Thursday, December 22, 2005

Knowing the Obvious

Just how much of this fancy fransy philosophy is enough to determine how we should respond to the obvious threat of jihad and social disintegration? Is any of this interior inspection of historical opinion making worth the time and trouble? We all know more or less what needs to be done, though we might differ on the details. Islam is a sick ideology that has many millions of poor and ignorant people perched on the verge of catastrophe, threatening not just the West but the world itself with war and annihilation. It's clear that any religion, so-called, that enslaves its female members, reduces them to sex toys and baby farms, that sexually mutilates little girls for the sake of controlling their behaviour, that's obsessed with appearances at the cost of achievement and productivity, that is in every respect an unworthy idea and a danger to the public good and the very safety of the common world of Humanity, that that ideology should be rooted out and destroyed as a matter of course, as a matter of ordinary decency and common sense, if not of prudence and self-preservation. Our political and social leaders, our intelligentsia and our moral leaders collude in the game of "Let's pretend Islam is a religion of peace and that the West is filled with racists." We don't need much detail to know that Islam is evil. And if we need any proof other than what we have and have had since day one, all we really need to debunk the idea that Islam is anything other than evil are these two words: "nine eleven." So why all this about philosophy?

If our reaction to Islamic madness is to counter it with dhimmitude and suicide, then we must look at ourselves to ask why we are reacting as we are. It's obvious that Islam is a madness, and that it's violence and savagery are a threat to us. That needs no further investigation. We do. We need to do some serious navel gazing. We have to ask ourselves how we can look at the obvious and not see anything sensible. How can we look at our own lives, in that case, and trust ourselves to act responsibly toward our children? We are definitely doing something extremely wrong, and we should give it a bit of thought before we commit ourselves to anything further.

Below we can take a look at looking and knowing. How we approach these things will tell us how we approach tomorrow and jihad without the dubious benefit of our leaders. We must, soon, learn to lead ourselves. We have to know how to see and know the real without being taken in by nonsense, even the most obvious nonsense that we convince ourselves is true.

Sorites Paradox

The sorites paradox is the name given to a class of paradoxical arguments, also known as little-by-little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved. For example, the concept of a heap appears to lack sharp boundaries and, as a consequence of the subsequent indeterminacy surrounding the extension of the predicate 'is a heap', no one grain of wheat can be identified as making the difference between being a heap and not being a heap. Given then that one grain of wheat does not make a heap, it would seem to follow that two do not, thus three do not, and so on. In the end it would appear that no amount of wheat can make a heap. We are faced with paradox since from apparently true premises by seemingly uncontroversial reasoning we arrive at an apparently false conclusion.

This phenomenon at the heart of the paradox is now recognised as the phenomenon of vagueness (see the entry on vagueness). Once identified, vagueness can be seen to be a feature of syntactic categories other than predicates, nonetheless one speaks primarily of the vagueness of predicates. Names, adjectives, adverbs and so on are only susceptible to paradoxical sorites reasoning in a derivative sense.

Sorites arguments of the paradoxical form are to be distinguished from multi-premise syllogisms (polysyllogisms) which are sometimes also referred to as sorites arguments. Whilst both polysyllogisms and sorites paradoxes are chain-arguments, the former need not be paradoxical in nature and the latter need not be syllogistic in form.


1. The Sorites In History The name 'sorites' derives from the Greek word soros (meaning 'heap') and originally referred, not to a paradox, but rather to a puzzle known as The Heap: Would you describe a single grain of wheat as a heap? No. Would you describe two grains of wheat as a heap? No. … You must admit the presence of a heap sooner or later, so where do you draw the line?

It was one of a series of puzzles attributed to the Megarian logician Eubulides of Miletus. Also included were:

The Liar: A man says that he is lying. Is what he says true or false?

The Hooded Man: You say that you know your brother. Yet that man who just came in with his head covered is your brother and you did not know him.

The Bald Man: Would you describe a man with one hair on his head as bald? Yes. Would you describe a man with two hairs on his head as bald? Yes. … You must refrain from describing a man with ten thousand hairs on his head as bald, so where do you draw the line?

This last puzzle, presented as a series of questions about the application of the predicate 'is bald', was originally known as the falakros puzzle. It was seen to have the same form as the Heap and all such puzzles became collectively known as sorites puzzles.

It is not known whether Eubulides actually invented the sorites puzzles. Some scholars have attempted to trace its origins back to Zeno of Elea but the evidence seems to point to Eubulides as the first to employ the sorites. Nor is it known just what motives Eubulides may have had for presenting this puzzle. It was, however, employed by later Greek philosophers to attack various positions, most notably by the Sceptics against the Stoics' claims to knowledge.

These puzzles of antiquity are now more usually described as paradoxes. Though the conundrum can be presented informally as a series of questions whose puzzling nature gives it dialectical force it can be, and was, presented as a formal argument having logical structure. The following argument form of the sorites was common:

1 grain of wheat does not make a heap.
If 1 grain of wheat does not make a heap then 2 grains of wheat do not.
If 2 grains of wheat do not make a heap then 3 grains do not.

If 9,999 grains of wheat do not make a heap then 10,000 do not.
10,000 grains of wheat do not make a heap.

The argument certainly seems to be valid, employing only modus ponens and cut (enabling the chaining together of each sub-argument which results from a single application of modus ponens). These rules of inference are endorsed by both Stoic logic and modern classical logic, amongst others.

Moreover its premises appear true. Some Stoic presentations of the argument recast it in a form which replaced all the conditionals, 'If A then B', with 'Not(A and not-B)' to stress that the conditional should not be thought of as being a strong one, but rather the weak Philonian conditional (the modern material conditional) according to which 'If A then B' was equivalent to 'Not(A and not-B)'. Such emphasis was deemed necessary since there was a great deal of debate in Stoic logic regarding the correct analysis for the conditional. In thus judging that a connective as weak as the Philonian conditional underpinned this form of the paradox they were forestalling resolutions of the paradox that denied the truth of the conditionals based on a strong reading of them. This interpretation then presents the argument in its strongest form since the validity of modus ponens seems assured whilst the premises are construed so weakly as to be difficult to deny. The difference of one grain would seem to be too small to make any difference to the application of the predicate; it is a difference so negligible as to make no apparent difference to the truth-values of the respective antecedents and consequents.

Yet the conclusion seems false. Thus paradox confronted the Stoics just as it does the modern classical logician. Nor are such paradoxes isolated conundrums. Innumerable sorites paradoxes can be expressed in this way. For example, one can present the puzzle of the Bald Man in this manner. Since a man with one hair on his head is bald and if a man with one is then a man with two is, so a man with two hairs on his head is bald. Again, if a man with two is then a man with three is, so a man with three hairs on his head is bald, and so on. So a man with ten thousand hairs on his head is bald, yet we rightly feel that such men are hirsute, i.e., not bald. Indeed, it seems that almost any vague predicate admits of such a sorites paradox and vague predicates are ubiquitous.

As presented, the paradox of the Heap and the Bald Man proceed by addition (of grains of wheat and hairs on the head respectively). Alternatively though, one might proceed in reverse, by subtraction. If one is prepared to admit that ten thousand grains of sand make a heap then one can argue that one grain of sand does since the removal of any one grain of sand cannot make the difference. Similarly, if one is prepared to admit a man with ten thousand hairs on his head is not bald, then one can argue that even with one hair on his head he is not bald since the removal of any one hair from the originally hirsute scalp cannot make the relevant difference. It was thus recognised, even in antiquity, that sorites arguments come in pairs, using: 'non-heap' and 'heap'; 'bald' and 'hirsute'; 'poor' and 'rich'; 'few' and 'many'; 'small' and 'large'; and so on. For every argument which proceeds by addition there is another reverse argument which proceeds by subtraction.

Curiously, the paradox seemed to attract little subsequent interest until the late nineteenth century when formal logic once again assumed a central role in philosophy. Since the demise of ideal language doctrines in the latter half of the twentieth century interest in the vagaries of natural language, and the sorites paradox in particular, has greatly increased.


I think these things are not only interesting but valuable for us as individuals. It's not for everyone, of course, but for those who enjoy it, this is fun, and with that, I wish you a Merry Christmas.

We'll be back tomorrow with more jihadi thrills and dhimmi chills.

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