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Category: Philosophy

The philosophy of science, empiricism, a priori reasoning, epistemology, and so on.

March 20, 2009 | 32 Comments

If Baby cries then we beat him

(This post is only a teaser, a brief introduction to the late philosopher David Stove’s philosophy of logic. I do not intend that today’s article will convince anybody. I do not have time to do more.)

Everybody—especially readers of this site—has had experience with logical arguments. People obviously use logical argumentation continuously, whether or not they are aware that the science of logic has been “made formal” by mathematicians and other such creatures.

Their ignorance of this formalization obviously—I hope it is obvious—does not mean that when these people offer a valid argument it is not made invalid because they are unaware of how to prove it valid.

It was David Stove’s contention that formal logic (to be defined in a moment) is a myth. That is to say, that all attempts to formalize logic were doomed to failure. This might sound like yet another post-modern attempt at skepticism. It is not:

My philosophy of logic is so far from being skeptical that it is if anything indecently affirmative. Not only do I believe, as I have implied, that there are logical truths, true judgments of validity or of invalidity; I believe that every normal human being is, in the extent of his knowledge of such truths, a millionaire. Only, I hold, as I have implied, that almost every logical truth which anyone knows, or could know, is either not purely formal, or is singular or of low generality. [p. 128; The Rationality of Induction]

What did Stove mean by formal?

An argument is formal “if it employs at least one individual variable, or predicate variable, or propositional variable, and places no restriction on the values that that variable can take” (emphasis mine). Stove claims that “few or no such things” can be found.

Here is an example of formality: the rule of transposition. “If p then q” entails “If not-q then not-p” for all p and for all q.

This is formal in the sense that we have the variables p and q for which we can substitute actual instances, but for which there are no restrictions. If Stove is right, then we should be able to find an example of formal transposition that fails.

First a common example that works: let p = “there is fire” and q = “there is oxygen”, then

    “If p then q” == “If there is fire there is oxygen”.

And by transposition, not-q = “there is no oxygen” and not-p = “there is no fire” then

    “If not-q then not-p” == “If there is no oxygen then there is no fire.”

For an example in which formal transposition fails, let p = “Baby cries” and q = “we beat him”, thus

    “If p then q” == “If Baby cries then we beat him”.

But then by transposition, not-q = “We do not beat Baby”, not-p = “he does not cry”, thus

    “If not-q then not-p” == “If we do not beat Baby then he does not cry.”

which is obviously false. (Stove credits Vic Dudman with this example.)

So we have found an instance of formal transposition that fails. Which means logic cannot be “formal” in Stove’s sense. It also means that all theorems that use transposition in their proofs will have instances in which those theorems are false if restrictions are not placed on its variables. (It’s worse, because transposition is logically equivalent to several other logical rules; we won’t go into that now.)

It is Stove’s contention that all logical forms will have an example where it goes bad, like with transposition.

Exercise: can we find counterexamples to the two most popular logical forms, modus ponens and modus tollens? I haven’t tried yet, but I rely on the way-above-average intelligence of our readership to provide some.

Modus ponens: “If p then q, p, therefore q, for all p, q”. Example: “If Socrates is a man then he is mortal, Socrates is a man, therefore he is mortal.”

Modus tollens: “If p then q, not-q, therefore not-p, for all p, q”. Example: “If Socrates is a man then he is mortal, Socrates is not mortal (he is immortal), therefore Socrates is not a man.”

March 16, 2009 | 23 Comments

Necessary but not sufficient


You often hear, if you manage to stay awake during the lectures, a mathematician or physicist say, “The following is a necessary but not sufficient condition for my theory to be true.”

We say this so often that we tend to blend the words together: necessarybutnotsufficient, and we forget that it can be a confusing concept.

It means that there is an item or a list of items that must be the case in order for my theory to be true. But just because that item or those items on that list are true, it does not mean that my theory must be true. It could be the case that the item is true but my theory is false.

This is all important in the theory/model building that goes on in the sciences.

For example, it is necessary but not sufficient that my theory be able to explain already observed data that I have collected. If I cannot at least explain that data, then my theory cannot be true. This is necessarybutnotsufficient in the weak sense: all theories must be able to explain their already-observed data.

Again, it is a necessary but not sufficient condition that my theory be able to explain future data. This is necessarybutnotsufficient in the strong sense: if my theory is right, it must be able to explain data that is not yet seen.

Understand: it can still be the case that my theory can predict data that is not yet seen and my theory could be false. This is true in all cases where we cannot deduce (know with certainty) the true of a theory. Most theories (outside math) are not, of course, deduced.

How about an example? Let’s us the following game.

The Game

Go to The Philosopher’s Mag and play this game called “Dealing with Induction”. It asks the question: “how easy is it to draw a wrong conclusion about the future from the evidence of the past?”

The game tests your inductive reasoning skills and asks you to infer the rule that accepts or rejects cards from a standard 52-card deck.

Let me be as clear as possible. The following conditions hold: (1) You believe that a rule that generates the card exists. (2) You will see a sequence of cards from which you will attempt to infer, through induction, the rule. (3) No matter how many cards are shown you will never know the rule with certainty; that is, you will never be able to deduce the rule from a set of premises.

Do not read further until you have played the game fully and discovered its secret.

Did you really play?

Tell the truth. Don’t cheat and read any more until you have played the game.

Continue reading “Necessary but not sufficient”

March 10, 2009 | 16 Comments

CBC’s How to Think Aboot Science series

The Canadian Broadcasting Corporation has a great web site with a series (so far on-going) How to Think Aboot Science.

I recommend the site as a great resource for interviews with the players in many different areas of the philosophy of science, on the sociology of science, and on what is happening at the far fringes and beyond.

While I encourage a visit to the site, I can hardly recommend some of the ideas presented there. A few of them are downright screwy.

For example, James Lovelock rolls out his tired Gaia hypothesis for the n-teenth time. This belief states, more or less, that the Earth is alive and in just the right condition—lest we continue being naughty and upset the balance—for human life. Also the life of viruses, infectious bacteria, rats and other vermin.

Actually, whenever Gaia supporters mention non-human lifeforms, it’s always the fuzzy or feathered kind. They always forget the nasty stuff. Anyway, the Gaia hypothesis is sort of the Strong Anthropic Principle applied to just the planet, and just the way the planet is now (forgeting orbital variations, for example).

Rupert Sheldrake talks about having psychic connections with plants—no, not really. But what he’s advocating is not too different. Sheldrake is a big ESP buff. He has the idea that, roughly, plants have mysterious aura-like fields that are necessary for their growth. Nobody else has been able to find them yet, but Sheldrake can.

Steven Shapin presents the standard relativist view (that we refuted yesterday) that “science is social all the way down, and that this in no way undermines its truth claims, truth also being, by nature, social.” Hey, Shapin, is that statement true? If so…well, you get the idea.

There are many nods to our modern sensitivities, as will be obvious from a cursory inspection of the speakers and topics.

Then again, there are some intriguing, even daring, ideas. Margaret Lock, who has studied menopause in North American and Japanese women “makes a surprising suggestion. She proposes that there are biological differences between [these] women.” Not just cultural, but physiological differences. Not superficial ones, either, like outward appearances, but something more fundamental. This is a politically dangerous area, as, say, Charles Murray would tell you.

Lee Smolin takes string theory to task, as he does in his readable and important The Trouble with Physics. Smolin claims that string theory is beautiful—and exceedingly complex—mathematics, but it doesn’t seem to be physics.

Allan Young talks about how post-traumatic stress syndrome was invented, created out of whole cloth, that is.

Christopher Norris and noted philosopher Mary Midgley try to bring realism back to the Western world (I would say it was always there, but ignored or denied). It was Midgley, incidentally, that gave the most scathing and damning attack on Richard Dawkins memes and self genes theories.

Maybe we should have audio interviews here with some of our—it has to be said—highly intelligent readers.

March 9, 2009 | 15 Comments

Relativism: an idea that failed before it started

The Books of Absolutes: A Critique of Relativism and a Defence of Universals
William D. Gairdner
McGill-Queen’s University Press
Recommendation: Read

Let’s play spot the flaw. In 1994, professor Mark Glazer said, “Cultural relativism in anthropology is a key methodological concept which is universally accepted within the discipline.” (It’s the very first sentence after the link.)

Don’t have it yet? Then let’s remind ourselves of what cultural relativism means: “Cultural relativism is the view that all beliefs are equally valid and that truth itself is relative, depending on the situation, environment, and individual.”

You surely have it by now, so let’s move on to the twelve objections to relativism as outlined by Gairdner in his Book of Absolutes.

Wait…what? You don’t see the flaw? Ah, I guess it’s hard to spot contradictions like this when we’re exposed to them so often that they seem natural.

If it is true that “Cultural relativism is the view that all beliefs are equally valid” etc., and that that proposition is “universally accepted”, then we are confronted with something that is true wherever you are. If “relativism” is true, then it is false because anthropologists everywhere believe it, and if they everywhere believe it, it is a universal truth, something that is true without regard to culture.

It gets even more asinine. If “Cultural relativism is the view that all beliefs are equally valid” etc., then how valid is the view that “Cultural relativism is false”? I’ll leave you to fill in the blanks.

Cultural relativism is an idea that is immediately seen as not just false but incredibly stupid, so you have to wonder how it originated and why it took such a tight hold on Western academia.

Gairdner relates the history and puts a lot of the blame on German export Franz Boas, an anthropologist who was horrified by World War I, eugenics, and other popular pastimes at the turn of the last century. Boas feared absolutes, such as those preached by the rising Socialist (National) party in Germany, because he felt that they could be used to justify any atrocity. Example: If it is true that Xs are inferior, then it is okay to exterminate them, where X is any group that is on the outs.

Boas was immensely influential, and if the story is right, transformed all of anthropology so that absolutes were seen as verboten. One of his students was Margret Mead, and we know where that story ended.

After going through the book, a good argument can be made for restricting all intellectual output of Germany, re: the romanticism of Nietzsche, its practical implementation under the uber-Nazi Heidegger—and then there’s the deconstructing, post-modernist pair of Foucault and Derrida, who were both French, but who lived so close to the German border that they soaked up too much of what was seeping out. The story of how these men captured the minds of academics is particularly interesting. It has been told before, but Gairdner was an inside witness and his anecdotes are interesting, especially the story of modern Saussarian linguistics and its eventual corruption by the cult of relativism.

There are separate discussions of human biology, language, law, and customs, which all have lists of universals of the constant, conditional and statistical kind. Constant means the trait, such as the taboo against murder, is shared by every culture. Conditional means that if trait A is present then B always is, but that trait A might not be constant. Statistical traits are found in most but not necessarily all cultures (and are thus not universal, but intriguing anyway).

Gairdner attempts a list of physical constants, which is a good enough idea, but times are changing in physics and the “constants” once held dear have become malleable. But never mind. His central idea is still right: there are truths that exist independent of human minds or thought. He also has a go at the stronger Anthropic Principle, but is not convincing. However, I’ve yet to meet with an argument for that Principle that is.

The amazing thing is that universals, or even the possibility of them, were so thoroughly rejected by highly paid, tenure-wielding, peer-reviewed professors. That is, during the twentieth century the intelligentsia gathered as one and said, “There are no universals, there is nothing that is true.”

Now that is a shocking statement. But it came from a consensus of professors, and who are we mere mortals to question a consensus? So it was believed, and from it came things like judicial activism, multiculturalism etc., etc. If there is nothing universally true, academics swooned, then think of the possibilities!

Of course, the flaw in that statement was always obvious, plain, and damning. For we can ask, “Is it true that there is nothing that is universally true?” The post-modernist professor must say yes, but as he does, he makes himself a fool, albeit one with a comfortable “research” budget.

Anyway, here are a few representative examples of relativism culled from Gairdner’s book, all of which share the same self-contradictory logical flaw. You will need some familiarity with the subjects to understand some of the statements (background for each is given in the book). That these blatant flaws were overlooked—usually in the name of “good intentions”—says quite a bit about how the desire for power can so easily blind.

* Dawkins, in his Selfish Genes, says our brains have grown so large that we can rebel “against our own natures.” “We along on earth, can rebel against the tyranny of the selfish replicators.”

* Yet another German, influential legal scholar Hans Kelsen, “rejected and derided outright the claims of ‘philosophical absolutism’, which insist there is a foundational reality that exists independent of human knowledge.”

* The post-modern interpretation of literature: “All texts, and the world itself, are nothing more than ‘a galaxy of signifiers.'”

* Nietzsche “protested that all religions and philosophies are but thinly veiled attempts by their to control others by persuading them of the ‘facts’ produced only by the logic of their pet theories.”

* Derrida: “no discourse has the objective capacity to analyze another discourse.”

* Foucault: “interpretation can never be brought to an end…because there is nothing to interpret.”

* Said’s and others’ anti-foundationalism: which argues there can be no foundation in philosophy.