion comes from outside of science, from politicians themselves, as was the case in the former Soviet Union with the work of Trofim Lysenko.

He was a friend of Josef Stalin’s whose policies were a disaster for Soviet biology and agriculture, setting both back decades and arguably resulting in the deaths of millions through starvation.

In short: A scientific consensus is a recognition of reality, and it can only be shown mistaken by the same process of science that gave rise to it with better data; it is based on facts as they are understood at the time; I’m perfectly able to see it as flawed, as long as it’s scientists, and not partisan politicians with a vested interest in keeping themselves in office, who attempt to show it wrong.

And if they do, then good on them!

It’s my view that if you have to use political thinking to debunk science, you don’t understand science, and it shows. This is why I don’t take conspiracy theories of evil leftist scientists hoaxing the public about climate change seriously, as they are remarkably fact-free and devoid of any valid evidence, with most of that alleged for the conspiracy being fabricated, misrepresented, or taken grossly out of context, as with the emails in Climategates I and II.

Ho hum.

Facts change over time, the truth born out by them changes accordingly, and both facts and truth, however transistory and however tentative, need a reality of some form both external and internal to the would-be believer of a truth to have any meaning at all.

A respect for facts underlies the need for integrity, and for some, there is the toughmindedness needed to accept what the facts say no matter what, even where the desire to surrender to our illusions is strong.

However spotty I may be in living up to this, it is to me something very much worth striving for, and something crucial to how I see the world and our place in it.

Still, to me, it’s one of many things worth living for here, in this world, here, in this life.

There’ll not likely be another.


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