On The Margins

Saturday August 30, 2008

[ Philosophy ] Logic and the Future

Many, who have poorly understood the power of analysis, logic and "scientific" prediction, put great weight on the so-called "analysis of facts" to predict the future. In Fact, Fiction and Forecast, Fourth Edition, philosopher Nelson Goodman writes: The problem of the validity of judgements about future or unknown cases arises, as Hume pointed out, because such judgments are neither reports of experience nor logial consequences of it. Predictions, of course, pertain to what has not yet been observed. And they cannot be logically inferred from what has been observed; for what has happened imposes no logical restrictions on what will happen.

2008-08-30 00:07:56.0 -- ; Permalink ; Trackback.
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Saturday January 19, 2008

[ Mathematics ] How Many

How many non-standards models of Peano Arithmetics exist? (Hint: The Gödel construction gives you many models. One can also prove the existence of many such models using the fact that there are  many primes.)

2008-01-19 07:44:09.0 -- Comments [1] ; Permalink ; Trackback.
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Wednesday June 06, 2007

[ Philosophy ] Truth -- What's Consistency Got To Do With It?

Frege used a 2-D notation for his logic.

Many years ago, while with the Graduate Group in Logic and Methodology of Science at Berkeley, I had written a little paper with a tease of a title: "Consistency--What Is Logic Got To Do With It?" After a recent discussion, I realized more clearly how that paper might have been making too far of a leap in logic. Perhaps, it should have been named "Consistency--What Is Truth Got To Do With It?"  By "consistency," all along, I had meant "consistency" as understood by mathematicians and scientists, not what we understand "consistency" to be when we speak of, say, "consistent" behavior, which is a totally different concept when compared to a "consistent" theory.

In the mathematicians' definition of truth, as expounded by Alfred Tarski, one can only speak of "truth" within the confines of a mathematically "consistent" theory. Thus, one arrives, in mathematical logic, at incomplete theories that meet mathematical "truth" criteria even as they remain incomplete. In a sense, their incompleteness is more true about these theories than their "truth." Their "truth" exists within their limited, incomplete domain, which, always remains positively finite or countable or of much lower cardinality than the continuum of claims that they can neither prove nor disprove.

2007-06-06 22:50:55.0 -- Comments [7] ; Permalink ; Trackback.
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Monday July 31, 2006

[ Philosophy ] Truth Criteria

[Note: Paul Hinz' entry, which draws a distinction between facts and opinions, motivated me to write the following little essay.]

Truth criteria is a very touchy-feely topic in epistemology, not to mention mathematical logic and ontology on two other extreme poles.

For example, in mathematical logic, Alfred Tarski had a model-theoretic criteria of truth for statements expressed in a given mathematical language. Anyone who knows about Kurt Gödel's incompleteness theorem and non-standard models knows where that definition will lead us.

"Facts" will always depend on the model of the world that one is dealing with and using to establish truth of statements.

In some models, a mathematical statement may be true and in others it may be false. In smaller models, the truth or falsity of the same statement may not even be possible to establish through any proof mechanism.

Now, applying the same concept, on a philosophical level, to the real world should have its obvious conclusions. Let's leave that as an exercise.

I should also mention that common scientists are successful in defining "facts" and "truth" to their satisfaction because they deal with a very simple, fictitious world-model, established for their very narrow and  particular purpose.

Here's another take, for example, which is more on the ontological side.

"Facts" are what one believes in based on what one has come to know of the world. Here, one's take of what "the world" actually is becomes key. In life, the "world-model" one uses depends critically on what one has come to really understand about the world through one's life.

"Assumptions" are "facts" in which one believes more than one believes in other "facts."

Except for sterile "scientific facts" (these, on their own, are discovered through consensus and agreement more than anything else), one man's "fact" becomes another man's "falsehood"...because they see the world in completely different ways.

So, if we bank on settling of facts as the main problem and on distinguishing fact and opinion as the main resolution, we're badly under-funded when it comes to understanding what's really going on.

On the other hand, we can submit to our partial understanding and agree that the best we can do when there's disagreement is to try to understand the various sides of the disagreement to the greatest possible extent. Often, we're just too lazy to do so. We tend to dismiss one side outright because of our prejudices. Understanding others can hardly be easy. It requires an ability to grasp the others' life as a possible life of our own to live, according to Bernard Williams, the late Cambridge philosopher, with not all of whose opinions I must say I agree.

2006-07-31 17:37:31.0 -- Comments [2] ; Permalink ; Trackback.
epistemology logic morality ontology philosophy truth

Thursday March 09, 2006

[ Philosophy ] Nuclear Opinions - or - The High Art of Mocking Morality

Morality used to mean something at the time of the great saviors. Skillful mocking of it has now become high art and fashionable.

Some are advancing "innovative" moral principles, for example:

• (a) The world is divided into friends and enemies.

• (b) Whatever my friends do (no matter how wrong), they have done right!

• (c) Whatever my enemies do (no matter how right), they have done wrong!

• (d) Apply the above principles where you can, and where you don't apply them, say you couldn't. This includes the paranthesis in items (c) and (b) above.

Opinion journalism more often than not will go astray, and take up this high art.

"This tailor cuts and sews," so goes the Persian saying, with no care whether the coat will fit the poor fellow who would wear it. The opinion journalists (M. Ledeen, etc.), particularly the ones who eagerly beat the drums of confrontation with Iran at every media corner and opportunity they find, will spare no effort to produce unreal accounts of what is at stake.

So, we read Richard Cohen (of Washington Post) enshrine the new policy principles (see above) with his sanctification of "Judicious Double Standards."

Mockery becomes more manifest when the joker imposes his own value system on others and takes no heed of the importance of consistency.

Not only does Cohen ridicule consistency of rules and standards, he also believes Iranian leaders must think they should want nuclear weapons, even if they don't. In fact, all Iranian political leaders (all of whom are elected officials, by the way) have said, on multiple occasions, that nuclear weapons do not fit their national defense doctrine. They have held such weapons to be not only costly and unnecessary but also ineffective and immoral, despite what Cohen would rather have Iranian leaders believe.

But facts and what others say matter little to opinion makers who are bent towards conflict, specially one that promises, if it ever happens, to be far more costly for the future of the West than for what will become of Iran, not in a physical sense, but in a wierd moral sense.

Here, I could choose at random and analyze every sentence in Mr. Cohen's rhetorical column, show its deep injustice and prove it false based on real events and facts but I have a day job to do and need some evenings to spend with my family instead of blogging.

I do have one quick advice for him to improve his rhetoric. The moral principle he should enshrine is not that double standards are good policy and should be defended but that different cases need to be measured according to their context.

However, all measurement, even if sensitive to the context of a case, will eventually require the same moral foundation, compass and measuring stick, and Mr. Cohen seems to posses only one very rusty and biased measuring tool in his toolbox — the one summarized in the first part of this essay.

Charged adjectives and accusations, deployed using the highest rhetorical techniques, may have a university campus quality but they can hardly turn halucinations into reality.

The moral that "whatever my friend does is right" is far lower in its value as a measuring stick and a guiding principle than the golden rule of reciprocity that says "treat others as you would like to be treated yourself" — in other words consistency on a very personal, deep level — "Do unto others as you would have others do unto you" (Gospel of Matthew 7:12 of the Christian Bible). (Unfortunately, when I re-examine the situation, I see that even this principle has been misinterpreted by some towards violence.)

What a great guide consistency can be and how far away, from where Mr. Cohen is taking us, it is!

Poor logic and poor facts when combined with good rhetorical skills — not once, but since the time of Alcibiades, have together dragged the great into wars, some ending like Melos, others like Syracuse!

2006-03-09 05:42:41.0 -- Comments [2] ; Permalink ; Trackback.
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