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Category: Philosophy

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

December 22, 2007 | No comments

The impossibility of there being no truth.

One of the premises frequently used for the argument that “all cultures are equal” (multiculturalism), or for the argument that you should not be judgmental, is relativism, which is the idea that there is no absolute knowledge, that is, that there is no truth. Some would write it, “there is no ‘truth.'” The scare quotes indicate the author’s derision of the word. As the philosopher David Stove has made clear, the scare quotes turn the word from its obvious meaning, that something is true, to something that is only believed by so-and-so to be true. Thus, the quotes also serve to give their users a self-made patina of superiority.

Roger Kimball, in his blog Roger’s Rules, told of his attendance at a colloquium to honor the philosopher Leszek Kolakowski. In a session on ?Enlightenment, Modernity, and Atheism,? one of the participants began her statement, ?I know, of course, that there is no truth.?

And it’s in this sentence that we have the proof that its own conclusion is false. Which is another way of saying that the woman’s statement is paradoxical, and therefore nonsensical.

Why? If it’s not already obvious to you, “to know” can only mean that you are aware of a truth. And the truth that you know cannot be that there is no truth, because then you would not be able to know it.

The original sentence cannot be saved by changing it to “There is no truth” because, as Bill Clinton might remind us, it depends on what that meaning of is is. And the meaning is existential, which is to say, that the thing of which it speaks (truth) exists. In any case, the sentence “There is no truth” is either true or false. If it is true, then there can be no truth, and so the sentence cannot be true, hence a paradox.

All arguments against the idea of truth fail for the same reason. Because no matter how cleverly you couch your language, no matter the strength of your authority, in the end either your argument is true or it is false. If it is true, then there is no truth, and your argument cannot be true, and you’re right back in the same paradox.

The non-existence of truth is then an impossibility, thus true things exist. So the task becomes identifying what those truths are. And that’s no easy task!

What does this have to do with statistics? A lot, actually, because all statistics is based upon probability, the nature of which we first have to understand before we can use any statistical method. One view of probability, and the dominate one in Bayesian statistics, is the idea that probability is subjective, nothing more than a construct in an individual’s mind. In other words, subjective probability is a philosophy of relativism. Those who hold this view believe that there cannot be objective, i.e. true, probability.

Naturally, I believe this is false. Stay tuned for more.

December 20, 2007 | 4 Comments

What is the environment?

The environment is, of course, something that only you can save. It is something to be preserved. It has a spiritual essence. In hotels anxious to reduce their laundry bill, the environment takes shape in a picture of a beaver or otter. Global warming adversely affects the environment. And everybody talks about it.

But what is it?

Is the environment the forest glen, or the woods and other various natural habitats, or the ocean, or the places in which man does not live? No, not exactly.

Here is what it is:

The environment is everything

Yes, everything. The house in which you live, the city around you, the car in your driveway, the grass and rocks in your yard, the woodlands nearby, the air which you breath, the ionosphere where the solar wind meets the atmosphere, just everything. Including you.

One thing that the environment is not is the “stuff without man.” For there is no such stuff or place, and there has been no such place since the first homo sapiens evolved.

Even more, it is impossible for any organism, any species, to not irrevocably influence its environment. Once you—or any organism—comes into existence, even before you take your first breath, you have permanently changed the world. Every action you take, including taking no action at all, necessarily implies interacting with your environment. And there is nothing that you can do to alter this fact. You cannot even avoid changing the environment by dying: once dead, you decompose, adding greenhouse gases to the air, as well as contributing nutritious (to various bugs and bacteria, that is) elements to the soil.

Further, there is no, never was, and never will be, a “natural” state where mankind lives in “harmony” with “nature.” Nature is, after all, only a synonym of environment.

Stronger still, you cannot even say that nature is “in harmony with” or even “indifferent” to man, or to any, species. To say that it is so imbues the word nature with a sentience and purpose which it simply does not have. There is nothing there that can be indifferent, or benign, or harmonious, or hostile, or that can have any intentional design.

Since it is logically impossible that man, or any species, cannot help but influence his environment—or to state this positively: Man, and every other species, must influence his environment—it becomes only a question of how much he does so, and does he do so to his own detriment or benefit, and can he purposely direct his influence to enhance his lot, or are his actions largely circumscribed.

If you imagine that pointing out these logical facts is only a prelude to a speech about how, since the environment is everything, and that mankind cannot but influence it, it is OK to pollute it, you are sadly wrong.

It is merely to emphasize that some changes to the environment due to mankind are inevitable and irreversible, and that the best political will cannot change this. It is even likely that we are unaware of what most of these changes are; but we do know of others. The most commonly known one, of course, is that man adds carbon dioxide to the atmosphere, and that, all other things being equal, more carbon dioxide means more infrared energy absorption in the atmosphere, hence a warmer planet.

But all other things are not, and cannot, be equal. Thus it is not clear whether this change is irreversible, and how much of it is inevitable. It is, however, a fact that it cannot be entirely deleterious (for example, plant life thrives in atmospheres with higher concentrations of carbon dioxide).

We hear a constant clamor to “Save the environment!”, especially from the perceived evils of global warming, but there is nothing to save. There is just the environment in one state or another. But the obvious connotation to these pleas is that we can define an ideal, at least in broad strokes, and it is this ideal that is to be sought. This can and has been done locally, and in limited scope: for example, we can pick up our garbage so as to, at the least, discourage disease-ridden vermin. Of course, nobody has yet attempted to define the ideal global environment, and I wonder at its practicality.

But the global ideal must be defined, and so must the extent of the inevitability and irreversibleness of man’s activity, and all this must be done before we invoke a bureaucracy that will tax and meddle and exhort and will, as history has taught us, seek self-perpetuation above all else.

December 6, 2007 | No comments

The Algebra of Probable Inference: Richard T. Cox

This is a lovely, lovely book and I can’t believe it has taken me this long to find and read it (November 2005: I was lead to this book via Jaynes, who was the author that also recommended Stove). Cox, a physicist, builds the foundations of logical probability using Boolean algebra and just two axioms, which are so concise and intuitive that I repeat them here:

1. “The probability of an inference on given evidence determines the probability of its contradictory on the same evidence.”

2. “The probability on given evidence that both of two inferences are true is determined by their separate probabilities, one on the given evidence, the other on this evidence with the additional assumption that the first inference is true.”

Cox then begins to build. He shows that probability can be, should be, and is represented by logic; he shows the type of function probability is, the relation of uncertainty and entropy, and what expectation is. He ends with deriving Lapace’s rule of succession, and argues when this rule is valid and when it is invalid. And he does it all in only 96 pages!. This is one of the rare books that I also recommend you read each footnote. If you have any interest in probability or statistics, you have a moral obligation to read this book.

October 6, 2007 | 1 Comment

The Rationality of Induction: David Stove

Is deductive logic empirical? No. Is inductive logic also empirical? No. Is induction justified and, if so, is it just an extension of logic? Yes.

These are Stove’s conclusions as he takes Hume (and current-day relativists,such as Popper) to task and shows that, yes, induction is rational. He also shows that the common belief that ordinary logical is formal is a myth. Knowledge of the validness of certain arguements must come from intution, as Carnap argued, and Stove proves. He shows that certain forms of logical arguments do not always give valid conclusions, and that all arguments must be judged individually. In his words, “Cases Rule”.

This is another in a series of books that I think are largely unknown by most statisticians and probabilists, especially those who tend toward so-called pure mathematics. But this book, like those by Jaynes and Cox, argue the case for logical, as opposed to subjective, probability forcefully and conclusively. They deserve to be more widely read because, I believe, they have a great deal to say on the foundations of our field.