Project Logicality: Generalizing & Classifying both Deductively & Inductively


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).

What Matters Most: Part II


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.

Certainty, Probability & the Fallibility of Factual Knowledge


Portrait of René Descartes, dubbed the "F...

Portrait of René Descartes, dubbed the “Father of Modern Philosophy”, after Frans Hals c. 1648 (Photo credit: Wikipedia)

[This entry has been revised, rewritten, and reposted from a prior version. The original meaning is unchanged.]

I’ve often stated my views of knowledge’s fallibility, of it being more or less certain but rarely if ever absolute. I’m not attempting to propound on the ultimate nature of truth, simply noting an observation made by scholars in both philosophy and the sciences: that concerning the failure of the quest for complete certainty as a criterion for knowledge.

This quest has evidently failed, because in the world outside of our heads and logical conceptions, the unexpected cannot be ruled out completely. In my view, this quest was a misguided one, for it presumed that certain truths of the world were to be found.

Pure mathematics and logic render certain truth of a sort, but this is due to the use of conventional axioms and those theorems based around them, axioms allegedly self-evident and true by definition, such as the statement that the shortest distance between two points is a straight line.

Within Euclidean geometry, this is true and internally consistent. Elliptical and hyperbolic geometries, however, have axioms that are self-consistent but inconsistent with those of the Euclidean model.

A good example is the axiom that the sum of the angles of a triangle can exceed 180 degrees, which is a perfectly accurate way of describing the geometries of bodies with strong gravity wells in General relativity.

The point is that there’s no single mathematical or logical system that alone completely and consistently describes all of reality — such systems are arbitrary constructions but useful when applied to describing what they are designed to describe.

We choose the systems that best fit the task we wish to perform, hence, using different tools made to purpose, each according to its own set of conventions.

Logical certainty is of two sorts: that which involves the validity of a statement, when the truth of its output, or conclusion, follows necessarily from its premises — certainty of a conditional and formal sort even when the content is probabilistic — and certainty in the content of the statement itself, when a statement is strictly defined and determinate in its meaning.

Logical certainty is of a sterile sort, working only within the context of the system. Arguments concerning reality must have some referent to it, and these need premises grounded in observation, experience, or experiment to strengthen the conclusion and justify it as a claim of fact.

Axioms and arguments alone tell us nothing of the world — and this is how logical proofs bereft of real factual content fail to do what they are intended. Ignoring empirical knowledge in one’s arguments, and demanding strict logical proofs for matters of worldly fact is to miss the point, and it is dishonest to argue this way when this is understood.

Psychological certitude, the personal feeling of conviction concerning a claim’s truth, is much too subjective and tells us nothing of whether a statement actually is true beyond mere say-so — an ipse-dixit appeal to authority — all too common in claims of private revelatory experiences, which all have their own rivals in the uncorroborated experiences of others.

As above, we cannot rule out the unexpected, since we are not omniscient — we cannot foresee and control for all possibilities — so we must limit ourselves to those we know of and which come to our attention, through knowing and finding out ourselves or learning of them from others.

Whether indeterminacy of a quantum mechanical sort does or does not spill over into the macroscopic world, that of human experience does seem to be ruled by some degree of randomness, and so our knowledge of it seems restricted to the more or less probable than the certain.

General Relativity

General Relativity (Photo credit: Wikipedia)

There are both calculable probabilities — those we can assign a numerical value to — and there is our innate sense of the plausible, that being what we can intuitively consider likely or unlikely based on our available stores of prior knowledge.

It’s possible to have an item of knowledge that is so well established through repeated tests and unsuccessful attempts to falsify it that it seems very close to certain. Some findings, like many of the fundamental laws of nature are so well-supported by the data that it would take mountains of even better data to dislodge them. With most, that has yet to happen.

Such ideas, while still supported by the evidence used to test them, are still subject to questioning and new testing by the research community with each new finding made.

Scientific research is a fiercely competitive enterprise, and it is the rivalries within a field of study that work to give science its self-correcting quality — new research workers are always trying to unseat older ideas to make their careers and establish their reputations.

This rivalry keeps science moving and allows it to be more of a process of thought and less of merely a body of knowledge, to discover new things and reliably produce techniques and technologies that will work for everyone who uses them, regardless of personal belief.

I think that, in an ongoing quest for understanding, we must be satisfied with what we can get, not what we merely wish, and not place the bar for real knowledge so high that we cannot possibly reach it.

The way to the truth…


Deutsch: Johannes Kepler war ein deutscher Mat...

Deutsch: Johannes Kepler war ein deutscher Mathematiker und Optiker. (Photo credit: Wikipedia)

I self-identify as a skeptic, and now and then fall short of the ideal — we all do — but like better and certainly more accomplished skeptics, I believe that, yes, Agent Mulder, the truth is out there…

…But also that the best way to the truth is through skilled, careful reasoning and systematically gathered evidence.

Skeptics tend to value logic and evidence as ways of knowing the natural and social worlds. Without claiming that skeptics “own” logical thinking, I can confidently say that some mix of solid reasoning and sound data evaluation have been very reliable throughout human history, in any profession involving occupational competence, whether a good mechanic, police detective, soldier, electrical engineer, landscaper, lab technician or astrophysicist.

It’s all a matter of using effective knowledge that one can reliably use in situations in the real world — without the universe thumbing its nose and saying “Nope, that just won’t fly.”

It could even be said that there is a set of principles, ideas and values that while not identical with modern skepticism and its use of critical thinking skills underlies both, as with the process of science.

Let me get something straight: skepticism is a set of methods, not a doctrine, belief nor a system of belief advocating any particular position on the nature of reality, so it can’t possibly be true or false.

It’s a method of finding out what’s true or false, or likely to be, and of reliably showing it to be when there’s enough data to come to a reasonable conclusion.

When skeptics are generally agreed that such-and-such a claim is false, likely to be false, or at least highly suspect, it’s because a commonly shared set of methods was used to reach that conclusion, not a taboo about or disinterest in the paranormal or the unconventional.

And conclusions are tentative — good skeptics are willing to change their minds upon the satisfaction of a level of proof appropriate to the claim.

Is there any other, at least as reliable, even superior way of knowing the truth besides reason and empirical data collection? If there are any, I don’t know of them, and I don’t know of anyone else who does and has been able to demonstrate it.

But there are many pretenders to “other ways of knowing.”

Faith, in the sense of belief not resting on sufficient reason or evidence, is out.

The reason for this is that faith in that sense denies reason and evidence to support belief, especially when those may falsify the belief in question. For every unsupported faith-claim, there are countless others just as groundless that contradict it and with no objective way to know which is correct. They certainly cannot all be correct, though they could well all be false. Strength of conviction proves nothing when the argument and data are against you.

The same applies to intuitive revelation as private, non-repeatable experiences with hosts of rival experiences from other mystics, almost all mutually inconsistent, and most unsupported by other facts of the very claims they are said to pertain to.

With no universally agreed-upon way to tell the true from the false, short of using other forms of evidence to corroborate them, some of claims based on these may occasionally turn out to be true or partly true as a lucky guess, but most have shown themselves highly unreliable as effective knowledge-gathering techniques despite their frequency of use by many cultures. If you put out enough random claims, some of them are bound to come true by chance alone, via the Law of Large numbers.

The problem is that most claims to knowledge based on unproven means of gaining input from esoteric sources (themselves unproven or even unprovable to exist) are unreliable, often true by chance alone, and sometimes even fraudulent, so care must be taken in evaluating them.

But care must be taken with any extraordinary claim to knowledge no matter the source and set of methods, any claim inconsistent with a well-supported body of established findings, and the more inconsistent the better and more copious the evidence needed to support it.

After all, claiming that I’ve read a book by a certain author is trivial when both book and author are well-known to exist and I can intelligently discuss the contents of the book with another, but to claim I had a twenty-foot tall eight-limbed radiation breathing alien dinosaur in my bedroom closet would be a claim requiring an enormous burden of proof on my part, since there is no proven knowledge that such beings exist, that any are on Earth if they do, much less the fact that the known dimensions of my closet are too small to contain such a being, and the fact that I show no signs of radiation exposure despite my claimed proximity to the alien.

And no ad hoc hypotheses would or should be permitted. Every link in my claim must hold and be capable of disproof if it is to be acceptable — no excuses!

At the very least, my obstinately persisting in that claim despite disproof would and rightly should raise questions of my honesty or my sanity, or perhaps what sort of joke I’m attempting to play and what the punchline is.

It would be interesting if there really were rival or even superior ways to the truth, but I know of none which currently exist. I suspect that any existing at a future date will most likely be a evolution, vastly improved, of current scientific methodology or something else like it and serving the same function, only better.

That, I think, may be something to look forward to, if not in my lifetime, then the lifetimes of those yet to come. Good or bad, we are living in interesting times indeed.