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Archive for June, 2011|Monthly archive page

Ideas

In duhem, holism, popper on 19/06/2011 at 12:39 pm

These are all notes I’ve had lying around for some time. Thought they deserved some fresh air after reading this article, especially this part:

What all this means, in practical terms, is that the best way to encourage (or to have) new ideas isn’t to fetishise the “spark of genius”, to retreat to a mountain cabin in order to “be creative”, or to blabber interminably about “blue-sky”, “out-of-the-box” thinking. Rather, it’s to expand the range of your possible next moves – the perimeter of your potential – by exposing yourself to as much serendipity, as much argument and conversation, as many rival and related ideas as possible; to borrow, to repurpose, to recombine. This is one way of explaining the creativity generated by cities, by Europe’s 17th-century coffee-houses, and by the internet. Good ideas happen in networks; in one rather brain-bending sense, you could even say that “good ideas are networks”. Or as Johnson also puts it: “Chance favours the connected mind.”

In his later years Popper generalized his proposal of falsifiability as demarcating science from pseudoscience: proposals can be assessed qua solutions to problems. Does the proposal solve the problem (rather than shift the problem), and how does it compare to other solutions?

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Credible Explanations

In experiments on 19/06/2011 at 10:35 am

Credible explanations grow from the combined testimony of three more or less independent, mutually reinforcing sources — explanatory theory, empirical evidence, and rejection of competing alternative explanations. (Edward Tufte)

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“Falsifiability”

In critical rationalism, popper on 18/06/2011 at 12:31 am

Recently, a friend of mine sent me this criticism of falsifiability published in Edge.org in 2008 by Rebecca Goldstein, the wife of Steven Pinker and author of a few decent (so I hear) books. Upon reading it, I knew I had to write up a good ‘fisk’ of the criticism, seeing as it provides a good opportunity to clear up some misconceptions.

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The Dialleus, pt. 2

In critical rationalism, skepticism on 17/06/2011 at 1:38 am

Who breaks a butterfly upon the wheel?

Imagine that you are writing out a complicated mathematical proof. Most philosophers would say that it would be irrational to believe you are justified in thinking that you have conducted a proper derivation without first checking over each short step in the proof. It’s obvious that you might have made a mistake.

One should always lower the level of confidence assigned to the conclusion of any argument, according to the probability that one has made a mistake in the argument. However, David Hume points out that this estimate in probability may itself be in error. We ought to seek out an estimate for this estimate, which may itself be in error … leading to an infinite series of corrections. This leads to systematic doubt over the truth of synthetic a posteriori statements. The very tools we use to check the truth of our fallible beliefs are themselves fallible.

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Presuppositionalism

In critical rationalism, fideism, justificationism on 16/06/2011 at 7:00 pm

A key moment in her [Rep. Bachmann’s] political evolution, as for many of her generation, was the film series How Should We Then Live by the theologian Francis Schaeffer, who is widely credited for mobilizing evangelicals against abortion, an issue most had previously ignored. A Presbyterian minister, Schaeffer argued that our entire perception of reality depends on our worldview, and that only those with the right one can understand the true nature of things. Christianity, he argued, is “a whole system of truth, and this system is the only system that will stand up to all the questions that are presented to us as we face the reality of existence.” Theories or assertions from outside this system—evolution, for example—can be dismissed as the product of mistaken premises. (Michelle Goldberg, Bachmann’s Unrivaled Extremism)

I don’t know what to say about people that are incapable of admitting fault. Ideology can be very powerful, psychologically, especially if it’s grounded in religious convictions: there are people that, if presented with evidence that challenges or discredits their beliefs, are capable of writing it off entirely.

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Priors

In induction, skepticism on 16/06/2011 at 5:52 pm

Assign a prior probability to a hypothesis h that takes into account our ignorance of the truth or falsity of the hypothesis. Even though a good deal of the predictions (p), in conjunction with some basic statements and initial conditions, of h may be true, either the hypothesis is true or is false. Outcomes of testing are transmitted back to the hypothesis: corroborating evidence e implies that h is true (for true hypotheses will always have their predictions corroborated), while evidence e that conflicts with prediction p, a logical consequence of h, implies that h is false.

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Ethics & Epistemology

In ethics, justificationism on 16/06/2011 at 5:02 pm

What have I done? If this is a victory, what’s a defeat then? Is this a victory or a defeat? Is this justice or injustice? Is it gallantry or a rout? Is it valor to kill innocent children and women? Do I do it to widen the empire and for prosperity or to destroy the other’s kingdom and splendor? One has lost her husband, someone else a father, someone a child, someone an unborn infant…. What’s this debris of the corpses? Are these marks of victory or defeat? Are these vultures, crows, eagles the messengers of death or evil? (Ashoka)

Some people think that there are no grounds on which to judge different cultures. The cultural practice of ‘honor’ killing is as equally justified as cultural practices that ensure freedom of speech, for instance. That’s how the argument goes.

In a (qualified) sense, I agree. There are no foundations one can appeal to, no (so far as I can tell) justification for human rights or human dignity that extend beyond culture. What I’m getting at is that we ought to remain agnostic over the existence of any ethical code that is inherent to the universe.

This same claim is directed towards different cultural theories of knowledge (Feyerabend, et al.): who am I to say that, since all theories of knowledge are cultural constructs, reading the entrails of goats is any better than the Western process of scientific discovery?

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The Dialleus

In justificationism, skepticism on 16/06/2011 at 3:34 pm

How will you look for it, Socrates, when you do not know at all what it is? How will you aim to search for something you do not know at all? If you should meet with it, how will you know that this is the thing that you did not know? (Plato, Meno, 2nd ed. tr. G.M.A. Grube (Indianapolis: Hackett 1981), 13 (80d).)

In its most general form, problems take place when our conjectures run up against some sort of difficulty, some sort of wall that impedes advancement. Our intuitions are stressed during rigorous testing. That is a problem. For instance, the following argument looks like a problem…

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Hints & Guesses

In eliot on 16/06/2011 at 1:40 am

These are only hints and guesses,

Hints followed by guesses; and the rest

Is prayer, observance, discipline, thought and action

(T.S. Eliot)

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Later Wittgenstein

In popper, wittgenstein on 16/06/2011 at 1:15 am

Early Wittgenstein is usually understood within positivist circles as setting forth the idea that the only meaningful statements are those that are possible to be known to be true or false; it must be possible to decide for or against the proposition by an appeal to Nature Herself. We present Her our sentences for review, and She either approves of our words or rejects them with a vengeance. For the moment, let us assume, along with the Later Wittgenstein, that this understanding of meaning as demarcating sense and nonsense is patently false.

This Later Wittgenstein agrees in part with the Würzburg School (Bühler, Selz, Külpe, and Koffka) and the Austrian School Reform Movement* in their rejection of the theories expressed in the Tractatus, along with the associationalist school of child psychology, which aligned itself with the implicit thesis of the Tractatus: a child may learn only through the repeated memorization of the atomic structure of words; instruction takes place only from without the subject.

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Light

In critical rationalism, experiments on 15/06/2011 at 9:22 pm

As the problem presented itself to us there were three possibilities. There might be no deflection at all; that is, light might not be subject to gravitation. There might be a ‘half-deflection,’ signifying that light was subject to gravitation, as Newton had suggested, and obeyed the simple Newtonian law. Or there might be a ‘full deflection,’ confirming Einstein’s instead of Newton’s law. I remember Dyson explaining all of this to my companion Cottingham, who gathered the main idea that the bigger the deflection, the more exiting it would be. ‘What will it mean if we get double the deflection?’ ‘Then,’ said Dyson, ‘Eddington will go mad, and you will have come home alone. (S. Chandrasekhar, Am. J. Phys. 47, 212 (1979))

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Silent World

In art on 15/06/2011 at 4:41 pm

Copyright Michael KennaOn the Shoulders of Giants, an interview with Michael Kenna.

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Probability, pt. 2

In induction, skepticism on 15/06/2011 at 4:11 pm

Take the statement A, “It will snow on Friday” and the statement B, “It will not snow on Saturday”. The content of the conjunction AB (“It will snow on Friday and it will not snow on Saturday”) will be greater than or equal to any of its components. The more a statements says about the state of affairs, the greater its content. However, note that the probabilities assigned to either A or B require that the probability of the conjunction AB will be smaller than either of the conjuncts A or B.

If we define 0 as ‘false’ (such as a contradiction: for instance “The ball is both all blue and all red at once.”) and 1 as ‘true’ (such as a tautology: for instance, “A prince is a prince.”) and the possible values between 0 and 1 are all the possible assigned probabilities, then AB will always be more improbable or as probable than either the conjuncts A or B. For instance, if we assign the number .5 to A and .5 to B, then AB equals .25. The more a statement says, the less probable it is.

That is to say, with progressive content of our theories (or when a succession of theories increase in their predictive power) they become more and more improbable.

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Newton & Einstein

In induction, popper on 15/06/2011 at 4:05 pm

“… (1) Newton’s theory is exceedingly well corroborated. (2) Einstein’s theory is at least equally well corroborated. (3) Newton’s and Einstein’s theories largely agree with each other; nevertheless, they are logically inconsistent with each other because, as for instance in the case of strongly eccentric planetary orbits, they lead to conflicting predictions. (4) Therefore, corroboration cannot be a probability (in the sense of the calculus of probabilities).

“… The proof is simple. If corroboration were a probability, then the corroboration of ‘Either Newton or Einstein’ would be equal to the sum of the two corroborations, for the two logically exclude each other. But as both are exceedingly well corroborated, they would both have had a greater probability than ½ (½ would mean: no corroboration). Thus, their sum would be greater than 1, which is impossible. It follows that corroboration cannot be a probability.

“… It would be interesting to hear what the theoreticians of induction … who identify the degree of corroboration (or the ‘degree of rational belief’) with a degree of probability — would have to say about this simple refutation of their theory.” (Popper, Karl. 2009. The Two Fundamental Problems of the Theory of Knowledge, xxivn. New York: Routledge.)

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Two Greeks

In borges, the ancient greeks on 15/06/2011 at 4:02 pm

Two Greeks are conversing; perhaps Socrates and Parmenides. It is best that one never learns their names; history will thus be more mysterious and more tranquil.

The subject of their conversation is abstract. At times they allude to myths in which neither believes. …

They do not argue. And they desire neither to persuade nor to be persuaded, they think neither to win nor to lose. …

Free from myth and metaphor, they think or try to think. We shall never know their names. This conversation between two strangers in some unknown place in Greece is the capital event of History. They have forgotten prayer and magic. (Jorge Luis Borges, “The Beginning”)

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Rutherford

In experiments, fallibilism on 15/06/2011 at 4:01 pm

The famous experiment of Geiger and Marson found that when they shot alpha particles at a very thin sheet of gold foil, a few of the alpha particles – about one in twenty thousand – were reflected by the foil rather than merely deflected. As Rutherford said later:

It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a fifteen-inch shell at a piece of tissue paper and it came back and hit you. (Ernst Rutherford, ‘The Development of the Theory of Atomic Structure’, in Background of Modern Science, edited by J. Needham and W. Pagel, Cambridge University Press, Cambridge, 1938, pp. 61-74.)

This remark of Rutherford’s shows the utterly revolutionary nature of the discovery: no one expected to see alpha particles rebound off gold, and yet it was conceivable. Rutherford realized that the experiment refuted J.J. Thomson’s model of the atom, and he replaced it by his own model of the atom.

This was the beginning of nuclear science.

It also happens to fit exactly within Popper’s method of falsificationism.

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Nozick

In justificationism, nozick on 15/06/2011 at 3:51 pm

Externalism assumes that internalism misses the very point of the act of justifying statements. Epistemic luck about justifiers should not be a significant factor in cases of true knowledge, not fortuitous ‘true opinion.’ The justifier can be independent of the beliefs of Adam, resting on the fact that the justifier is in fact a proper justifier. In other words, if The Times is an accurate predictor, it does not matter if Adam have awareness of his access to an accurate predictor.

Even if Adam cannot provide a good reason why The Times is a reliable source, as long as The Times is in fact a proper justifier of p, and if Adam forms the belief p after reading The Times, and if the content of The Times is in fact true, then Adam is in possession of knowledge. To generalize, in the externalist program Adam will have a justified true belief iff

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Gettier

In gettier, justificationism on 15/06/2011 at 3:45 pm

Assume that a reliable belief-formation process (whatever it may be) determines when one possesses good reasons. For instance, Adam reads in the New York Times the prediction p: “the Queen of England will be visiting New York City on the fifth of June.” Adam’s reasonable belief in The Times‘s accuracy in predicting visiting dignitaries is a justifier for p. The Times often employs fact-checkers that catch mistakes, it is prima facie reasonable to assume that Adam’s copy of The Times is not a forgery, and so on. Taking all this into consideration, Adam now believes that p. As it so happens, The Times was correct: p is true. This is a good description of insufficient but good reasons. To generalize, the internalist program says that Adam will have a justified true belief iff Adam

  1. has access to a justifier for p,
  2.  believes that p, and
  3. p is in fact true.

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Through a Glass Darkly

In fallibilism, fideism, kuhn, popper on 15/06/2011 at 3:41 pm

There exists some way to certify statements as true or false. There must be some reason for believing them, a reason that may rest on other reasons (for example, z rests on y; y rests on x), but there must be some sort of instrument — call it a ‘touchstone’ — that sorts out true from false statements. There exists entrance examinations that determine truth and falsehood, similar to academic standards of admittance. If analogies to instruments and standards are not enough, then a religious allusion may be necessary: true statements are touched with grace by good reasons. This paragraph, in brief, sums up the prism through which the justificationist views the world.

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Duhem

In duhem, holism, induction, popper on 15/06/2011 at 3:21 pm

The Duhem problem can be expressed as follows:

A physicist disputes a certain law; he calls into doubt a certain theoretical point. How will be justify these doubts? From the proposition under indictment he will derive the prediction of an experimental fact; he will bring into existence the conditions under which this fact should be produced; if the predicted fact is not produced, the proposition which served as the basis of the prediction will be irremediably condemned. (Duhem, The Aim and Structure of Physical Theory, Princeton University Press. Translated from the French by Philip P. Wiener.1954, p. 184)

By means of this mode of inference we falsify the whole system (the theory as well as the initial conditions) which was required for the deduction of the statement p, i.e. of the falsified statement. Thus it cannot be asserted of any one statement of the system that it is, or is not, specifically upset by the falsification. Only if p is independent of some part of the system can we say that this part is not involved in the falsification. (Popper, The Logic of Scientific Discovery, 76)

A naive theory of science might say that when testing a theory T, if an observation-statement O is found to agree or disagree with the logical consequences of T, O either supports or refutes T. This can be expressed as follows:

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