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Archive for the ‘popper’ Category

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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“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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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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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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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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Pendulums

In holism, popper, quine on 15/06/2011 at 3:06 pm

Suppose a man were translated to a planet, the sky of which was constantly covered with a thick curtain of clouds, so that he could never see the other stars. On that planet he would live as if it were isolated in space. But he would notice that it revolves…” (Henri Poincaré, Science and Hypotheses)

Poincaré goes on to note that this man would, if he were observant, notice that a free-swinging pendulum — something akin to Foucault’s pendulum — gradually rotates.

Assume, for the moment, that this man looks around him, at the birds flying through the sky, the trees undulating in the breeze, the houses firmly rooted to the ground, and thinks that the planet does not–cannot–rotate. This is a commonsense conclusion to make. After observing this rotation, the thought-experiment man may conjecture that the planet does or does not rotate.

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