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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 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 either.

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).

Project Logicality: the Unexplained vs. the Unexplainable


Massimo Pigliucci

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This post has been rewritten from its earlier form and updated for this release. None of the meaning has been changed, and dead links have been removed and replaced by new. ~ Troythulu

Confusing the currently unexplained with the forever inexplicable…

This is a common fallacy, and an easy one to commit, in confusing whatever is currently unexplained with that which has no explanation at all, or at least no reachable one.

I hear this fallacy a lot from believers in the paranormal and supernatural, both online and face-to-face, and it’s is a close cousin to the argument from ignorance in inferring that because one can’t think of an explanation that there is none, and in a further move in reasoning in assuming that this strengthens the case for anything beyond nature or normality.

First, what is the unexplained?

What is the unexplainable?

How do we tell them apart?

Anything that currently lacks a known explanation may, possibly, have an explanation out there somewhere waiting to be found, even if you, anyone you know, or anyone you don’t, is unaware of what the explanation is at this moment.

The point is that you cannot say that something is truly unexplainable at least until you actually look, and in your inquiry exhaust all conceivably possible explanations and find none. Even then, no matter where you look, you cannot be certain on a finite data set.

Is it truly unexplainable even then?

Not so fast.

One can never be certain that someone, somewhere, doesn’t, can’t, or won’t know how to explain a given seemingly mysterious phenomenon, since humans are not omniscient, and it is therefore impossible for any one person to know what everyone else in the universe knows, and from this, safely assume that an explanation is both unknown and unknowable anywhere in spacetime.

Merely because YOU don’t know, or can’t, does not apply to everyone else, and assuming that it does is arrogant and unreasonable in attempting to impose your own cognitive limitations on everyone else.

There is always someone who knows more than you do, or who does or can imagine things you don’t or can’t.

As for the truly unexplainable, philosopher Massimo Pigliucci has noted two different sorts, first, those phenomena which absolutely have no reasonable explanation, and second, those phenomena which do have a rational explanation somewhere out there, but which is inaccessible due to human limitations in reasoning and comprehension, sort of like my kitten understanding the math for quantum mechanics (sorry, Mister Eccles…) or relativity theory.

Scientific inquiry, and any other useful process of gathering knowledge about reality, requires some humility and open-mindedness in understanding the limits of what we currently know and a willingness to at least consider new ideas…

…and saying that “ID did it,” “God did it,” “ET did it,” “a ghost did it,” or “psi did it,” explain nothing and most definitely will not get you past peer-review nor win you the JREF million dollar challenge.

Everything that science has ever examined has turned out to be both natural and normal, not magic.

Consider that before proclaiming something to be unexplainable, when the explanation you don’t know about may be just where you haven’t or won’t look.

Project Logicality: What is Argumentation?


Cropped image of a Socrates bust for use in ph...

Cropped image of a Socrates bust for use in philosophy-related templates etc. Bust carved by by Victor Wager from a model by Paul Montford, University of Western Australia, Crawley, Western Australia. (Photo credit: Wikipedia)

This post was originally published in 2011, and since then I’ve decided to give it new life and clear up difficulties in the text. I decided to use it once for for the pilot entry of my current Project Logicality. I hope it adds to the online discussion of the virtues of reason despite the decidedly unreasonable tendencies of the human species.

What is it that I mean when I say ‘argument?’ When I use this term, I don’t mean quarrelsome bickering accompanied by yelling and screaming, nor do I mean a mere shadow of an argument where debaters try to undermine the legitimacy of each others’ position without attempting to reach a real understanding or settling anything.

When I say, “argument” I mean it in the context of any rational discussion with constructive intent, not an attempt to thwart constructive ends through fallacious means.

Here, I mean that the parties involved act to offer reasons, premises, rationales, and justifications for the statements, the claims, and the ideas that they put forth. They want others to accept these, not merely by pandering to their prejudices or appealing to their biases, nor upon the use of legal or physical force, but by winning the free assent of that audience — an audience treated as though it were in principle intelligent, educated, and capable of exercising rigorous critical judgement.

I refer to argument in the sense of modern argumentation theory, a vibrant field of study involving the making and use of messages to influence others, by appealing to their willingness to cooperate — this is essential for the conditions of a viable free society.

Any coherent social structure, especially a functioning representative democracy with a large number of people needs some means of mutual influence between its members, of and for the viability of its governing system, however imperfect its governing body in practice. Perfection in matters of human endeavor is a chimera.

Argumentation as a field of study crosses paths with three other areas of intellectual endeavor:

First, it converges with Logic, the broader study of the structures we use in all processes of reasoning — this includes formal logic, mathematical and symbolic logic where the conclusion of a valid argument is alleged to be certainly true if the premises used to support it are also true.

But argumentation concerns itself more with informal logic, the everyday reasoning we engage in within typical discussions — in which the statements we wish to support do not follow with certainty, but to a degree of probability depending on the strength of our reasons and the willingness of the audience to accept them.

In argumentation, even the very idea of certainty depends on the audience addressed.

Language is important in informal logic, because informal argumentation depends heavily on the use of language as the content of the argument. Language is more than merely decorative window-dressing for an informal argument, but an essential part of the argument’s inherent meaning. The language that an argument is cast in cannot be taken from the argument itself without rendering it sterile and empty.

Second, argumentation converges with Rhetoric, originally one of the seven Liberal Arts — it is more than just vacuous or bombastic and flowery ornamentation in speech as is commonly supposed, but in the technical sense it is the broader study of how people are influenced by messages.

It is from Rhetoric that argumentation gets the concern with the requirements of an audience — its needs, disposition, and outlook must be considered by the arguer in making their case.

Third, argumentation crosses over with dialectic, a term that many people still associate with the concept of an opposition between grand historical forces, like the opposition of capitalism and communism depicted in Marxist social theory.

This concept has a different meaning, and dates at least since the Socratic method,  given in the dialogues of Plato, and others, in which fictionalized persons are seen to engage in a sort of give and take exchange of questions and answers to resolve a dispute or reveal the truth of a matter.

This sort of questioning is similar to the use of cross-examination of witnesses in modern legal courts by the prosecuting attorneys in a case to uncover inconsistencies in testimony and to reveal possibly questionable motives.

Argumentation is the meeting point of all of these fields, and with it, we can clarify our understanding of our positions, resolve disputes, reach sound decisions for collective actions we may undertake, engage in formal and often productive debates, and, with ourselves as the audience, think through personal problems we may face or get out of a rut.

Argumentation as a process of giving reasons for our claims is one of the most important abilities we have as humans, and no matter our level of education, we can all benefit from the ability to arrive at better answers to questions and make more sound decisions than we otherwise might.

Argumentation isn’t just for egghead academics: Clear thinking and having good reasons for what we believe and do are for everyone. As humans, we are not always rational, but we have a sense of reason, one that once nurtured and practiced can serve us and enfranchise us as informed, effective, and smart voters very well indeed.

 

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Evaluating Arguments & the Creeping Spectre of Gullibility


I’ve strived from the start to be a fair skeptic, to see arguments as they are, to analyse and evaluate them in such a way that I see errors in reasoning, logical fallacies, only where they actually exist, and so to avoid attacking straw-person caricatures of what is being argued…to see an argument as it really is, and to attack it only on its merits, or lack of them.

But as someone diagnosed with an illness like mine, I find that the real danger is not seeing fallacies of argument where they are not, but failing to see them where they are, and this I find unsettling. It’s sometimes the case that I’ll read or hear an argument, and while a skeptic without my disorder would easily note the error, rather than to not make out the sense of a reasonable argument, I sometimes make out too much sense out of unreasonable arguments — I sometimes see valid arguments where they are not.

While my treatment plan helps substantially with the more overt forms of delusional thinking, aided to a degree with skeptical thinking, I can and sometimes do, without thinking carefully, experience a feeling of sensibility when none is actually warranted.

Sometimes, I catch myself, with a brief mental “Aha! Gotcha!” followed by a rejection of the spurious feeling of sensibleness, sometimes, though, it slips past me, and lo, I am fooled.

This means that I sometimes miss what would be obvious and glaring logical errors to others with even the same knowledge and experience as I, minus the diagnosis of course.

I’m currently expanding my understanding of logical and rhetorical fallacies, and this has been very helpful, but I know that if anything, I must learn more and train my intuitive faculties further still. There is much to learn, still much to take in.

I must always be on the lookout for my overactive intuition, and I’m engaged at reining it in, to limit its purview to — mostly at least — those things that actually do make sense once truly understood, and not misleading fallacies, deepities, and word-salad with no real meaning at all.

While I can’t ever be absolutely certain to avoid that, so what? I’m not convinced that anything in the world can be known as absolutely certain, nor needs to be absolute to count as knowledge.

That it does is a claim that I’m deeply suspicious of, and maybe that’s a good sign.

Funny thing, that, the common phrase denoting claims to absolute knowledge, “set in stone,” when it doesn’t take a scientist to know that a stone wears away with time, and even the universe has a lifespan.

There’s hope yet. And where there is hope, there is life.

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Why I get my science from scientists and not #FauxNews…


I feel up to blogging for this morning, and during this day and the next I’ll be reading up on SF approaches to zero-point energy production for a friend of mine, which should be fun.

*waves at @Ravenpenny*

Especially important in looking into zero-point energy is avoiding any use of blatant pseudoscience from so called “free energy” machine sellers…

Rubber science is acceptable within the context of fiction, implausible technological quackery is NOT!

So far, I’ve got two reference pages out of five candidates in separate browser tags. The other three candidate pages are all crank sites, with obvious red flags. I won’t sully my reputation, such as that is as a relative no-name in the skeptical community, by using those last as sources.

This raises a question…

Out of the arguments of both proponents and critics of any claim, how do I decide which claimant is more credible?

There are a set of steps I use that make for a useful start of any inquiry, and I’ll put these into three groups of related questions:

  • First: Which side in a given controversy, genuine or manufactroversy, commits the fewest logical fallacies? Which side has the most valid or cogent arguments and makes the fewest errors in reasoning? Once these are compared and an answer obtained, I then choose the side with the best arguments and go to step two. Remember though, to take care to see fallacious arguments that are actually there, and not the result of wishful seeing. And so…
  • Secondly: Which side has the better factual support for their claims. Do their respective claims add up under adequate fact-checking using reliable sources? Do credible sources support or reject the claims made? Which sources have the better track-record and reputation as a valid and reliable? Next…
  • Thirdly: Related to the second, but worth it’s own step: Which factual statements, when checked, even if and when true, are actually relevant to the claims and counterclaims made? Does the alleged factual support of a given claim actually have anything to do with it?

These three points are a basic rundown of the steps I use.

Answering these questions on science and science-relevant news are one reason I tend to support climate scientists over so-called climate sceptics, and professional biologists over the various species of creationists found online and in religion and politics.

They are the reason that I tend to give more credence to the statements of astronomers than I do astrologers, Physicists and psychologists more than psychic claimants, chemists over alchemists, and neuroscientists over phrenologists.

These questions are the reasons I don’t get my science from clergymen, religious apologists, allegedly fair and balanced media outlets, politicians or radio talk-show propagandists.

Those are not what I would call credible sources.

I get my science from scientists, and science-writers with a real background in the field, thank you, not preachers, partisan bloggers, or people who loudly decry government and taxation while also running for public office so they can get paid a rather handsome salary, with kickbacks and bribes paid by lobbyists, otherwise funded by my taxes.

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