Saturday, July 20, 2013

Greatness, By Definition

The goals for this blog have always been two-fold: (1) to bring students and professionals in the sciences into close acquaintance with centrally important topics in Bayesian statistics and rational scientific method, and (2) to bring the universal scope and beauty of science to the awareness of as many as possible, both within and outside the field - if you have any kind of problem in the real world, then science is the tool for you.

Effective communication to scientists, though, runs the risk of being impenetrable for non-scientists, while my efforts to simplify make me feel that the mathematically adept reader will be quickly bored.

Helping to make the material on the blog more accessible, therefore, and as part of a very, very slow but steady plan to achieve world domination, here are two new resources I've put together, which I am very happy to announce:

  • Glossary - definitions of technical terms used on the blog
  • Mathematical Resource - a set of links explaining the basics of probability from the beginning. Blog articles and glossary entries are linked in a logical order, starting from zero assumed prior expertise.

Both of these now appear in the links list on the right-hand sidebar.

The new resources are partially complete. Some of the names of entries in the glossary, for example, do not yet correspond to existing entries. Regular updates are planned.

The mathematical resource is a near-instantaneous extension of the material compiled for the glossary, and is actually my glacially slow response to a highly useful suggestion made by Richard Carrier, almost one year ago. The material has been organized in what seems to me to be a logical order, and for those interested, may be viewed as a short course in statistics, delivering, I hope, real practical skills in the topic. Its main purpose, though, is to provide an entry point for those interested in the blog, but unfamiliar with some of the important technical concepts.

The glossary may also be useful to those already familiar with the topics. Terms are used on the blog, for example, with meanings different to those of many other authors. Hypothesis testing is one such case, limited by some to denoting frequentist tests of significance, but used here to refer more generally to any  ranking of the reliability of propositions. 

The new glossary, then, is an attempt to rationalize the terminology, bringing the vocabulary back in line with what it was always intended to mean, not to reflect some flawed surrogates for those original intentions. For the same reason, in some cases alternate terms are used, such as 'falsifiability principle', in preference to the more common 'falsification principle'.

Important distinctions are also highlighted. Morality, for example is differentiated from moral fact. Philosophers are found to be distinct from 'nominal philosophers'. Equally importantly, science is explicitly distanced from 'the activity of scientists'. As a result, morality, philosophy, and science are found to be different words for exactly the same phenomenon.

In a previous article, I warned against excessive reliance on jargon, so it's perhaps worth explaining how the current initiative is not hypocrisy. That article was concerned with over use of unnecessary jargon, which often serves as an impediment to understanding. Symptoms of this include (1) jargon terms replaced with direct (but less familiar) synonyms result in confusion, and (2) vocabulary replaced with familiar terms with inapplicable meanings goes unnoticed. By providing a precise lexicon, we can help to prevent exactly these problems, and others, thus whetting the edge of our analytical blade, and accelerating our philosophical progress.

On a closely related topic, there is a fashionable notion going along the lines that to argue from the definition of words is fallacious, as if definitions of words are useless. This is not correct: argument from definition is a valid form of reasoning, but one that is very commonly misused.

Eliezer Yudkowsky's highly recommendable sequence, A Human's Guide to Words, covers the fallacious application very well. His principal example is the ancient riddle: if a tree falls in a forest, where nobody is present to hear it, does it make a sound? Yudkowsky imagines two people arguing over this riddle. One asserts, "yes, by definition: acoustic vibrations travel through the air," the other responds, "no, by definition: no auditory sensation occurs in anybody's brain." These two are clearly applying different definitions to the same word. In order to reach consensus, they must agree on a single definition.

These two haven't committed any fallacy yet, each is reasoning correctly from their own definitions. But it is a pointless argument - as pointless as me arguing in English, when I only understand English, with a person who only speaks and understands Japanese. Fallacy begins, however, as in the following example.

Suppose you and I both understand and agree on what the word 'rainbow' refers to. One day, though, I'm writing a dictionary, and under 'rainbow,' I include the innocent looking phrase: "occurs shortly after rain." (Well duh, rain is even in the name.) So we go visit a big waterfall and see colours in the spray, and I say "look, it must have recently rained here." Con artists term this tactic 'bait and switch.' I can not legitimately reason in this way, because I have arbitrarily attached not a symbol to a meaning, but attributes to a real physical object. 

To show trivially that there is a valid form of argument from definition, though, consider the following truism: "black things are black." This is necessarily true, because blackness is exactly the property I'm talking about when I invoke the phrase "black things." It is not that I am hoping to alter the contents of reality by asserting the necessary truth of the statement, but that I am referring to a particular class of entities, and the entities I have in mind just happen to all be black - by definition. 

One might complain, "but I prefer to use the phrase 'black things' not just for things that are black, but also for things that are nearly black." This would certainly be perverse, but it's not in any sense I can think of illegal. Fine, if you want to use the term that way, you may do so. I'll continue to implement my definition, which I find to be the most reasonable, and every time you hear me say the words "black things," you must replace the words with any symbol you like that conveys the required meaning to you. Your symbol might be a sequence of 47 charcoal 'z's marked on papyrus, or a mental image of a yak, I don't care. 

Yes, our definitions are arbitrary, but arbitrary in the sense that there is no prior privileged status of the symbols we end up using, and not in the sense that the meanings we attach to those symbols are unimportant.

Here's an example from my own experience. Several times, I have tried unsuccessfully to explain to people my discovery that ethics is a scientific discipline. (By the way I'm not claiming priority for this discovery.) The objections typically go through 3 phases. First is the feeling of hand-waviness, which is understandable, given how ridiculously simple the argument is: 

them- No way, its too simple. You can't possibly claim such an unexpected result with such a thin argument.
me- OK, show me which details I've glossed over.
them- [pause...] All right, the argument looks logically sound, but I don't believe it - look at your axioms: why should I accept those? Those aren't the axioms I choose.
me- Those aren't axioms at all. I don't need to assume their truth. These are basic statements that are true by definition. If you don't like the words I've attached to those definitions, then pick you own words, I'm happy to accommodate them.
them- YOU CAN'T DO THAT! You're trying to alter reality by your choice of definitions....

And that's the final stumbling block people seem to have the biggest trouble getting over.

Definitions are important. If you think that making definitions is a bogus attempt to alter reality, then be true to your beliefs: see how much intellectual progress you can make without assigning meanings to words. The new <fanfare!> Maximum Entropy Glossary </fanfare!> is an attempt to streamline intellectual progress. If you engage with anything I have written on this blog, then you engage with meanings I have attached to strings of typed characters. In some important cases, I have tried to make those meanings clear and precise. If you find yourself disagreeing with strings of characters, then you are making a mistake. If you disagree with the way I manipulate meanings then we can discuss it like adults, confident that we are talking about the same things.

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