Wednesday, January 02, 2008

Justifying the scientific method: Introduction

Central to the claim that science is the only useful epistemic method is the connection between private, individual knowledge and public knowledge. The scientific method is simple: Find the simplest explanation that accounts for the facts. There are four components to the scientific method: Facts, explanations, accounts and simplicity.

An explanation is any instance of manipulating symbols using some sort of deterministic method; ordinary logic is an instance of a deterministic symbol manipulation method. If you start with some set of axioms, and apply inference rules in a particular order, you will always reach the same conclusion.

An account (or an explanation that accounts for) is an explanation that differentiates between valid and invalid conclusions. Again, ordinary logic in an instance of account: we interpret a conclusion reached by applying inference rules to axioms as valid, and the inverse of that conclusion to be therefore invalid. Since we can derive "2+2=4", that conclusion is valid, and "it is not the case that 2+2=4", its inverse, is invalid.

Just having an explanatory method which generates accounts is not sufficient. We must relate the validity of the conclusions to some facts to discuss the notions of truth and falsity. Without such a relation, the sentence "2+2=4" is no more meaningful than "@=@+$". Arithmetic is equally "valid" even if we manipulate the axioms without any reference at all to our understanding of counting actual things in the real world; Arithmetic is true precisely to the extent that it provides an explanatory account of facts about how we actually count (some) things in the real world.

Simplicity just consists of counting the number of irreducible premises, axioms or stipulations, plus the number of inference rules required to determine the account.

I leave the definitions of "explanation" and "account" minimally defined precisely not to presuppose all of propositional calculus and other forms of mathematics and logical symbol manipulation. We have to find that propositional calculus is deterministic and does distinguish between valid and invalid. We can compare alternative methods on their simplicity. We also find that we can generate agreement with the facts by just by choosing axioms; we do not need to alter the fundamental method. For this reason, we usually take propositional calculus for granted except under esoteric circumstances.

The scientific method is fundamentally different from the deductivist method. The deductivist method says: Find those statements which are derivable from true premises.

I compare the two methods in more detail in my first article on the scientific method, The Failure of Deductivism. Briefly, we seem to have an insuperable problem finding true axioms from which we can derive anything useful. Premises simple enough to use deductively seem impossible to generate foundationally (without deduction), and statements we can generate foundationally (especially statements about perception) are too complex to deduce anything interesting from.

Probably the most important difference between the deductive and scientific methods are that the deductive method is truth-finding, and the scientific method is falsity-finding. We can never be sure that some explanation accounts for the facts not yet in evidence, and we can never be sure that the explanation really is the simplest. We can, however, be sure when some explanation fails to account for some facts that are in evidence. We must simply bite this bullet to employ the scientific method. (Besides the foundational problem, the deductivist must bite his own bullet: He cannot be sure that the inverse of his theorems are themselves non-theorems. Even with a perfect axiomatic foundation the deductivist can never be sure of falsity.)

The facts are statements uncontroversially accepted as true. This is a general definition; the meanings of "uncontroversial" and "accepted as true" depend on the level we are employing the scientific method.

Philosophers often blithely assert that the scientific method requires the importation of a considerable amount of metaphysical baggage, notably metaphysical realism, the presumption of consistency, the presumption of the reliability of the senses, and the a priori intelligibility of language. Science, or so these philosophers assert, is a complex socially constructed language game, and has little or nothing to do with the fundamental philosophical issues of epistemology and ontology. I believe such philosophers are mistaken, and they are mistaken because an enormous amount of fundamental scientific work has already been performed by evolution: We human beings come to the task of philosophy with cognitive tools that seem a priori but are actually posterior to at least five hundred million years of evolution. (The first nervous systems appear at least in the Cambrian, if not the late Proterozoic era; if we admit some degree of symbolic representation of the outside world to bacteria, we can go back four billion years.)

The justification for the scientific method as a fundamental epistemic method rests on four pillars: It is metaphysically sparse; we can, in theory, build up to our present-day panoply of knowledge by nothing more than conscious employment of the scientific method; we can show that the social construct of institutional science depends essentially on our sparse formulation of the scientific method; and we can explain our actual history by relating the scientific method directly to the process of evolution.

I will address each of these pillars in my next series of posts.

7 comments:

  1. the connection between private, individual knowledge and public knowledge.

    I'm not sure what you mean by "public knowledge". Knowledge - along with every other intentional state - seems to be essentially a private thing. That is to say: That lots of people know that p just means that lots of people have the right private intentional state to know that p.

    The scientific method is simple: Find the simplest explanation that accounts for the facts.

    This is a version of Ockham's Razor, not what is generally called the scientific method, which has to do with experiment and verification. But we can proceed on this footing.

    An explanation is any instance of manipulating symbols using some sort of deterministic method

    On this definition, "2+2=4" is an explanation. Do you really want to say this? If so, it seems to me that you're using "explanation" rather strangely.

    An account (or an explanation that accounts for) is an explanation that differentiates between valid and invalid conclusions.

    How can mere symbol manipulation differentiate between valid and invalid conclusions? Your very limited definition of "explanation" hurts you here, since you now need to deploy a formal language for a task usually solved in a metalanguage. Indeed, if you want to be able to differentiate between valid and invalid conclusions in the formal language, you'll run into Goedel's incompleteness results; this is what happens when you include these notions at the same level as your formal system.

    The facts are statements uncontroversially accepted as true.

    Whoa! So, six hundred years ago, it was a fact that the Sun revolved around the Earth? That's a tough row to hoe, neighbor.

    Philosophers often blithely assert that the scientific method requires the importation of a considerable amount of metaphysical baggage

    You forgot a big one: Why should we think that the Universe works in the simplest way imaginable-by-humans? Because, on your story, science is committed to just this claim.

    Science, or so these philosophers assert, is a complex socially constructed language game, and has little or nothing to do with the fundamental philosophical issues of epistemology and ontology.

    The set of philosophers who assert these things is certainly not coextensive with the set of philosophers who assert the metaphysical baggage business. Bad form to lump them all together like that, you know.

    I believe such philosophers are mistaken, and they are mistaken because an enormous amount of fundamental scientific work has already been performed by evolution: We human beings come to the task of philosophy with cognitive tools that seem a priori but are actually posterior to at least five hundred million years of evolution.

    This is a serious misunderstanding of the difference between a priori and a posteriori, I'm afraid. This may be the core of some of your complaints, actually.

    Here's the difference: a priori truths are knowable without having any particular experiences. That is: I can learn that "I am here now" is always true when sincerely uttered without ever hearing any specific utterance of the sentence. Similarly, I can learn that "all bachelors are unmarried men" without knowing any particular bachelor. And so on.

    a posteriori truths, on the other hand, are such that they require some specific experience in order to be learned. It would be impossible to know that "Hesperus is Phosphorus" without a specific astronomical experience about the planet Venus; it would be impossible to know that "James had a muffin this morning" without some observation of James and his eating habits, and so on.

    The evolution thing is really, honestly, a complete non-starter in this argument. The evolutionary development of human cognition is a fascinating subject (though evo psychology as generally practiced is pretty seriously flawed; see David Buller's excellent Adapting Minds), but to say "evolutionary processes make 'all bachelors are unmarried men' an a posteriori truth" is just, well, strange.

    I look forward to the rest of this series.

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  2. Knowledge - along with every other intentional state - seems to be essentially a private thing. That is to say: That lots of people know that p just means that lots of people have the right private intentional state to know that p.

    This is a definition of knowledge, but it is not necessarily the definition of knowledge. It's mostly vacuous, because it just pushes the question to what the "right" private intentional states actually are.

    By "public" knowledge, I mean to reference the prosaic definition of public: shared by multiple people.

    This is a version of Ockham's Razor, not what is generally called the scientific method...

    What is "generally" called the scientific method is of little interest to me. I am not interested in philosophology. I may be doing it well or poorly, but I'm trying to do original philosophy. It wouldn't be original if I agreed with what is generally accepted.

    ... you're using "explanation" rather strangely.

    See the above response about doing original philosophy.

    How can mere symbol manipulation differentiate between valid and invalid conclusions?

    Are you unclear on the grammatical usage of "that", which introduces a clause that additionally restricts the antecedent?

    Whoa! So, six hundred years ago, it was a fact that the Sun revolved around the Earth? That's a tough row to hoe, neighbor.

    It's helpful to read all the words I write, especially a sentence following a seemingly controversial sentence. I will repeat myself:

    This is a general definition; the meanings of "uncontroversial" and "accepted as true" depend on the level we are employing the scientific method.

    Let me draw your attention to the word "Introduction" in the title of the post, indicating to the literate reader that controversial ideas may be explained later. Let me also note that your incredulity clearly indicates that the idea that the sun revolves around the earth is indeed controversial.

    Why should we think that the Universe works in the simplest way imaginable-by-humans?

    Let me refer you to my earlier article The Metaphysics of the Scientific Method.

    Bad form to lump them all together like that, you know.

    Oh good grief. Let me reiterate: I'm not interested in doing philosophology; I'm doing the best I can to do original philosophy. I don't bother to take pains to accurately represent the detailed views of anonymous philosophers to make a rhetorical point.

    Here's the difference: a priori truths are knowable without having any particular experiences.

    You should at least read Two Dogmas of Empiricism before spouting off on a priori truths with such zealous certainty. Especially when you conflate the analytic with the a priori.

    The evolution thing is really, honestly, a complete non-starter in this argument.

    I quite disagree. In addition to showing that our knowledge can be constructed by the conscious application of the scientific method, I think it's important to show that the knowledge constructed before we became conscious follows a procedure reducible or corresponding to the scientific method.

    If it were the case that our "built-in" knowledge was constructed by a substantively and irreducibly different method than the scientific, we would have adequate grounds for denying the fundamental claim that science is the only useful epistemic method.

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  3. It wouldn't be original if I agreed with what is generally accepted.

    While this is, in one sense, true, the sort of agreement I meant to reference has to do with what words mean. If you are not using words in the way most people do, communication becomes difficult or impossible.

    Are you unclear on the grammatical usage of "that", which introduces a clause that additionally restricts the antecedent?

    Of course I am. Let us consider the original sentence:

    "An account [...] is an explanation that differentiates between valid and invalid conclusions."

    Recall also your claim that: "An explanation is any instance of manipulating symbols using some sort of deterministic method".

    So an account is any instance of manipulating symbols using some sort of deterministic method that differentiates between valid and invalid conclusions. That's what you get when you add a provability predicate to your formal system, and that's when the incompleteness results bite you.

    Did you mean something else?

    Let me draw your attention to the word "Introduction" in the title of the post, indicating to the literate reader that controversial ideas may be explained later. Let me also note that your incredulity clearly indicates that the idea that the sun revolves around the earth is indeed controversial.

    If "uncontroversial acceptability" is your criterion for facthood, you are forced either to use a temporal definition of acceptability or an atemporal one. If you use a temporal definition of acceptability, then it was once a fact - by your lights - that the Sun orbited the Earth. If you use an atemporal definition of acceptability, then you are appealing to some sort of completed science, to which we do not have any access whatever. So either we can't know anything about facts by virtue of not having access to what statements count as facts, or there are facts that are false. Either way, your definition is at best poor. While I hope that you can extricate yourself from this dilemma (due to Hempel, for reference), it will require rather a lot of work.

    Let me refer you to my earlier article The Metaphysics of the Scientific Method.

    Your earlier article does not in any way answer the relevant question. Let me phrase it more pointedly: There is no such thing as an observation which can demonstrate that the Universe operates according to the simplest rules imaginable by humans. The simplest rules imaginable by humans are excellent guides to forming models of the universe as we interact with it, but it is not possible within science to demonstrate that these simple models in any way reflect the true structure of the objects in the universe. What is your argument for the claim that the Universe is simple?

    You should at least read Two Dogmas of Empiricism before spouting off on a priori truths with such zealous certainty. Especially when you conflate the analytic with the a priori.

    Not to be disagreeable for the sake of disagreement, but I have not conflated the analytic with the a priori. There are examples of analytic truths which are a priori, and these are generally the easiest way to introduce the distinction between a priori and a posteriori knowledge.

    To clarify: There are three relevant distinctions: necessary/contingent, an ontological claim; analytic/synthetic, a semantic claim; and a priori/a posteriori, an epistemic claim.
    You should note that "Two Dogmas" has nothing to say about either the first or third distinction. It would be better to cite relevant papers if you would like to attack the extent of my reading in philosophical texts.

    In addition to showing that our knowledge can be constructed by the conscious application of the scientific method

    I suppose this will be dealt with in a later post, but let me put this out here: It will be exceptionally difficult to show that all our knowledge can be derived from the scientific method.

    I think it's important to show that the knowledge constructed before we became conscious follows a procedure reducible or corresponding to the scientific method.

    What do you mean by "the knowledge constructed before we became conscious"? Actually, back that up: what do you mean by "knowledge"? You seem to be using the word strangely.

    If it were the case that our "built-in" knowledge was constructed by a substantively and irreducibly different method than the scientific, we would have adequate grounds for denying the fundamental claim that science is the only useful epistemic method.

    You don't need that at all. All you need is a single instance of knowledge gained through something other than the scientific method. There are lots of these examples.

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  4. Much of your critique depends on how you define knowledge. I think the definition you cite in your first comment is completely inadequate.

    Since I am specifically discussing the scientific method, and since I explicitly define the term, it seems fair to expect the reader might be clued in that I might not agree with other definitions, especially since the the topic is a matter of no small controversy in philosophy.

    I simply want to forestall the objection of disagreement per se with canonical or well-established philosophy. That characteristic is, as we say in my business, by design. If my definition disagrees with any canon, then I am obliged only to offer and defend my own definition.

    Keep in mind that I am employing English as a metalanguage to specify a class of formal languages. I try to write in something approaching idiomatic English, so if a slight imprecision can be cleaned up by a charitable reading, I expect the reader to be charitable.

    The whole point of employing a factual foundation for the scientific method is that we need not be so concerned about completeness or consistency as formal notions in our formal explanatory language, because validity is not taken directly as truth. The formal explanatory language needs to provide only precision, i.e. the degree of univocality afforded by a deterministic procedure.

    All other features of our explanatory language can be evaluated post hoc by agreement or disagreement with fact.

    To a certain extent, we can be relaxed in some sense even about facts, at least to the extent that the method can tolerate people being mistaken about facts. As noted both in this essay and elsewhere, the scientific method is concerned with falsity detection. Using uncontroversial statements as a foundation allows us to do that even if we are mistaken about some particular uncontroversial statement. Being mistaken about the lack of controversy just means we cannot find some particular falsity; it does not preclude us from finding other falsity. Furthermore, we can detect a mistake about controversy merely by controverting a statement, and find different relevant statements that we have good reason to believe would be uncontroversial even to our predecessors.

    The scientific method is about generating knowledge, not truth. Truth is mystical and undefined, and we're not at all concerned with how the world really works independently of our knowledge: by definition we cannot know anything independently of our knowledge. Kant's noumena is, in some senses, as unfalsifiable and vacuous as God.

    What we really care about is whether our explanations are good. Hence the employment of (pragmatic) utility in the definition, rather than appeals to mystical "truth".

    I'm surprised that you dismiss Quine in your appeal to analytic statements as a priori. As I read Two Dogmas, analytic statements require the experiences of learning a language; as analytic statements are statements about the language ("the set of unmarried men consists of unmarried men" does not seem to tell us anything about unmarried men) Quine makes a good case for considering supposedly "analytic" statements a posteriori synthetic statements about the language.

    In this sense, not even deduction can escape the evil clutches of the scientific method: To know that "2+2=4" is a theorem of arithmetic, we must actually perform the deduction (or hear a mathematician tell us she has deduced it), an experiential task. And, of course, to relate the validity of arithmetic to the real world, we have to relate experiences to arithmetic.

    I understand that we need only to find a counter-example. But a counter-example you yourself cite is a priori knowledge. Quine disposes of supposedly "analytic" knowledge, but there are no small few beliefs that we have, beliefs that appear to be extremely reliable (notably at least our naive notions about realism) that do not appear to be consciously constructed.

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  5. Much of your critique depends on how you define knowledge. I think the definition you cite in your first comment is completely inadequate.

    This should be unsurprising, since I haven't really even offered a definition of knowledge; all I named was a necessary condition on knowledge. I take it that knowledge is justified true belief (that satisfies the Gettier condition), but I think we can leave the details of what counts as justification to one side for your purposes here.

    Keep in mind that I am employing English as a metalanguage to specify a class of formal languages. I try to write in something approaching idiomatic English, so if a slight imprecision can be cleaned up by a charitable reading, I expect the reader to be charitable.

    Charity can only extend so far. As written, there is a fairly serious problem with your definitions of "explanation" and "account". This will need to be fixed if the project as a whole is to be salvaged.

    The scientific method is about generating knowledge, not truth. Truth is mystical and undefined, and we're not at all concerned with how the world really works independently of our knowledge: by definition we cannot know anything independently of our knowledge. Kant's noumena is, in some senses, as unfalsifiable and vacuous as God.

    This is a very, very strange paragraph to me. Are you claiming that we can know things that aren't even true? Perhaps further discussion on this will have to wait until you get round to writing a description of "knowledge" in your system.

    As I read Two Dogmas, analytic statements require the experiences of learning a language; as analytic statements are statements about the language ("the set of unmarried men consists of unmarried men" does not seem to tell us anything about unmarried men)

    Again, the relevant difference is not between analytic and synthetic statements, but between two epistemic categories. Language use is a necessary precondition for gaining a priori knowledge, but once you speak a language - say, English - you no longer need to have any specific experiences to recognize a priori truths expressed in English.

    Quine makes a good case for considering supposedly "analytic" statements a posteriori synthetic statements about the language.

    No, Quine makes a good start on a case that would show that the distinction between "analytic" and "synthetic" is not well-formed. There really isn't anything in "Two Dogmas" about a priori or a posteriori knowledge.

    In this sense, not even deduction can escape the evil clutches of the scientific method: To know that "2+2=4" is a theorem of arithmetic, we must actually perform the deduction [...], an experiential task.

    Performing a deduction is not, in any ordinary understanding of these terms of art, an experiential task. If you want to stretch your definition this far, your claims are true, but only by fiat.

    But a counter-example you yourself cite is a priori knowledge. Quine disposes of supposedly "analytic" knowledge,

    You seem very confused here. The set of analytic statements is not coextensive with the set of things which can be known a priori. "I am here now" can be known a priori whenever sincerely uttered, but it's certainly not analytic.

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  6. I take it that knowledge is justified true belief

    This is precisely the definition I disagree with; the only think I think is right about it is that knowledge is indeed a belief. I think philosophical epistemology has gone far down the wrong track with this sort of definition. Told ya I was trying to be original.

    Charity can only extend so far. As written, there is a fairly serious problem with your definitions of "explanation" and "account". This will need to be fixed if the project as a whole is to be salvaged.

    You have not yet made it clear what the actual problems are. Godel's issues are not severe if we are employing the terms merely to speak precisely.

    Are you claiming that we can know things that aren't even true?

    Yes, it's counterintuitive. We can know things, but we can't know that they are true. The best we can know affirmatively with the scientific method is that some proposition is not yet known to be false.

    ...you no longer need to have any specific experiences to recognize a priori truths expressed in English.

    But "all bachelors are unmarried" does not express a truth about bachelors, unless you admit that "all bachelors are bachelors" expresses a truth about bachelors, in the same sense that "all unicorns are unicorns" or "all X are X".

    The only "truth" you're stating is the axiom of identity. And the axiom of identity is itself considered a useful axiom only for its power to explain our experiences.

    Why should we bend over backwards in our epistemology to rescue such a boring, self-defined kind of "truth"?

    "I am here now" is no better, it's still completely analytic, because the definition of "here" and "now" is where and when I am. One should also note that the conceptions of both space and time are, Kant notwithstanding, acquired experientially, unless you are asserting such knowledge was magically placed in our minds.

    Performing a deduction is not, in any ordinary understanding of these terms of art, an experiential task. If you want to stretch your definition this far, your claims are true, but only by fiat.

    I'm astonished. Do you not perform deduction in your mind? Are you not consciously aware of the act? How is the mental act of deduction any less of a subjective experience than subjectively "knowing" one is hungry?

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  7. This is precisely the definition I disagree with; the only think I think is right about it is that knowledge is indeed a belief. I think philosophical epistemology has gone far down the wrong track with this sort of definition. Told ya I was trying to be original.

    Original, yes. But if you give up truth and justification requirements on candidate beliefs, you stick yourself with uncomfortable conclusions. If one can know things that are false, then I could know that a unicorn killed my dad in a Saigon brothel. If one can know things without justification, then I could know, based on the testimony of the crazy shouty guy who stands across the street from my office, that a unicorn killed his dad in Saigon.

    You have not yet made it clear what the actual problems are. Godel's issues are not severe if we are employing the terms merely to speak precisely.

    The biggest problem is that your definitions of "explanation" and "account" are completely severed from the world. They're fully formalized. You need a way to connect your "facts" - which are still intensely problematic - to your explanatory mechanics.

    Yes, it's counterintuitive. We can know things, but we can't know that they are true.

    That's not what I said. Your account, as given, lets us know things that are false. Knowing that p and knowing that "p is true" may or may not be different things, but if they are, then the latter is not required for the former.

    The only "truth" you're stating is the axiom of identity. And the axiom of identity is itself considered a useful axiom only for its power to explain our experiences.

    Ok, then. Goedel's first incompleteness theorem is an a priori truth. So is Henkin's completeness proof. Goldbach's Conjecture is either a priori true or a priori false, but we don't know which yet. "There is no largest prime number" is a priori true. The identity examples are just the easiest ones.

    Why should we bend over backwards in our epistemology to rescue such a boring, self-defined kind of "truth"?

    Because if we don't, our epistemology is lacking.

    ne should also note that the conceptions of both space and time are, Kant notwithstanding, acquired experientially,

    This is a common misreading of Kant. The intuitions of time and space are the way in which we experience the world. They're not non-experiential, nor are they, strictly speaking, acquired by experience, because they come along with experience from the very first.

    o you not perform deduction in your mind? Are you not consciously aware of the act? How is the mental act of deduction any less of a subjective experience than subjectively "knowing" one is hungry?

    One of them is a perceptual experience. The other is not. "Experience" in this discussion means "perceptual experience". I thought you knew that. Sorry for the misunderstanding.

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