I: I having been interviewing you about Logical Positivism now, with the hope of finding a theory of knowledge that will serve my investigation into ethics and ethical matters.
LP: You are assuming of course, that there is something to be *known* about ethics. Would you admit the possibility that you might be undertaking a task similar to knowing witchcraft and how to cast spells, or knowing the anatomy of the unicorn?
I: I admit the possibility that there is no such thing as ethics, or at least, that ethics is not what we think it is, which may or may not be the same thing. However, when we concluded last time, I pointed out that the Positivist faces a problem I suppose any theory of knowledge faces, and that is, when do we stop looking, and decide that the object of our inquiry does not exist, that is, we are looking for truths concerning things about which there are no truths. That sounds awkward, but --
LP: I understand. That is a difficult problem. Physicists searched for "ether" -- the substance in which light "waved" -- and found it did not exist. Alchemists studied the evolutionary process of substances, and finally discovered, through the more sophsicated system of chemistry, that elements did *not* evolve. Some time you have to call it quits and admit your search is futile, that what you are looking for does not exist, or merely that what you are looking for is not what you thought it was.
I: Yes, that has to be, unless we think that everything -- every claim anyone makes -- is true, and that evidence exists for its truthfulness --
LP: That would be absolute nonsense --
I: Which would not preclude followers of an entire theory of knowledge from adopting such a principle.
LP: That's -- ridiculous!
I: That happens to be the position of my next interviewees, the post-Modernists. You can appreciate my concerns. But an all-inclusive theory of knowledge", the principle that "every claim is true in its own way -- from some point of view", presents problems.
LP: It certainly does. It shreds the very notion of "truth".
I: Well its interpretation of "truth" certainly is different from the Positivist interpretation. But I want to get back to a problem I have with Positivism, which to me seems to err too much the other way. Reductionism, as I have said, is a useful methodology for conflating -- merging and reconciling -- theories about two or more different sorts of things --
LP: You should say "apparently different". If the reduction can be made, then there is in fact only one kind of thing, explicable under one theory.
I: I appreciate that. The apparent difference, I would argue, comes from scientists "tunneling" from different sides of the mountain, and meeting in the middle.
LP: Not a bad metaphor, but I would prefer to think of it in terms of the detective metaphor: two detectives seeking two men, each with a different name, discover that one name is an alias and that they are really looking for the same man. There never are 'two suspects', merely two different descriptions of the same object of their search.
I: My concern, as I have said, is that Positivism is too limiting in its search, and hence fails to acknowledge the existence of certain entities -- commonly experienced entities, I might add. In other words, the search is terminated prematurely, or never even initiatited. I believe this has to do with too heavy a reliance on "reductionism", and, I suppose as well, what Positivism ultimately attempts to reduce things *to*.
LP: ?
I: Well, let's go back to the original Positivist schema. Mathematics -- or I suppose we ought to take another step back -- formal logic, is the grounding for positivist knowledge. In formal logic we simply have rules, and a priori statements -- statements whose truth is not dependent on any specific state of affairs; they are *always* true, like "A = A", "A & B = B & A", and so forth.
LP: Correct. I would also add that formal logic is sound and complete, that is, no true statements are left out, and no false statements (or mere nonsense, like "A & = B") are included. The "cut" between truth and falsehood is clean.
I: As we would hope for in any theory of knowledge. The problem is that once you move from formal logic, which consists of symbols that don't * mean* anything -- they are simple objects manipulated according to formal rules -- to bona fide mathematics, where "1" and "+" and "=' and other objects actually *mean* something, we encounter difficulties, namely Godel's claim that any such interpreted system of mathematics must necessarily be incomplete. All of the provable statements of mathematics are *true*, but not all of the true statements of mathematics are *provable* (namely, those proofs that go on forever and never terminate).
LP: We can repair any mathematical theory, however, simply by adding more axioms. The "seed" of arithmetic is the set of five Peano axioms. With those five simple axioms, we can prove a great deal of the theorems of mathematics.
I: Actually, with *four* Peano axioms. The fifth axiom -- the mathematical induction axiom, requires the concept of infinity, which is hardly a trivial assumption to toss in as "obviously true", which axioms are supposed to be. Then there is the Axiom of Choice -- axiom six if you will --
LP: Yes, yes. W end up trying to "fill out" mathematical theory by adding an infinite number of axioms --
I: Which I guess you can do if you accept the Axiom of Infinity earlier on enough. The problem is not only that to flesh out mathematics -- which is the model for Positivist knowledge -- you have to go on adding axioms ad infinitum. An even more serious problem is that -- as in the case of Euclid's fifth postulate, you have mutually exclusive choices -- three in the case of Euclid's postulate -- which serve as "forks in the road". You make one choice regarding the fifth postulate, and you go down one road to form a particular theory of mathematics. Pick another alternative, and you go down another, different, road to form a different, but also sound and complete, theory of mathematics --
LP: Ah, but in that particular case you can pick all three by dropping the fifth postulate: you get "projective geometry".
I: And in doing so, give up the fairly intuitive notion that parallel lines meet. By "giving up" fairly ordinary and commonplace truths for the sake of preserving the integrity of a theory, we seem to be losing something fair more valuable --
LP: Well, the fact that parallel lines meet in Euclidian geometry should not imply that they must meet under all interpretations of the theory of mathematics --
I: Well, I suppose you could defend that unsettling comment by arguing that it is not true that parallel lines always meet, only that under specified conditions, parallel lines will meet -- which raises a question I have about Positivism, and that is the standard of truth. It seems to me that Positivism almost harkens back to Leibnizian Rationalism -- another logic and math-based theory of knowledge. This severe theory of knowledge demands an insanely high degree of truth. In Leibniz's view, a statement is true if and only if it *must* be true. "A = A" is true because it cannot ever be false, which sounds okay, but "The Moon revolves around the Earth in 28 days" must also, to be true, be *necessarily* true -- which implies that the Moon and the Earth must necessarily exist also, and that they necessarily revolve around each other. That is insane.
LP: Well, Positivists are not Rationalists. Unlike Leibniz, we allow for "initial conditions to vary, which means, for the Moon, that given its initial position and momentum and the laws of motion -- and the existence of the Moon -- it *has* to revolve around the earth in 28 days. However, the initial conditions *could* have been different, and the Moon could have revolved around the Earth in 14 days, or two years, or fallen down onto the Earth, had things been different -- which they could have.
I: My point, to get back to it, is that the structure that Positivism imposes on the *physical* world is a mathematical one. Everything in the physical universe gets reduced to numbers -- initial conditions and laws of nature as you put it -- and presumably, those numbers get reduced to the initial axioms, which in turn, I suppose, are reduced to formal logical symbols, which have no meaning per se, but are moved around, like hollowed-out walnut shells under the procedures of logical inference, no matter where the pea may be. The question I have -- and it is a very serious question -- is this: how do you justify the claim that no truth claims are overlooked -- or worse -- thrown out -- in this process of obtaining knowledge? To expand upon this a bit, Positivism -- as a theory of knowledge -- may, in the process of applying its rules and procedures, and drawing upon previously accumulated knowledge, generate a structure of truth claims -- it does, in fact -- *but* how are we to be assured that this set of truth claims is sound and complete? Even if we grant soundness -- which is a bit of a stretch -- since the mathematics that Positivism is modelled on is itself an *in*complete theory of knowledge, what about completeness? Aren't we in danger of leaving out knowledge. Not only that, but, given the way in which Positivism was established, shouldn't we even *expect* Positivism to omit whole categories of potential knowledge, using Occam's Razor to slash away knowledge with abandon?
LP: Oh, no. In our tour of knowledge, we may miss some things the first time around. But eventually, by applying Positivism, we ought to be able to eventually cover the ground --
I: Even infinite ground? It is possible to iterate a process indefinitely and not exhaust all of the possibilities --
LP: We cannot cover ever instance, but if we discover the underlying laws --
I: Your natural world "axioms" --
LP: Nature's axioms -- the kernel of the laws that govern existence. Understand them and you understand everything.
I: The mythical "theory of everything". The question is whether such a theory exists, whether it is attainable, *and* given that we had such a kernel of knowledge -- one which entails *all* knowledge -- we are still not assured that we could derive any particular truth from them. By that I mean that given some assertion, say, that the highest possible atomic number of an element is 153, or that there are exactly 121,938,995,004 stars in the Milky Way Galaxy, or that there is intelligent life that evolved somewhere other than on the Earth, we cannot be assured that we can deduce the truth or falsehood of any of these from our axioms and our accumulated knowledge. We may have to accumulate further evidence, in which case our present knowledge is *not* complete. Or, the evidence we need may be unobservable. Or, we may not be able to generate the proof that the statement in question is true (or false). In which case, we would have questions about the universe for which we do not, and perhaps cannot, have answers. Thus our Positivistic knowledge may be limited.
LP: Still, if this is the only way to assure knowledge, then we have at least maximized the amount of knowledge we *may* have --
I: But Positivism does not do that. It actual shuts out certain questions, certain subjects and avenues of investigation. For a more than a century, there have been whole areas of knowledge simply cut off from us because of the Positivist program's methodological blinders -- knowledge that is not public, reproducible, general and -- to date -- reducible to Positivist fundamentals --
LP: Such as?
I: The color red. What is it?
LP: Red is the lowest band of visible light energy, having a wavelength of about 7000 angstroms.
I: So when I fry my index finger on a hot stove burner, my finger begins emitting -- or reflecting, I guess -- wavelengths of light in the 7000 angstrom range. . .
LP: It does.
I: And someone looks at my finger and says, "You finger is bright *red*! Did you burn it?" How does she know this? The issue here is knowledge: epistemology, not metaphysics. How does she *know* my finger is red?
LP: From repeated observation that burned flesh appears red.
I: "Appears"? Elaborate.
LP: We obtain data through our senses -- that is the key source of information about the empirical world, as I believe we covered earlier. From our observations, we infer commonalities and generalities about the world.
I: Go on.
LP: Your observer learns at an early age that a certain color is "red", and visually matches the color of your finger to other observed cases of red -- apples, sunsets, blood, certain roses and the like.
I: What about color-blind people?
LP: Or people with their eyes shut, or standing in the dark? Positivism presumes "standard conditions", as objects and events may "appear" differently to us under different conditions. We need access to the appropriate sense-data to make a correct judgment as to the true color of the -- finger in this case.
I: So a color-blind person -- a normal-sighted person in a dark room -- is not in "the standard conditions" for perceiving red --
LP: No, just as someone not equipped with an electron microscope or a radio receiver is in standards conditions for detection molecules, or X-ray stars -- or radio signals.
I: And similarly, I am not in the standard conditions required for "reading" your thoughts, or for sensing whether your wife is in love with you, or detecting the presence of ghosts or hearing God speak --
LP: That is hardly the same thing.
I: Why not? If, according to Positivism, perception is a matter of finding the appropriate "standard conditions", then it stands to reason that if one does not perceive something, then the standard conditions are not in effect, and that one needs to establish the standard conditions for sensing, say, kryptonite, or unicorns --
LP: Now you are being facetious --
I: Not at all, if you wish to argue that everything exists, but that only some things are detected by our senses owing to a lack of standard conditions for viewing. What methodology does Positivism have for distinguishing between the unperceived and the nonexistent?
LP: Well now you've put your finger upon the essence of Positivist knowledge: the "verifiability theory of meaning" --
I: Which is --
LP: Knowledge consists of that which is verifiable.
I: Verifiable by Positivist methodology, which as I pointed out earlier, may have serious gaps in its purview --
LP: Look. One may speculate ad infinitum as to what sorts of things there are, and as long as one does *not* know what is the case, there are many genuine, legitimate *possibilities* to be entertained. Positivism gleans out what is the case. Even if there are practical limitations on what we may discover, we at least do not come to believe what is false.
I: "Soundness", if not "completeness"?
LP: I'm sure you would agree that if we cannot know everything, we should at least be sure of what we do claim to know. Positivism seeks to attain knowledge, not to reinforce mere belief. That is why Positivist knowledge consists of analytic truths --
I: Truths that are necessarily true, or that necessarily follow from contingent truths --
LP: -- and empirical data.
I: This is where I have a problem with your concept of "red". Certainly if we observe some fact of the matter in nature, we can deduce other, perhaps non-observable facts of the matter --
LP: That is often the case. Consider what we know about atoms, radiation, energy waves, micro-organisms -- our knowledge of these comes from logically derivable relations between sense-data -- visible observations. I should point out that by "visible" I do not just mean detectable by sight, but detectable by *any* of our senses.
I: So when I claim that -- this carpet -- is red, the truth of my claim is supported by my perception of its hue, and the logical chain of cause and effect from . . .
LP: The entire process that we understand to be involved in seeing "red": a light source, an object that reflects red light, the eye that perceives this sense-data --
I: And if no such logical link from object to perception can be established --
LP: Then the claim being made is not only not true, it is meaningless.
I: *Meaningless*?
LP: Yes. That is an essential part of the verifiability theory of meaning. Knowledge -- in any theory of knowledge -- deals in propositions -- truth claims, which of course are either true, or false, provided they have meaning --
I: What do you mean? Are you saying that some truth-claims are meaningless?
LP: Of course. "This carpet is a certain shade of red" is meaningful, because "red" is the color produced by a certain wavelength of reflected light -- say, 6950 angstroms of wavelength. But to say "This carpet is pretty" is to utter nonsense. "Prettiness" is not a property of objects. Likewise, "There is a unicorn standing on this carpet" is meaningless as there are no unicorns. --
I: Are we deceiving ourselves, then, when we make aesthetic or ethical value judgments?
LP: Certainly, if in saying that "this carpet is pretty", or "your action is polite", you mean that the carpet, or the action itself possesses the property of "prettiness" or "politeness". Such claims are meaningless, because they are neither analytical, nor verifiable through empirical study. You can't examine the carpet for prettiness, nor, say, my act of offering you a chair for politeness. It is not to be found in the object or action under study. You cannot infer it from the nature of the carpet, or gesture. Unlike "bachelor", which entails the notion of never-married but eligible to be married male, "carpet", or even specifically "this carpet here underneath our feet", does not entail prettiness. Nor can you empirically detect "prettiness" through the most intense and thorough study of the carpet.
I: What is "prettiness", then? Or, is it anything at all?
LP: This leads us to the set of things that do not exist, rather than things that we are unaware of, that you were concerned about earlier. We are capable not only of discerning actual properties of actual objects, we are also capable of imagining fictitious properties of actual objects -- "holy water" for example -- and even fictitious properties of fictitious objects. Such attributions -- such spurious truth claims -- are meaningless. To make such claims meaningful, we need to ground them in analytic truths and actual empirical observations.
I: Let's get down to "red". Describe for me -- in Positivist discourse -- what is actually happening when I perceive -- unmistakenly, I believe -- that this carpet is red.
LP: Very well. The ceiling fixture emits white light -- the full complement of visible light -- ranging from dark red at 7800 angstroms to violet light at 3900 angstroms. This light shines down on the carpet which absorbs the spectrum of light from about 6200 angstroms to 3900 angstroms, and reflecting the remainder -- 7800 to 6200 angstroms -- which is the band of red light. This light reflects off of the carpet, and travels to our eye. The lens focuses this band of light wavelengths onto the retina at the back of the eye, where it strikes the "rods and cones" that convert these electromagnetic wavelengths into chemically generated electrical impulses that travel along the optic nerve to the brain.
I: And --
LP: And then this information is processed by the brain for inspection, or stored in memory, or synthesized with other sense-data to form judgments: "this is red, this is shaggy, this lies flat on the floor -- this is a red carpet."
I: At the beginning of your description of "seeing red" you used the term "7800 angstrom-length electromagnetic wavelength", then at some point between "conversion to chemically generated electronic impulses" and "judgment formation" you drop the expression "7800 angstrom-length electromagnetic wavelength" and substitute "red" for it from then on. Explain -- and justify -- this semantic shift. Are they equivalent? Or, did an undisclosed transformation occur during the process?
LP: Well in natural processes you may have all sorts of transformations of objects, of properties, of energy states, of forms, of information --
I: Yes, but in keeping with the spirit of Positivism - of "verifiability" -- all of your truth claims -- your knowledge -- must be logically connected -- hence the "logical" in "Logical Positivism". You start with sense-impressions, or sense-data, empirical observations -- whatever you wish to call them -- and with analytical knowledge -- logic and inference, and combine them to form legitimate general (or particular) propositions about the world. *But*, you need to do two things, it seems to me, for that strategy to work. First, you must be able to try all of the "links" in the chain, test them for strength --
LP: Otherwise, what is the point? True premises will yield false conclusions if the reasoning is not good.
I: Exactly -- and the other point is that, in addition to good reasoning, you need good premises -- good data to work with.
LP: Otherwise, it's "garbage in -- garbage out", as they say.
I: I agree. But, second, you need a good working phenomenology --
LP: Phenomenology?
I: Literally, the "study of appearances", as described by Franz Brentano, Alexius Meinong, Edmund Husserl, Martin Heidegger, Jean-Paul Sartre and others. You need to make the logical connection between what is perceived *by an observer*, and what there is that is being observed. The color red, for example.
LP: How so?
I: Well, in your description of the process of "seeing red", you miss a link -- the link between the brain receiving an electrical impulse carrying vital information about 7800 angstrom-length waves of life bouncing off this garish rug and into your eyes and mine, AND, the color red -- the bright, intense wash of warm color extended along the floor of this room that we both experience. As a Positivist, can you complete the chain by forging this missing link?
LP: I don't see any missing link at all. All of the steps from light bulb to mental impression are included in my description.
I: But that is not the case at all. If I may break the process down step-by-step: first, the heated filament in the ceiling fixture glows, emitting visible light with a range of wavelengths from 7800 to 3900 angstroms. I believe that light waves are compression waves (that move back and forth like a "slinky" coil, first stretched out, then compressed) along the line of travel, but I may be mistaken --
LP: I believe you are right, but the waveform does not matter. It is the length and frequency that makes the color -- or sound pitch, or radio wave, or whatever -- but continue.
I: Then: this collection of waves of various wavelengths hits the rug, as waves on a lake hit the lakeshore --
LP: Some of them absorbed by the lakeshore -- or the rug in this case -- and others reflected off of the object --
I: Correct. This step acts as a kind of "filter" -- which removes some of the wavelengths from the ray of light cast onto the rug --
LP: And then to our eye.
I: Right -- and this is the important point, despite being reflected -- the energy entering our eye -- passing through the lens and striking the rods and cones in the retinal sheath at the back of the eye --
LP: And absorbed by those light wave-sensitive rod-and-cone-structures --
I: Yes, up to this very point, this light is *still* -- er -- light, is it not?
LP: Yes, it's still the same stuff emitted from the light bulb: light waves vibrating in the 7800-6200 band of visible radiation -- give or take. Whatever wavelengths are filtered out of the original complement of light waves ranging from 7800 to 3900 angstroms and reflected onto the lens of our my eye --
I: And, at the point at which this 7800-6200 band of wavelengths strikes the eye -- the rods and cones at the back of the eye -- there *is* a transformation, is there not? We are no longer dealing with light waves, are we?
LP: Well, at this point, technically, the medium in which the color information is being transmitted changes, from visible light to chemically-generated electrical impulses. When a rod or cone of the right type is hit by the appropriate wavelength of light, the light wave itself is absorbed -- like a wave absorbed by the shoreline. It disappeared. In its place, we have an electrochemical impulse generated by the rod or cone which carries the same information that was in the wave, in a different form, in the new medium of electrochemical energy. An analogy might be, if you were watching waves on a lake, and you saw those water waves hit a buoy, and the energy was transferred from the water to the buoy. You would see wave patterns in the water moving along, until the water hit the buoy, and then the water ceasing to move towards shore, but now the buoy rocking back and forth or moving up and down. Same quantity of energy, same pattern of impulses, but in a different medium. By observing the buoy, one could infer the movement of the water surrounding it -- even at night, when the water was invisible in the darkness, if there were a light mounted on the buoy.
I: That is a good example of how a great many invisible phenomena are made visible, while preserving critical information about the phenomena.
LP: That is exactly the case with most of the "astronomical" and "subatomic" phenomena that would otherwise -- as it had been for thousands of years -- be completely invisible to us. By following the causal trail, we can infer truths about all that lies outside our immediate perception.
I: However, you still have a problem concerning "red". You got as far as the retina, where "red" light waves strike the rods and cones embedded in the retina. Just as the buoy in the water converts water waves into the swaying of the light mounted on it, the retinal array of sensors converts electromagnetic radiation into electrochemical pulses -- which are still not "red".
LP: Well, to continue the analysis, yes, at this point, the information carried by --
I: "Information"? What information? All we have so far is "only" physical phenomena.
LP: Ye-s. It isn't information until it is interpreted -- call it phenomena if you like.
I: But what are "phenomena", according to the Positivist account?
LP: The objects, the events of the physical world -- the things we see, observe --
I: Wait a minute. You do appreciate that there is a fundamental distinction between what we perceive, and what there is -- ?
LP: Of course. But we do not see all that there is, and what we do see we do not always see clearly --
I: We see *what* we see.
LP: But we do not always correctly *interpret* what we see --
I: Hence your goal of "reducing" human observations to scientific phenomena --
LP: Yes. The Positivist goal is to discover how things actually are, not how they appear to us. Post-modernists -- and other cranks -- prefer the latter --
I: Like Don Quixote, preferring the appearance of giants to the reality of windmills --
LP: Exactly. So many people -- otherwise serious, intelligent, educated people -- are engaged in the study of appearances, of ideas -- concepts that exist only in their own heads, with no grounding in reality --
I: That takes us back to the "verifiability theory of meaning": the meaning of propositions, like "They resemble windmills, but they might be giants" rests on the verifiability of concepts like "giant", "windmill", "resemble", "be" and "they" -- and "might". How does one verify the actual physical entity we refer to as "might", by the way? For example, "This might be a windmill"? Is "might" an object, or a property of physical objects, or -- what?
LP: Well, there is no mysterious aspect to "might" as the Positivists use it. In the process of perceiving a phenomenon -- oh, say, a light-emitting object in space that satisfies the description of either a comet *or* a planet -- it *might* turn out, on further examination, to be a planet, say, and not a comet after all. "Might" refers to our anticipated result of discovery, not to the object itself, which is either a planet, or a comet, or something else. It also applies to quantum theory, when we have an indeterminacy, such as an atom that has or has not broken down into smaller particles, but until we observe it, its status is indeterminate.
I: Like the health status of Schrödinger's cat. I notice that you seem to be using "phenomena" to denote two entirely different things. On one hand, phenomena are the actual, specific manifestations of things, of objects and their properties and the events in which they are involved -- like a particular wave crashing into a particular buoy, setting it swinging in a particular manner -- and on the other hand -- phenomena as "what appears to us", what we *see* happening -- like the buoy light bobbing up and down, seen as an indicator of the rhythm of the waves on a dark night. Now "appearance" and "reality" are hopefully related in some way, when we are using observed phenomena to infer the status of reality -- but surely you would agree that one is *not* the other.
LP: Of course. Phenomena -- things as they appear to us -- give us clues as to what is actually out there.
I: But what sort of clues? And what is this relation between objects and appearances? How do we discover it? We cannot even perceive "causality" -- the relation between one set of circumstances and the next, as Hume so drolly pointed out -- how can we assert that a bobbing light at sea at night is a reliable indictor of ocean waves patterns, and not, say, a sailor with a flashlight sending an SOS?
LP: Through "constant conjunction", as Hume pointed out -- the observation that two separate phenomena -- here I mean two actual events -- are associated by proximity in space and time -- like associating the crackle of thunder with lightning flashes.
I: But again, that supposes a great deal -- including that (a) we see -- perceive -- all that is significant in rendering judgments about the world --
LP: Which is by no means simple and straightforward, but may require a great deal of work, and error, always with less than the amount of data we might wish for.
I: True, and (b) that we are looking for the right things, in the right places. This brings us back to the problem of justifiable "reduction", and the tendency for Positivism to summarily throw out whole classes of things that may provide us with insight into reality.
LP: Such as --
I: Well, such as "people". For example, in your reduction of "red" -- which I would like you to complete for me -- you refer to waves of light, of electricity, to eyes and other objects -- but when we left off, we were no closer to understanding what "red" is than when we started -
LP: Ah, well, let me continue --
I: We left off at the optic nerve, which was transmitting an electrochemical signal analog of our red light wave along to the -- well, where does this signal go next?
LP: To the visual cortex, a part of the brain that processes sense-data -- in this case, visual data that comes from the eye.
I: Uh-huh. What does "processing" consist of?
LP: Well, I am not a biologist, or an expert in brain-processes --
I: You're among friends --
LP: Ha! Well, just as a TV set takes a stream of electronic impulses and assembles them into a two-dimensional picture with color and shading, so too, the visual cortex assembles, organizes the data coming from the eye through the optic nerve to form an image in the brain --
I: A *mental* image?
LP: People tend to refer to it is a "mental" image, but in fact it is *all* physical. So-called "mental" states and phenomena and processes are really a special type of physical states and processes --
I: Our talk of "mental" thoughts, memory, reasoning -- that's all really physical stuff occurring in the brain, which is also physical --
LP: Yes. Unfortunately we do not "see" ideas, or memories, or reasoning as such. We only perceive their results through behavior of beings with minds, or rather, brains.
I: This purely physical view of mind is a tenet of Behavioralist psychology, correct?
LP: Yes, "mind-talk", as well as "personality", "feelings", "spirituality" and the like are terms that suppose -- wrongly -- that there is a *separate*, non-physical feature of persons called "mentality" --
I: Gilbert Ryle disparagingly called it "the ghost in the machine" --
LP: We Positivists don't believe in ghosts either, or other entities that do not refer to anything in the actual, physical world.
I: So all mental phenomena "reduce" -- completely -- to physical phenomena --
LP: Yes.
I: So let us return to the Positivistic / Behavioralist account of "red". We have been following our quantum light waves on a long trek now, from being emitted from light sources to bouncing off of carpets and apples and fire trucks and Little Red Riding Hood's hood, into the eye, through the eye, then into the brain itself where the visual cortex "organizes" these waves once again. We seem to be no nearer to "seeing red" than when we started. Are you familiar with the "step paradox"?
LP: Not the term. What is it.
I: It is a classic fallacy in "taking the limit' of an ongoing progression. It comes up in calculus, where limits are very important of course. First, let's look at a good example of taking a limit; the example of Achilles chasing the tortoise --
LP: Is that the one in which Achilles starts out some hundred feet from a tortoise, and with each time interval, he races forward, cutting the distance between himself and the tortoise, but never reaching it?
I: Yes. In the first interval, Achilles runs one hundred feet to where the tortoise stood -- er -- sat -- lay -- at the beginning of the race. But over the same time interval that Achilles moves forward to where the tortoise is, the tortoise is moving, however slowly, ahead, say, ten feet.
LP: And so Achilles has not yet caught up to the tortoise. Zeno used this example and the one about the arrow to prove that we cannot move -- clearly an absurdity.
I: Well, our understanding of motion and change has -- changed -- since Zeno. Now that Achilles has moved to where the tortoise was, and the tortoise has moved a bit further along, Achilles spends the next time interval covering the ten feet between himself and the tortoise, but as he does this, the tortoise, moving at the same rate of speed (one tenth of Achilles' rate), moves ahead a foot.
LP: Yes, yes. The point being -- from the perspective of modern calculus and the summation of infinite converging sums -- that the tortoise does not -- as Zeno opined -- elude Achilles forever, racing all over the planet, but that the sum of their respective steps meets at a point that is 111.1111... feet from where Achilles first stood.
I: Exactly. Now the "step fallacy" exploits this notion of an infinite series, but to bad end. It is used to prove that the diagonal of a unit square is equal to two.
LP: That's ridiculous.
I: And false as well, which is the crux of the fallacy. The point, I will say in advance, is that infinite "process" is *not* the same as infinite "progress". Here is the fallacy. We begin with a unit square -- one foot by one foot if you prefer specific physical measurements. If you draw a line from the upper left corner of the square to the lower right corner -- a downward sloping ramp -- you have a line that measures the square root of two units in length --
LP: According to the Pythagorean theorem -- one squared plus one squared equals two, and since the square of the diagonal is two, the length of the diagonal must be the square root of two -- and not two.
I: But -- instead of drawing the diagonal outright, let us sneak up on it by approximation, as we did with the calculation of the length of Achilles' path, by adding up an infinite series of lengths. Suppose that instead of moving directly along the diagonal of the square from the upper left to the lower right, we move along a step: drop one-half of a unit -- half a foot -- straight down from the upper left corner -- then move to the right half a foot (to the center of the square), then drop down to the bottom of the square -- in the middle of the base -- then over half a foot to the lower right corner.
LP: That would form a zigzag path from the upper-left-to the lower right corners --
I: Consisting of four half-foot-long segments -- which adds up precisely to two feet.
LP: But a zigzag is *not* a diagonal line. The diagonal of a square is not a zigzag path, but a straight line.
I: And this is where the notion of converging limits comes in. Why stop with half-foot steps that clearly do not follow the diagonal, but diverge considerably from the diagonal? Let us take smaller steps, and sum them up, getting a path that is closer to the diagonal. Starting again at the upper left corner, we drop down only a quarter of a foot this time, keeping closer to the diagonal than the half-foot-step process did, then moving right a quarter of a foot, then down another quarter, and so on. You now have a path that still zigzags, but far less than the previous path, cleaving more closely to the diagonal line. and, adding up the steps of the path -- twice as many as before, but each only half as long as before, and we get the sum of eight quarter-feet rather than four half-feet --
LP: -- and you get the same length -- two feet. But that is *still* not a diagonal line, but a series of up-and-down, left-and-right steps. The slopes are different -- as are the lengths.
I: But we can continue making the steps smaller and smaller, producing a path that is closer and closer to the diagonal line all the while remaining exactly two feet long, some point-eighty-six feet longer than the diagonal --
LP: But -- dammit! -- you never get a diagonal line -- even if you go splitting up those steps until doomsday -- or infinity. Yes, your zigzag path *appears* to resemble a diagonal line more and more -- if you are talking about very high resolution computer graphiscs you can still get a visual "match" at about a thousand steps. But at no point in this process -- *ever* -- does your path bridge the gap between an alternating vertical / horizontal line and a forty-five degree slant, which is the diagonal. Look --if you were to add up all of the infinitely many diagonals of all your infinitely many -- sub-squares, or right triangles -- the total length of all of these sub-diagonals sum up to the square root of two, while the height and bases of all of your sub-height and width lines would add up to *two*. All of your steps -- however many of them -- *never* closes the gap between the length of the diagonal of a square and what really amounts to the sums of the sub-lengths of the two sides of the square --
I: No?
LP: No.
I: So you admit that an epistemic process which makes no progress towards its goal is futile?
LP: Absolutely.
I: Well, to put it delicately, your efforts -- and those of many Positivistic "psychologists", or "mind-scientists" -- Paul and Patricia Churchland to cite a prominent example -- to describe mental phenomena, such as "seeing red" or "hearing middle C on a piano", or the "aroma of a warm cinnamon bun" -- to say nothing of far more complex and involved "mental" phenomena, do not succeed at all. All this talk and hand-waving and excruciatingly detailed analysis of wave-transformation and signal patterns -- while significant in its own right -- gets us nowhere with the sorts of questions being posed about human experience, about mental phenomena -- certainly about human behavior, in particular deliberate, intentional "rule governed practices", and certainly *not* "ethics", which Positivism puts in the same basket as superstition, mysticism, and other "meaningless" -- that is to say, non-referring -- concepts such as unicorns and four-sided triangles.
LP: Well, look -- one may have an idea *of* anything, but that does not entail that that idea corresponds *to* anything in reality --
I: What about our perceptions? Do *they* exist?
LP: I don't know what you mean.
I: I have the idea of a unicorn -- I imagine it in terms of sights, sounds -- even smells. There is no unicorn, only a collection of ideas associated in my mind *as if it were a complex sense-datum*, or, if you will, a set of sense data. I see a red unicorn, say. I am almost certainly mistaken in my judgment that there is a red unicorn "out there". but, am I mistaken in my judgment that I am sensing something -- at the very least, that I am having an experience *of* something, even if it is only an imagined something, no more than a loose collectin of sense-data, old memories --
LP: A fragment of beef, a bit of underdone potato? Seriously, you mistake perception with imagination.
I: Well, perhaps imagination -- the act of conjuring up "images" in our minds -- I know you don't believe in "minds", but bear with me for a moment -- is a mental construct, that is, a form of "information" processing that is very loose, and prone to error or distortion. But does that mean that we truly do not have any internal experiences *of* things, real or imagined, or somewhere in between, as when one sees a statue in the distance, and mistakes it for a live human being?
LP: If you are saying that we make mistakes in perception, I would agree. Hence the need for careful objective measurements using scientific instruments --
I: Doesn't a perceptive human witness make for a good observational tool, in its own way, as much as a camera, or a fingerprint kit?
LP: Now you're being very dismissive -- and very dramatic.
I: [Sigh] Getting back to your account of "red", the "information" stored in the visual cortex -- pertaining to 7000 angstrom wavelengths -- what exactly *is* it, in reality?
LP: Eh -- as I said, I an not an expert on brain structure and process -- but it would be something analogous to formatted computer data, stored in a flesh and blood medium, rather than silicon chips. Information about this sense-data would be stored as biochemical structures --
I: Just a moment. Let us stipulate that from the moment light is emitted from a ceiling bulb or lamp, to the moment the visual cortex converts, organizes, stores and presents analogous data from the "red" band of this beam of light that there is some physical state of affairs: light waves traveling from an electrified bulb filament, light reflected off of the surface of an apple, light being refracted by the lens of an eye, light hitting photosensitive cells in the retina, electrical signals generated by these cells traveling along the optic nerve to the visual cortex -- let us grant all that, and that Positivist empirical science gives us a richly detailed and unimpeachable account -- which it has -- of this complex process. Now that we are at the visual cortex, what is "red" -- the color we experience *as* red. Where is it? How do we perceive it as such? Is this structured matrix of cells in the visual cortex "red"?
LP: Of course not.
I: That is fortunate, for we not only experience things as "red", but as "ice cold" or "razor sharp" or "as big as a house" -- and we certainly can't have frozen, razor sharp objects as big as houses stuffed into our brains --
LP: Certainly not. What is in the visual cortex is *information*, which is read by the conscious brain --
I: Did you say "read', or "red"? The latter is certainly not the case --
LP: I appreciate your pun, but no, I mean this information is read -- r-e-a-d -- by the brain, as a scanner or electric eye or other mechanical device "reads" the presence and the structure of information pertaining to "red".
LP: Worse and worse! When we see the red apple, we are "reading" the apple for its color, aren't we?
I: Y-es, in a manner of speaking. We -- as physical beings -- sense physical phenomena through sense organs designed to detect that information. That is "reading", in a sense, much as we read words, or symbols on paper.
I: Well, now, several long and complex steps later, we have a brain state -- a collection of cells that - like a region of a computer memory chip, have some physical status -- not one's and zeros, surely, but a "code" of some sort, causally produced by the red band of the beam of light that enters our eyes -- but no "red". Now you say that this physical brain state -- a wad of protein-based nerve filaments insulated in fat -- adipose, lipids, what have you -- exists, rearranged in some way, like a computer chip, or a school chalkboard, so that -- if read by an observer -- that observer can infer that red is present.
LP: Yes.
I: Well, this "brain state" -- which as I say is nothing more than information -- like a stop sign message, or a slip of paper with the word "red" printed on it -- is not *red*. If we poked in a well-lit brain biopsy tube and looked at this area of the physical brain, it would not look any different if it contained information about "blue", or "the smell of bacon frying", or "middle C on the piano".
LP: Of course not.
I: Then where is the "red"? By that, I mean, on your account of "seeing red", where, and how and why does "reading" the formatted information at this brain site *look* red?
LP: Well, of course, there are other parts of the brain that interpret this data. Somewhere in hardwired memory -- just like a computer -- the information -- based on its content -- is transformed into the color red.
I: How so?
LP: Well as I say, in a computer, "red' is usually symbolized by a particular code. In the RBG system -- or is it RGB -- I forget -- all of the colors that appear on a computer color monitor are encoded as combinations of the three primary colors of light: red, blue and green. So in the coding "990000", the "99" would indicate medium intensity red (on a scale of zero to 255 -- in hex -- base sixteen), while "00" would indicate no blue and no green, meaning that "990000" represents pure red -- pure magenta, that is. Other codes would indicate other colors in the visual spectrum.
I: So when a computer is processing a program, and comes upon the instruction: "display 990000" onscreen, a spot of red appears on the computer monitor?
LP: Exactly!
I: What part of the human brain -- or any other part of the body -- corresponds to a computer display monitor?
LP: Er --
I: Well, you would agree that a computer that "sees", or detects "990000" produces the color red -- magenta -- onscreen. Real, bona fide red we can see -- like we see when looking at an apple. What is the analog in human beings as far as color perception is concerned.
LP: Well, our brains don't have computer screen displays --
I: Or a slot in which we can insert "a penny for your thoughts" and have our thoughts projected for public display --
LP: Seriously, the "screen" as you put it might be thought of as our "consciousness" -- the part of our brains that "visualizes" mental images: colors, shapes, relations between objects --
I: The "mind's eye"? On the Positivist account, what is the part of the brain that "visualizes" red? Or "feelings" cold, or sharpness? Or senses the expanse that is "as big as a house"?
LP: I -- am not an expert on the details of cognitive perception --
I: But you don't have to be to appreciate the claim that is being made here by positivists. Positivists -- at least every Positivist I have ever come across will grant that we "see" red as *red*, and not as waves of a certain frequency. Nor will positivists dispute that if we move along the *same* electromagnetic spectrum we will come across another band of frequencies we "hear" as noise or music or speech, and that this experience is *nothing* like seeing. And, neither seeing nor hearing is symbolic of something else, in the sense that the word "red" printed on a sheet of paper, or an F above middle C note on a music sheet are semantic symbols of some other phenomena. Red is red; middle C is middle C, as the flavor of caramelized sugar is not that of ketchup or mustard or rancid oysters, notwithstanding the fact that is there is associated with these tastes a complex chemical interaction between the molecules of a blob of mustard and the taste buds on the surface of one' tongue --
LP: Granted that this is our interpretation of colors and sounds and condiments, but --
I: Interpretation? Then this *is* a matter of semantics? Do we *learn* to experience mustard as a flavor and not a note in the alto range? Or is it a matter of "waves" again? Look, if at some point 7000 angstrom light waves -- however processed, translated, manipulated or transmogrified -- are perceived as "red", then there is something that is being perceived as such -- what is it, and how does this perceptual experience, on the Positivist account, occur?
LP: I was just thinking -- this debate goes back to the Empiricist debate over "secondary qualities".
I: Which are?
LP: Well, primary qualities of objects inhere in the objects themselves: physical extension, shape, heat, stickiness and so forth. They are clearly *in* the object itself. A sugar cube is, say, 3/8th of an inch in height, width and depth, while our impression or conception -- experience you would say -- is *not* extended, otherwise we certainly could not have the idea of the Moon in our heads as it would be some two-thousand miles in diameter. But color is the paradigm example of a "secondary quality" -- one that does seem to exist in our heads, and not in the object itself. As you say, when the light is turned off, or the viewer is color-blind, the color of an apple, say, is absent.
I: That is both interesting and obliging, but -- what are secondary properties or qualities, and more to the point, *where* are they, and *why* are they? Why is red "red", and where in the brain -- or in your sense-perception schema -- is red located?
LP: I -- really do not know. It seems to me, now that I have reflected upon it, that an appeal to "reduction' is appropriate here. We can trace the wave effect from light to apple to eye to brain -- and clear through the entire brain process, even when one is giving a psychological account of a driver stopping in response to a red light.
I: So along with magic, unicorns, local customs, ethics and other states of mind, we give up color as well?
LP: We don't give it *up*, exactly, but at some point we lose our objective viewpoint. Mental experience is "private", while waves of light are not --
I: You could, given your faltering account of electrochemical sense-data perception, invoke an homunculus located between the visual cortex and the "left-brain" which process quantitative data -- a little man sitting between the frontal lobes like a couch potato in a leather chair who looks at the input from the visual cortex and cries out "magenta!" --
LP: In response to the little man inside *his* head who sees the light wave -- seriously, the perception of sense-data by humans eventually leads into a subjective world --
I: Do you mean that color is subjective -- a function of the individual person?

"Roses are red, violets are blue,
For me at least, if not for you?"

LP: [Laughing] It's not as bad as all that. Remember, the image we see -- we have in our minds -- of a red apple is of the *same* red apple --
I: But how do we know that? You have brought a classically objective sense-datum into serious question. Worse, you seem to be saying that there is no knowable fact of the matter as to what is going on in a given human mind. Granted the Behaviorist theory of mind is sparse, even impoverished -- but -- no *color*?
LP: Well, as you have done previously in our conversation, you have played fast and loose with Positivist doctrine. I say again that Positivism deals with what is publicly and generally knowable, with what can be proven by Positivist methods --
I: But as someone who sees an apple, and experiences the color of that apple, as well as attributes meanings and significations of all sorts to that apple: deliciousness, *mine*, happiness, juiciness, worms and brown spots -- which may not have been perceived at all through sense-data -- are my experiences of, my meaning of, my -- constitution -- of that apple -- are these all "subjective"?
LP: Of course. They are not true OF the apple, you see. At least, they are not -- invoking the verificationist theory of meaning -- logically or causally related to the apple you see. These -- impressions -- are in your head, not in the apple. They are not true OF the apple, and hence, they fail the "meaningfulness" test -- they do not refer to things in the world.
I: Could I at least say that these ideas -- experiences, impressions, constitutions, meanings, exist in my mind? For example, the apple looks red to me, hence I take it to be ripe, and therefore edible. So, by Behaviorism, I reach out for it.
LP: Well, we can infer from your behavior in reaching out for the apple that you desire it --
I: But you really have no commitment to "states of mind", do you? Preferences, feelings, interpretations, and the like.
LP: Only insofar as they manifest themselves as behavior in the physical world.
I: Why do I stop when I see a red light?
LP: Ultimate, internal state programming. You perceive 7000 angstrom light waves, which prompts a brain state that causes you to stop your car.
I: Why do some people race through the red light then?
LP: Different programming states. 7000 angstrom light waves interact with brain states to produce a signal in the right leg that presses down on the gas pedal.
I: What goes on in our minds as far as "consciousness" -- self-awareness -- introspection into our mental states -- er -- brain states?
LP: On the atomic level of causality -- which is what "mental activity" reduces to -- a causal chain of physical interactions.
I: A different causal chain of interactions for each person thinking about different things?
LP: Probably. If the internal state of two persons were the same, they would be thinking about the same thing.
I: And if the internal states of two persons were different, they would have to be thinking about two different things?
LP: Undoubtedly
I: How would you know?
LP: By examining their physical brain states.
I: If I were thinking about a red apple, what would my brain states have to be?
LP: I'm sure I don't know. But whatever they were, they would reflect the causal nature of their origin -- that is, they would be the causal result of the beam of light bouncing off of the apple.
I: What if I were thinking of an apple without there being an apple present to produce the causal sense-data?
LP: Then your mental state -- "image" -- of an apple would be derived from memories -- stored sense-data -- acquired on an earlier occasion.
I: And if I were thinking of a unicorn -- with no previous sense-data experiences to draw from?
LP: You would draw that image from a picture -- an artist's conception -- you had seen of a unicorn.
I: And where did the artist get his conception of a unicorn from?
LP: As Locke would have put it, from the fanciful assembly of images of things you had seen -- a horse, a lion, a deer, and so forth.
I: Imagination is the concatenation of observed, experienced sense data?
LP: Yes.
I: What motivates the original assembly of the body of a horse, the tail of a lion, the hooves of a deer, the horn of some other animal, and so forth, into a unicorn? What causes that image?
LP: The mind is free to assemble, or to abstract out, sense-data images. I can think of a triangle without it being any color, or assembling basic geometric shapes to come up with a new building design.
I: And the motivation, the impetus, for this production of original ideas?
LP: Purely causal.
I: I see we are running out of time. I would like to follow up on your views of human behavior, what humans perceive, and why, what humans *are*, and what Positivism can tell us about specifically human properties, such as free will, ethical and other rule-governed practices, as well as purpose and meaning.
LP: Well, we can take a stab at it.
I: As the post-Modernists would say, that is "doing violence to language" -- but that will come later. I still have to ask you about humaan experience.
LP: I look forward to it.

I: Last time I pointed out some potential problems with Logical Positivism, and I wish to explore these further, with regard to knowledge in general, and ethical knowledge in particular --
LP: And I said that you might not be pleased with my answers --
I: And I raised the point that this may reflect faults with Logical Positivism as a theory of knowledge.
LP: Well --
I: Now Positivistic knowledge is based on the logic of generalities: All X are Y, no W are Z, some U are V, and so forth.
LP: From true generalities we can deduce true instances.
I: But how do we establish the truth of the generalities in the first place?
LP: Well, to take an example from mathematics, all even integers are evenly divisible by two --
I: There are infinitely many integers. You can't test them all individually. You'd never finish examining infinitely many numbers --
LP: And one doesn't. We construct the set of integers in such a way that we know they have common properties. And then we use these properties to infer other properties using mathematical induction --
I: The "falling domino" principle. IF something is true for the first of a series of cases, and IF it is true that if it is true for an arbitrary case it must be true for the next case, then it is true for all cases, even infinitely many cases.
LP: Yes.
I: But in such a case you are presupposing a general truth -- about all of the objects under consideration --
LP: But validly. The set of integers is well-defined. We *know* integers have certain properties (like evenness) in virtue of the fact that we created them that way --
I: But that begs the question. How can one validly go from analytic truths about numbers to truth claims about the natural world -- the orbits of planets for example? How do you justify such a huge leap?
LP: Because it has been shown time and again that that the physical universe operates upon mathematical principles --
I: But *which* mathematical principles? The Ptolemaic model of the solar system, mathematical as it was, was wrong. The Newtonian model of the universe was very accurate -- but wrong. The Einsteinian model not only is still under revision, it seems that parts of it entail uncertainty -- hardly a plus in a theory of knowledge.
LP: Well in practice, two or more models may approximately fit the natural phenomenon. Greater precision settles the matter as to which one is more correct.
I: But if there are limits on precision -- as their certainly seem to be, especially given uncertainty, then we must remain ignorant of fundamental aspects of the universe -- again, hardly a recommendation for a theory of knowledge. And when you say "in practice", doesn't the acquisition of knowledge imply practice? It seems disingenuous to say that "in theory" we know what the orbit of Mars is, but in practice we don't. Isn't knowledge about practice in some fundamental sense?
LP: Well there is a difference between being able to find out things and not being able to -- that I think is a more important difference than whether we choose to find out things based on economics, or personal or social interests.
I: But doesn't this take us back to the problem of mathematical proofs,, where, if you are unfortunate enough to seek an answer that can't be proven in a finite number of steps -- a *small* finite number of steps, I should hasten to add -- then you must remain ignorant of the answer to your question?
LP: In practice -- heh-heh -- I shouldn't say that, should I? Well -- let me put it this way, the assumptions and methods of Positivism screen out mysticism, relativism, occultism -- spurious claims, contradictory claims -- and it provides a basis -- an underlying structure for knowing -- actually discovering what is true and what is not. If we cannot learn everything that is so with our finite minds and finite resources -- including the very important resource of time -- we can at least do our best to pick he truth out from the various rational possibilities. Look -- Pi -- the ratio of a circle's circumference to its diameter -- is infinitely long, and the sum of an infinite mathematical series, but if one wished to build a circular table, we know that 22/7 is a good value to choose for Pi, and that 7/22 is a bad value to choose, and that ten decimal places is more than we would need for almost any physical application. That is useful knowledge; it is enough to answer the questions "how do I construct a round table five feet in diameter?" and "is this a round table?" with acceptable accuracy. If our measurements are not perfect, they are at least based on perfection, and not error, like those who wrongly maintain that Pi is a rational number.
I: So because the usefulness of Pi is a function of its decimal length -- the first dozen or so decimal values are the most important, the next dozen or so less important, and so forth, we can "contain", and access, the most useful knowledge of Pi, the most characteristic value of Pi, in the first dozen digits, and write off the rest.
LP: Exactly. We cannot always get exactness, but we can contain it within a reasonable margin.
I: But this still leaves us with questions whose answers do not fit into this paradigm -- the jellybean problem, for example. Suppose we were to assemble a million jars of jelly beans --
LP: I thought they were "jelly bellies" --
I: Even better -- they are smaller, and have a wider variety of flavors --
LP: Over a hundred, I understand.
I: We have, let us suppose, a million jars of jelly bellies, each jar containing a thousand jelly bellies in any permutation of more than a hundred flavors (and colors) --
LP: One of them all coconut, one of them half licorice and half caramel --
I: Well, we don't know what are in the jars -- the jars are opaque --
LP: We are talking about a billion jelly bellies --
I: Not only that, but grouped into a million jars, with each jar characterized by the composition of jelly bellies it contains. One jar may, as you say, to be precise: one thousand coconut, while another may be 499 licorice, 500 red cinnamon, and one tutti-frutti.
LP: Sort of like gene pools, each jar can be characterized by a "string" or formula, like a molecule: C(12)H(14)O(8) -- twelve coconut, fourteen honey and eight orange --
I: Exactly. Only characterizing the content of all of the jars means opening up a million jars and counting a billion jelly bellies --
LP: At one JB a second, that would take over three years --
I: Longer, as there are a hundred thousand warehouses like the one we are considering --
LP: A hundred trillion -- you would need more counters, but the principle is the same.
I: But the knowledge is *not* the same. Determining the exact contents of one jar is fairly straightforward, but classifying one hundred billion like jars is a formidable task. As the subject of study becomes more complex, or more populous, or both, the surety of our knowledge drops drastically.
LP: But as usual, there are methods that provide drastic shortcuts. Statistical sampling, for example. . .
I: But there are fundamental limits as to what kinds of knowledge statistics can tell us.
LP: Well, it certainly is no substitute for an exact count, but that rarely makes a difference in such large quantities. An ordinary glass of water contains much greater numbers of hydrogen atoms, one of which may turn out to be a deuterium -- a "heavy hydrogen" -- atom instead, but so what?
I: So what? In cases where it makes a difference whether all of the atoms are hydrogen atoms (one electron and one proton) or deuterium (the same, but with a neutron thrown in), it is the difference between things being a certain way, and things *not* being a certain way. Either/or.
LP: Yes, but one would have to have a reason for making that sort of distinction in practice. In physics it rarely makes a difference -- at least on a daily basis. And if the "odd-man-out" *does* make a difference -- as for example when we were trying to discover the *existence* of the very elusive neutrino -- then we look at the oddball case, and not all of the normal cases -- that shortens the search considerably.
I: So if, to use the "rare atomic particle search" analogy, if we take a large enough sample from the one billion JBs, we can get a "probably" answer to the question "are there any licorice JBs among the coconut ones --
LP: Supposing that there are nearly a billion coconut ones, and -- oh, say -- two licorice ones, we could make a good estimate as to how many jars to open up, and how many JBs to take from each jar and examine in order to have such and such degree of probability that there are, or are not, any licorice ones in the mix -- right?
I: If the proportion of coconut to licorice ones was about even -- fifty-fifty -- we could probably take a sample of a dozen JBs from only one jar to discover our errant licorice JB --
LP: And if the proportion of licorice ones were smaller, say one percent, or one hundredth of one percent, we would want to open up more jars -- 20, say -- and examine more JBs -- a hundred say, to be confident. Again, it is a matter of probability, as a shortcut to examining all one billion, or all one-hundred trillion, JBs, which is certainly impractical, and would not shed any more light on the question.
I: Well, that depends upon what the questions is. Supposing we were interested not in the presence or absence of a particular flavor of JB, but a composition. Suppose we wanted to know if there is a jar, among our million, that contains exactly 42 coconut and 21 licorice JBs?
LP: Now you are talking about "species" of jars.
I: Well, only if, say, in our warehouse of jars it turned out to be the case that a number of jars shared some distinct properties. If it turned out that certain jars -- a thousand, say, -- each had exactly one hundred cinnamon JBs in them, that would see to be a pattern, especially if this characteristic were not part of a normal random distribution -- a "bell curve". If the only time cinnamon JBs appeared in our jars was when exactly one hundred, no more and no less, appeared in the given jar, and this occurred for a significant number of jars, then it would seem we have a significant pattern.
LP: An example of an expression of a law of nature --
I: Or an example of an expression of policy at the Jelly Belly packing plant. In any case, it would be like the normal "species" of candies a company produces: chocolate candies, chocolate candies with nuts, without nuts, with caramels, with nuts AND with caramels, cherry-filled, cream-filled, et cetera. We would have bona fide "kinds".
LP: Yes, and this can be done very well with statistical sampling --
I: But only if species are of a certain nature, and a large degree of simplicity.
LP: Simplicity?
I: Sure. In the case of atomic elements, there are about a hundred different elements, characterized by very simple permutations of protons and neutrons, including isotopic variations. All you have to do is to count the protons, and that gives you the element. one proton is hydrogen, seventy-nine is gold, ninety-four is plutonium, and so forth. But supposing -- as I suggested last time -- there were not one hundred elements, but one hundred *thousand* elements, the identity of each element being a function of *all* of the more than 200 known subatomic particles. Imagine trying to do chemical analysis upon materials (made up of invisible parts of some one-hundred thousand kinds) and discover patterns among them. We might still be trying to discover the precise chemical composition of water, using the stoichiometric methods of the early 19th century. And that is assuming that "kinds" fall into neat and discrete groups. One hundred elements go to form a half million naturally appearing compounds, a very few of them so common as to appear familiar to us in every day life.
LP: And your point is that in the case of our jelly bellies, unless they happen to appear in jars in simply and commonly occurring combinations, we would end up with -- let's see -- one thousand JBs per jar, and 100 flavors -- that would be ten to the three hundredth power (10^300) possible combinations in a jar.
I: With ten to the eightieth power (10^80) being Eddington's estimated number of subatomic particles in the known universe. That would make the number of possible jar combinations ten to the two hundred and twentieth power times (10^220) as plentiful as the number of subatomic particles in the universe.
LP: Which would make statistical sampling look pretty good -- compared to counting all of those combinations of JBs.
I: But your assumption is that the "essence", the "essential properties", of these jars can be captured using your traditional statistical methods -- can they?
LP: I'm not sure I understand.
I: Well, suppose that, as in the case of the atomic elements, only the proton count is essential to what makes an atom this element and not that. Suppose in the case of the JB jars that only the count of the licorice JBs matters to the "essential characteristic" of the jars -- do you follow?
LP: I think so -- you are supposing that what "matters" in differentiating the million jars of jelly bellies in your warehouse is solely the number of licorice ones in each, just as the proton count in an atom determines what periodic element it is.
I: Exactly. And, suppose further that the possibilities for each and every jar are very low -- say, zero, one, two or four licorice JBs, and that no other combinations appear. In our imagined jelly belly physics, only zero, one two or four licorice JBs ever appear.
LP: Our licorice "quantum numbers", eh?
I: In a matter of speaking, only this time around "color" and "flavor" are not abstract names, but actual properties. You can actually look at (and lick) the JBs to determine their classification. How would your statistical samplings work in such a case?
LP: Well, uh -- the problem lies in that most of the JBs in a given jar are "noise" -- they don't affect the L-number -- they could be any of the other ninety-nine flavors and it wouldn't make any difference to our "kinds" of jars. Only the zero or one or two or four black ones would matter.
I: And so in taking a statistical sampling of the million jars in each warehouse (one hundred billion jars in all!) you would have to take a sampling of jars from the set of one million jars -- say, ten jars --
LP: You'd need a larger sample than that! For the accuracy you would need to make a good estimate --
I: Well, you take X jars -- ten, a hundred, a thousand -- as your sample of the one million jars in the warehouse, and then you have to take a sample from each jar to "guesstimate" how many licorice JBs are in that jar.
LP: Yes -- but your situation is ridiculous -- you would need huge samples from each jar to be assured that the number of licorice jelly bellies in that jar was *not* zero, but one or two or four. Otherwise you would come to the possibly highly erroneous conclusion that there were no licorice JBs in the vast majority of the jars, when it could easily be the case that most, if not all of them, had at least one or perhaps two or four licorice JBs in the jar. If you give me a few minutes to do the math, I can tell you how many jars, and how many JBs from each jar you would have to sample in order to get even a standard plus-or-minus 5% error margin --
I: It would be a lot of jars, and a lot of JBs, wouldn't it.
LP: It would be an absurdly high amount. Your hypothetical situation is most unusual --
I: Oh, but it isn't usual at all. It simply is not a situation well-suited to statistical analysis, as much of physics and chemistry and other material sciences tend to be -- that is what the statistical tools were designed for -- those aspects of nature in which the typical cases fall *within* the standard deviation of the bell-curve -- the big hump in the middle -- the "ends" of the curve are very small and skinny -- terra mathematical incognita, so to speak.
LP: To be sure, but nature is not like that.
I: Oh, but parts of it is. All human DNA is some 99.98 % identical between all persons, and yet every person is a permutation of six billion base pairs, each of which has four values: AG, GA, CT or TC. That's four to the six billionth power, or ten to the 3.612 billion power base pairs. Now take 0.02 % of that -- the part that varies significantly -- and you still have an enormous number --
LP: Overall similarity, with critical differences --
I: Yes, for it is the *differences* -- the 0.02% -- that characterizes the individual human. And it get worse if we look at the multiple states of the hundred billion neurons in the typical human brain. Again, unlike the carbon atom, which we identify by its *similarities* to other carbon atoms, in the case of persons, we look to the *differences* for characterization.
LP: Still, that is mere number crunching. Mathematics is a powerful tool; we can handle numbers in any quantity --
I: But not in real time. It is just like the problem with those mathematical theorems that take a billions years for a computer to prove. For all practical purposes, we can't get answers to questions of that type -- we lack such knowledge.
LP: But you are assuming that the important questions are all of this excessively long type. Science --
I: I am not assuming that *all* questions are of this type: the "too-large" answer type. I am only pointing out that any question we pose that has an answer of this type is unanswerable -- for all practical purposes, theory be damned. There are practical limits to Positivist number-crunching.
LP: Well, one serious objection to your gloomy perspective is that there are no "patterns" -- that nature deals with the random and the arbitrary *and* that the important knowledge tends to be "too big" or too complex to be discovered. In fact, many laws of nature tend to be elegantly simple; e = mc^2, for example.
I: I am not arguing that all important facts about the universe are too complex for Positivism to handle, or that there are no practical methods for handling them. For example, in the jelly belly case, supposing it were the case that all of the jars were packed by one manufacturer, who sells three mixes: a fifty-fifty coconut/licorice mix, a 25-25-25-25 cinnamon / tutti-frutti / tropical punch / chocolate mix, and a 30-35-35 mix of licorice, cinnamon and coconut. In such a case, a relatively small sampling would give a very accurate accounting of the warehouse's contents -- however many jars there were of each mix --
LP: Of course -- stock personnel would have an easy time of it.
I: But that is a cheat -- you are assuming a pattern, then look for confirmation of it. You may assume that your warehouse is stocked with items by Candy Distributor A -- the three defined mixes -- and that the jars were filled according to A's three "recipe" mixes. But, what if the jars were in fact packed by Candy Distributor B -- which has seven entirely different mixes? What if there was a packing error in A's mixes -- a fifty-fifty coconut / cinnamon mix, for example? Would your statistical sampling pick that mistake up if you assume you are looking at A's mixes correctly packed?
LP: Well, with enough testing, with a sufficiently precise sampling we could discover the inconsistency between A's mixtures and what was in the warehouse --
I: But again, aren't you going to find only what you are looking for?
LP: Well, that reminds me of the search for the various subatomic particles some of them, like the neutrino, very hard to detect at all, others, like the various mesons and leptons, too short-lived, or too rare, to observe. but you will remember that there was relationship between all of these particles. They weren't merely arbitrary mixes of beans in a jar; they had roles to play in the mechanism of the atom. The neutrino, for example, was originally an accounting concept. It was discovered that there were several "quantum numbers" as they were called: charge, mass, spin and so forth. When an atom broke down into parts, the quantum numbers of these parts had to "add up" to the quantum number of the whole atom. If they didn't add up, you had either properties and particles disappearing into thin air, or worse, popping up out of thin air. It was found that time and again, a certain set of quantum numbers: zero mass, no charge and certain other positive or negative numbers kept coming up again and again. That immediately suggested a missing piece -- a particle with those properties. The neutrino, as it turned out.
I: So again, you are depending on the principle of "neat and simple consistent patterns" to rescue you from such dilemmas --
LP: They are not ad hoc solutions -- not like "mystical forces" that are never explained, or even revealed, mere appealed to. That is superstition.
I: But again, if you assume certain principles, like "homogeneity", or "stoichiometry", or even "Occam's razor", aren't you making assumptions you never really prove --
LP: Well, they ARE supported by our findings. Atoms -- even atoms in the Andromeda galaxy -- give off spectral patterns of light just the way atoms on Earth do when heated up. Gravity seems to be the same everywhere --
I: But you are missing the point. To say that results of an investigation are "as if" they were the result of the *same* underlying causes is *not* the same as demonstrating that they ARE the result of the same underlying causes.
LP: I feel a reference to Bayes Problem coming up --
I: Yes. Bayes worked out important results in probability, namely that given a set of certain possible causes C1, C2, C3 and so on, and an effect E, we can determine from the fact of E the likelihood that C2, say, was the cause of E, as opposed to C1 or C3.
LP: Yes. We can "work backward", so to speak, to determined causes from the effect they produce. That is an important tool on probability. It applies to your jelly belly case: given that we have a warehouse with a certain assortment of jars and their contents, we can calculate the likelihood that they were packed by Candy Distributor A and not B, or that they were packed correctly by A, or incorrectly by C, and so forth.
I: The problem is that you are assuming what possible causes there are to begin with --
LP: We aren't just pulling them out of thin air --
I: Well, the reverse is also a problem -- you may be trying to link a result to one of a pre-selected set of known and familiar causes rather than uncover a new and previously undiscovered cause.
LP: The case of the age of the sun. In the 19th century, physicists assumed that the sun was made of conventional fuel, and tried to estimate how long it have been burning, and how long it would continue to burn. They all assumed, in those pre-atomic energy days, that caloric content could be estimated by known types of combustion -- if the sun were a lump of coal, or a glob of kerosene, and so forth. They had no idea of the yield that atomic fusion could produce, and so they came up with estimates that supported a Biblical history length of the age of the sun and Earth -- some ten thousand years -- and then a somewhat longer age -- ten million years -- still a very sort time, which was inconsistent with biological and geological evidence.
I: It seems that Positivism relies upon the universe being a certain way, and then only responds when it hits a wall.
LP: That is not a bad method -- especially when you start out in total ignorance and there are so many limitations put upon investigation.
I: But would you agree that the sort of knowledge yielded by Positivism is of a certain sort -- if I may characterize it:
- You are looking for instances of easily generalizeable cases of simple universal laws.
- You are looking for *similarities* that characterize instances of general cases, rather than differences that distinguish exceptions to general cases, or simply to things in themselves, regardless of whether they are members of some "kind" or not.
- You are looking for properties that are overtly visible to the senses, and to traditional scientific instruments and methods.
- You are looking for *repeatable* experimental results.
- You are using mathematical structures as your paradigms -- not only that, you are looking for *simple* paradigms in which to fit your observations.
LP: I get the idea. But these are appropriate principles for the sorts of entities we have been studying in the 20th century -- atoms, stars, planets, gravity, heat, light, even molecules and living cells. These are good paradigms for these sorts of objects --
I: I would agree -- the problem I have is with "reductionism" --
LP: The principle that more complex and mysterious phenomena are reducible to simpler and more easily understood phenomena -- what's wrong with that?
I: There are a number of problems with that. First, in saying that "these are appropriate principles for the sorts of entities we have been studying" you are arguing in a circle. You observe certain kinds of things (physical objects and phenomena), and not others, so you develop methods for studying these things, and not others. You are pleased with the results -- which are many, and deep and fruitful -- and commit the fault of "cherry picking" --
LP: Cherry picking?
I: Just as in mathematics, where the theorems provable by some algorithm or other method are the ones we accept as true, and the unproven, or unprovable, theorems are given a different, lesser status. Because they are unproven, or even unprovable by our methods, we push them off into a suspect category, or even into the realm of mysticism. They are "less true" by the Positivistic standard, and by public perception.
LP: Surely you don't want to accept as true statements that are unproven, putting them on an equal status with statements that *have* been proven!
I: That is exactly the point I am trying to make: Positivism equates proof with truth, rather than with knowledge. What we *know*, and what is *true*, are two very separate and distinct things. The fact is, under the tradition of Positivism that has dominated our institutions of knowledge this last century, truth has become what is "official" -- proven according to certain standards that are not suitable or successful for *all* truths, only for certain kinds of truths, mainly, those that are covered by the traditional "scientific method". And we use those findings to construct -- even define -- our notion of reality, which in turn reinforces the methods we accept and use to add information to our store of knowledge. We end up with a reinforced, self-perpetuating and skewed picture of reality.
LP: Now that is unfair -- and false. Logical Positivism does not introduce falsehoods into the picture, or ad hoc them, as many other systems of knowledge do. We do not presume the existences of souls, or "The Good", or angels or dragons or humors or ghosts simply because tradition dictates they exist. That has been the problem with so many systems of knowledge that operate on "Occam's Shopping Cart" -- grab what you want from the shelves and toss them in the cart, then wheel them to the cash register and ring them up. All sorts of pseudo scientific knowledge arises in this way -- look at the most recent fad: "Intelligent Design". Assume God exists, and that God is this and that, and does things this way and not that way -- and then proceed to find evidence that supports your assumptions. When the police do that, it is called framing a suspect. Hardly just, and certainly not defensible as truth, much less known truth -- knowledge.
I: But just because you are cautious in screening out spurious truth claims does not mean that you are unbiased. There is a telling problem in mathematics where it has been established by Gödel and others that the theory of arithmetic is *sound*, but not complete. That is, all of the theorems of mathematics you *can* prove are indeed true, but at least some of the theorems you cannot prove may also be true as well. You are missing information.
LP: Well of course. No one claims that in practice one can know everything!
I: But -- to return to the analogy of the jelly bellies -- there is more to this issue than missing minute statistical details , than an nth degree of precision. If a jar of jelly bellies is a jar of *coconut* jelly bellies with an occasional licorice JB thrown in, that is one thing. But if we are considering jars of jelly bellies in terms of jars with no licorice JBs, one licorice JB, two licorice JBs or four licorice JBs, then we are assessing entirely different facts of the matter. Rather than being statistical anomalies -- the occasional and minor packing accident -- these minute appearances of licorice JBs serve as fundamental characteristics of the "kinds" of jars under consideration, just as the "Y" chromosome in a cell is not merely a variation on the "X" chromosome -- one of 26 pairs of chromosomes in a random cell, but the indicator that the body in which this "Y" chromosome is found is a male and not a female -- a pretty big difference.
LP: Nonetheless, Positivism does pick up on these differences, and very well, despite your skepticism.
I: Does it? We can gather empirical evidence, we can examine it, and not understand what we are looking at. The truth may be staring us in the face, but we may not recognize it. Consider the ancient astronomers who saw specks in the sky and could not tell that one of those specks was the Andromeda galaxy, and not another ordinary star. Or consider the alchemists who say all of the chemical reactions we see today, but read "evolution of primary substances" into the processes they witnessed, and not "recombination of elements". Consider the more modern -- very recent really -- history of microbiology, as depicted in "The Microbe Hunters" and "Rats, Lice and History". Data, data, data -- on disease, on patterns of spread, on symptoms, on superficial observable generalities, and all the while the entity underlying these illnesses is invisible not merely to our senses, but to our methods for seeking data.
LP: Of course, the early medical researchers did not know what they were looking for --
I: And that raises the question: if we do not know what we are looking for, how does our Positivistic methods for attaining knowledge help us? How do we form justifiable generalizations if we do not perceive the very individuals we are generalizing about? We construct our generalities based on what we see, but what we see is not all that there is -- even worse, how we see what we see may not reveal what there is. We "see" the contents of a million JB jars by picking a few of them at random, and sample a few of the JBs in each jar. The vast majority of the jelly bellies we make judgments about we never even see. We see stars, but do not see the galaxies among the stars -- and we certainly do not see the black holes, asteroids, extra-solar planets and other items in space. We see the effects of disease, but not the agents of that disease. So when we form generalizations, we are making mathematical models based on our mathematical concept *of* the individual objects in question, and not on the transcendental nature of the objects themselves. We generalize abstractions, and obtain generalizations about abstractions --
LP: But we can fill in the gaps in the abstractions with further investigations --
I: Investigations into what? Into what we see? In "seeing", we do not apprehend all that there is, only what we detect. And that does not merely mean we are missing information, even important information, but that we are *interpreting* that information in light of our preconceived notions of just what it is we are looking at. We see specks in the sky, discover that they are stars, and then see a galaxy, which looks just like a star to the naked eye, or to a weak telescope, and judge it to be a star as well, which goes to support our generalizations that objects in the sky are stars --
LP: But further examination reveals dissimilarities, and the truth that it is a galaxy and not a star that we are looking at.
I: But how does this "further examination" fit into the Logical Positivist model? LP has "Occam's Razor", which removes spurious hypothetical claims about our observations, but not "Occam's Shopping Cart", which would, presumably, add to our list of knowns by embracing the possibilities of new entities. Such imagination, and discovery of exceptions to the established generalities really "lies outside" the LP process. Where in the Positivist epistemology does it say: "If you observe X, then X may be a good candidate for being something new" -- that is, something not yet detected and generalized, but needs to be added to the "known" -- the terra cognita? What part of "The Scientific Method" addresses *that* situation?
LP: You are asking for an algorithm that handles the unknown. That is like looking for a suspect in a criminal data base who is not in the data base, because he has never been arrested or printed --
I: Exactly! And -- to use your analogy -- should we assume that "all of the usual suspects" (in our data base) include *all* suspects, including our perpetrator, who may not be in any criminal record?
LP: Of course not. But to appeal to Occam's Razor, should we routinely assume that the suspect is *not* in the database, and that we should not look there as our first step?
I: That sounds reasonable, but look at the nature of the search as it is practiced. Such searches take time, and one may -- acting as a dutiful Positivist -- spend one's entire efforts looking in the database of existing knowledge, and never find reason -- according to Positivism -- to look outside the database. There are famous examples of this happening. The Pythagoreans, who denied the existence of irrational numbers, because such numbers did not fit their theory of number, or Einstein, who looked for a unified field theory based on "hidden forces" (of the type to be found in the old and established classical physics). One may limit one's search not only to "known land" but to familiar methods -- appropriate or not -- and never discover what one is looking for, because it is not to be found within the scope of inquiry, or by set methods.
LP: But one can always enlarge one's search scope, and certainly expand one's methodology.
I: Can, yes, but will -- perhaps not? Once one defines the parameters of the search, is it not reasonable to end the search once it is discovered the object of your search is not in the realm you are searching, or that it is not revealed by vetted methods? At some point, on occasion, one needs to say, X is not the case, because X has not been found to be the case.
LP: And your fear is that the search may have been prematurely called off, or the area of search too limited. Again, I say, one may always expand the search, or the methods used to conduct the search.
I: Well, this brings us to my second point: reductionism.
LP: Conflating two or more theories -- bodies of knowledge -- into one, by explaining, let us say, everything in theory A by the elements of theory B, the classic case being explaining all chemistry objects and phenomena in terms of atomic physics.
I: Yes. The danger, of course, is that sometimes the "reduction" is not full and complete. The theory being "reduced" may be reduced not by complete successful adaptation of theory A into theory B, but that, like the guests who sleep in the bed of Procrustes, the parts that don't fit may be cut off. Unquestionably many aspects of chemistry are reducible to physics, as many aspects of biology are reducible to chemistry, and many aspects of psychology are reducible to biology. But often the reduction is too quickly accepted, and unjustifiably so.
LP: But surely you would agree that if chemical entities are made up of physical entities, then chemical theory is reducible to physical theory --
I: Only if *all* aspects of chemistry are explainable purely in terms of physics. I would argue that in practice this reduction is assumed to be doable, rather than demonstrated as having been done. I find it curious, giving the Positivist deduction to "proof" that in its most critical cases, proofs are assumed, or swept aside. What I am leading up to is the failure, in practice, of reductionism. I see our time for today is up, but next time I would like to address a couple of faux reductions that turn out to be linked: the reduction of the color red to energy wavelengths, and the reduction of mental objects to physical states.
LP: You are going to introduce "subjective experiences" into the field of objective knowledge.
I: That is how it may appear to a Positivist. but in fact, I will be introducing individual phenomena that are "facts", but ones which may not lend themselves easily, or at all, to generalization. That is a different thing entirely.