betterthanwell comments on The Useful Idea of Truth - Less Wrong

77 Post author: Eliezer_Yudkowsky 02 October 2012 06:16PM

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Comment author: betterthanwell 04 October 2012 10:53:49PM *  0 points [-]

I also can't think of a philosopher who has made an explicit connection from the correspondence theory of truth to "there are causal processes producing map-territory correspondences" to "you have to look at things to draw accurate maps of them..."

Karl Popper did so explicitly, thoroughly and convincingly in The Logic of Scientific Discovery. Pretty influential, and definitely a part of "Mainstream Academia."

Here's an interesting, if lengthy, footnote to Chapter 84 - Remarks Concerning the use of the concepts 'True' and 'Corroborated'.

(1) Not long after this was written, I had the good fortune to meet Alfred Tarski who explained to me the fundamental ideas of his theory of truth. It is a great pity that this theory—one of the two great discoveries in the field of logic made since Principia Mathematica—is still often misunderstood and misrepresented. It cannot be too strongly emphasized that Tarski’s idea of truth (for whose definition with respect to formalized languages Tarski gave a method) is the same idea which Aristotle had in mind and indeed most people (except pragmatists): the idea that truth is correspondence with the facts (or with reality). But what can we possibly mean if we say of a statement that it corresponds with the facts (or with reality)? Once we realize that this correspondence cannot be one of structural similarity, the task of elucidating this correspondence seems hopeless; and as a consequence, we may become suspicious of the concept of truth, and prefer not to use it. Tarski solved (with respect to formalized languages) this apparently hopeless problem by making use of a semantic metalanguage, reducing the idea of correspondence to that of ‘satisfaction’ or ‘fulfilment’. As a result of Tarski’s teaching, I no longer hesitate to speak of ‘truth’ and ‘falsity’. (...)

A (short) footnote of my own: Popper's writings have assumed the status of mere "background knowledge", which is a truly great achievement for any philosopher of science. However, The Logic of Scientific discovery is a glorious book which deserves to be even more widely read. Part I of the book spans no more than 30 pages. It's nothing short of beautiful. PDF here.

Comment author: lukeprog 05 October 2012 05:15:41AM 2 points [-]

Could you please quote the part of Popper's book that makes the explicit connection from the correspondence theory of truth to "there are causal processes producing map-territory correspondences" to "you have to look at things to draw accurate maps of them..."?

Comment author: betterthanwell 05 October 2012 10:38:46AM *  0 points [-]

Could you please quote the part of Popper's book that makes the explicit connection from the correspondence theory of truth to "there are causal processes producing map-territory correspondences" to "you have to look at things to draw accurate maps of them..."?

Right, this is the obvious next question. I started looking for the appropriate "sound bites" yesterday, but encountered a bit of difficulty in doing so, as I shall explain. Popper's embrace of (Tarskian) correspondence theory should be at least somewhat clear from the footnote I quoted above.

It seems clear to me, from my recount of the book that "you have to look at things to draw accurate maps of them" is one of the chief aims, and one of the central claims of the book; a claim which is defended, by a lengthy, but quite convincing and unusually successful argument - the premises to which are presented only one at a time, and quite meticulously over at least several chapters, so I'm not exactly sure how to go about quoting only the "relevant parts".

My claim that his argument was convincing and successful, is based on the historical observation that popperian falsificationism (the hypothetico-deductive framework) won out over the then quite prevalent logical positivist / verificationist view, to such an extent that it quickly became the default mode of Science, a position it has held, mostly uncontested, ever since, and therefore is barely worthy of mention today. Except when it is, that is; when one encounters problems that are metaphysical (according to Popper), such as Susskind's String Landscape of perhaps 10^500 vacuua, the small (but significant) observed value of the cosmological constant, the (seemingly fine tuned) value of the fine structure constant, and other observations that may require anthropic i.e. metaphysical explanations, since these problems are seemingly not decidable inside of standard, i.e. popperian science.

I feel faced with a claim similar to "I don't believe any mathematician has convincingly proven Fermat's last theorem." To which I reply: Andrew Wiles (1995) The obvious next question is: "Can you please quote the part where he proves the theorem?" This is unfortunately somewhat involved, as the entire 109 page paper tries and succeds at doing so around as concisely as Wiles himself managed to go about it. Unfortunately, in the Popper case, I cannot simply provide the relevant Wikipedia Article and leave it at that.

I suppose that having made the claim, it is only my duty to back it up, or else concede defeat. If you're still interested, I shall give it a thorough look, but will need a bit of time to do so. Hopefully, you'll have my reply before monday.

Comment author: betterthanwell 05 October 2012 11:09:51AM *  0 points [-]

A (very) quick attempt, perhaps this will suffice? (Let me know if not. )

I begin with the tersest possible defense of my claim that Popper argued that "you actually have to look at things to draw accurate maps of them...", even though this particular example is particularily trivial:

Page 19:

(Thus the statement, ‘It will rain or not rain here tomorrow’ will not be regarded as empirical, simply because it cannot be refuted; whereas the statement, ‘It will rain here tomorrow’ will be regarded as empirical.)

To paraphrase: You have to look actually out the window to discover whether it is raining or not.

Continuing, page 16:

The task of formulating an acceptable definition of the idea of an ‘empirical science’ is not without its difficulties. Some of these arise from the fact that there must be many theoretical systems with a logical structure very similar to the one which at any particular time is the accepted system of empirical science. This situation is sometimes described by saying that there is a great number—presumably an infinite number— of ‘logically possible worlds’. Yet the system called ‘empirical science’ is intended to represent only one world: the ‘real world’ or the ‘world of our experience’.*1

Various objections might be raised against the criterion of demarcation here proposed. In the first place, it may well seem somewhat wrong-headed to suggest that science, which is supposed to give us positive information, should be characterized as satisfying a negative requirement such as refutability. However, I shall show, in sections 31 to 46, that this objection has little weight, since the amount of positive information about the world which is conveyed by a scientific statement is the greater the more likely it is to clash, because of its logical character, with possible singular statements. (Not for nothing do we call the laws of nature ‘laws’: the more they prohibit the more they say.)

My proposal is based upon an asymmetry between verifiability and falsifiability; an asymmetry which results from the logical form of universal statements.*4 For these are never derivable from singular statements, but can be contradicted by singular statements. Consequently it is possible by means of purely deductive inferences (with the help of the modus tollens of classical logic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the ‘inductive direction’; that is, from singular to universal statements. *4 This asymmetry is now more fully discussed in section *22 of my Postscript.

(Oops, comment too long.)

Comment author: betterthanwell 05 October 2012 11:10:23AM *  0 points [-]

(Continued)

Page 20:

According to my proposal, what characterizes the empirical method is its manner of exposing to falsification, in every conceivable way, the system to be tested. Its aim is not to save the lives of untenable systems but, on the contrary, to select the one which is by comparison the fittest, by exposing them all to the fiercest struggle for survival.

[a number of indicative, but not decisive quotes omitted]

I had hoped to find some decisive sound bite in part one, which is a brief discussion of the epistemological problems facing any theory of scientific method, and an outline of Popper's framework, but it looks like I shall have to go deeper. Will look into this over the weekend.

I also found another, though much more recent candidate, David Deutsch in The Beginning of Infinity, Chapter 1 on "The Reach of Explanations". Tough I'm beginning to suspect that although they both point out that "you have to look at things to draw accurate maps of them...", and describe "causal processes producing map-territory correspondences" (for example, between some state of affairs and the output of some scientific instument) both Deutsch and Popper seem to have omitted what one may call the "neuroscience of epistemology." (Where the photon reflects off your shoelace, gets absorbed by your retina, leading to information about the configuration of the world becoming entangled with some corresponding state of your brain, and so on.) This is admittedly quite a crucial step, which Yudkowsky's explanation does cover, and which I cannot recall to have seen elsewhere.

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