Insight chapter 4 typescript (manuscript A)
Archival Number: A402
Author: Lonergan, B.
Typescript (manuscript A) of Insight chapter 4
Database and descriptions © Copyright 2017 by Robert M. Doran
Transcription:pt 103, l. 10 text (ts 1): ts reads, `Finally, from an examination of infinities and of limits, there was effected ...'
pt 103, l. -9 (ts 1): ts does not contain the words `on which the concrete converges.'
pt 104, l. 3 (ts 1): ts has `If applied science depends upon pure science science involves ...'
pt 104, l. -13 (ts 2): ts has `However, though the duality is a fact, one admits ...'
pt 104, l. - 1 (ts 2): ts: `heuristic structures and empirical canons constitute ...' This was changed in ms B.
pt 105, l. 12 (ts 3): the following paragraph precedes section 1 in ts, but is crossed out:
Such then is the program of this chapter. Classical and statistical investigations are complementary as forms of knowing. They also are complementary inasmuch as the universe they examine involves a conditioned series of schemes of recurrence, to which both classical and statistical laws are relevant.
pt 105, subtitles. 1.1 is typed in, but before that both the number and title of section 1 are added by hand, and so is the title of section 1.1.
pt 105, l. - 3 (ts 3): ts has `are or are not reducible ...'
pt 108, l. 3 (ts 5): ts has crossed out an earlier beginning to section 1.3. It reads:
1.3 Thirdly, classical and statistical formulations are complementary.
For classical laws hold under the proviso, other things being equal. Still, what are the other things? In what does their equality consist? As has been argued at some length (Chapter III, § 6. ), events occur on the fulfilment of a diverging series of conditions, and the totality of patterns of such diverging series form a non-systematic aggregate. Now classical laws are verified in events, and so it follows that they are verified as often as a relevant pattern of diverging conditions is fulfilled
pt 108, l. -12 (ts 5): ts has `... the advance of science. For there is a solidarity of classical and statistical investigations; For the advance of science ...'
pt 108, l. -3 (ts 5): ts has no hyphen
pt 109, l. 7ff. (ts 6): ts has an earlier attempt at this paragraph, which is crossed out. It reads:
While there seem to be those that would answer this question affirmatively, I cannot see my way to agreeing with them. My reason runs as follows. Statistical laws refer to evets. Events stand to defining conjugates, whether existential experiential or pure, as the answer, "Yes," to a question for reflection stands to the descriptive or explanatory answer to a question for intelligence. For the event is simply the happening, the occurring, that stands in need of definition and can obtain it only by shifting from the question, "Whether?" to the different type of question, "What?" or "Why?" or How?" On this showing, then, as long as "Yes" obtains its precise meaning by reverting to a prior question,
pt 109, l. 9 (ts 6): ts has: The answer, "Yes," to ...
pt 109, l. 12 (ts 6): ts has no comma after occurring
pt 109, l. 19 (ts 6): ts has no comma after then
pt 110, l. -1 (ts 7): ts has text that appeared in 1st ed., beginning `On the other hand ...'
pt 112, l. 2 (ts 8): ts: `to one another, and so that there must be ...'
pt 112, l. 3 (ts 8): the word `genuine' is added by hand in margin
pt 112, l. 10 (ts 8): ts has `Newton that' and `Laplace that'
pt 112, l. -16 (ts 8): ts has `those definitions'
pt 114, l. 5 (ts 10): ts: `that is no less explained'; this is changed in ms B.
pt 114, l. -9 (ts 10): ts has `and the equality of other things amounts ...' No change indicated. Changed in B.
pt 118, l. 16 (ts 13): ts: `to upset a scheme'
pt 116, l. 22 (ts 13): the word `economic' is written in margin; no comma is indicated
pt 116, -2ff. (ts 13): ts: `Then, the scheme, P, can function though neither Q nor R exist; the scheme, Q, can but may not be functioning, if the scheme could not function unless the scheme, P, is already operative; the scheme, R, could not function unless both P and Q were functioning can function, though R does not exist; but Q cannot function unless P is already functioning; and R cannot function unless Q is already functioning can function, though P
pt 119, l. -13 ff. (ts 14): ts: `... the probable seriation exhibits not only the alternatives that have been realized but also the alternatives that would have been realized has to exhibit the cumulative ramifications of probable alternatives, a line of maximum probability, and a series of lines of lesser probability has to exhibit ...'
pt 119, l. -10 (ts 14): ts: `there are a set ...' changed in B
pt 121, par. There also exists (ts 15): An earlier start on this paragraph is crossed out: There is also a probability for the survival of schemes of recurrence. For the scheme involves a combination of classical laws which hold concretey under the proviso, other things being equal. Now that proviso, as has been seen, refers to the non-systematic and is subject to statistical evaluation
pt 122, l. -1 (ts 17): ts: on a million occasions
pt 123, l. -7 (ts 17): An earlier start on the paragraph Sixthly is crossed out: Sixthly, however, stability is not the only point to be considered. For schemes with high probabilities of emergence and of survival are apt to be a road-block on the way to development. They provide a highly secure basis for later schemes, but they are likely to prevent the emergence of any later schemes. Because their probability of emergence is high, they tend to occupy a large proportion of possibilities of development; and because their probability of survival is high, they cling tenaciously to the opportunities they have seized. A universe that consisted mainly of the inert gases would be highly stable, but it would purchase stability by excluding development. Accordingly, the line that combines both stability and developmental potentialities would make use of a floating population of earlier schemes that were both common and fleeting; because they were common, the collapse of some would be easily replaced by the emergence of others; because they were fleeting, their rapid disappearance
pt 123, l. -2 (ts 18): ts has the word `earlier' in margin, with a comma following it; also, something is crossed out here: `... would be for the earlier, conditioning schemes to be a floating population of common but fleeting schemes to have a high ...'
pt 124, l. 2 (ts 18): ts: was low
pt 124, par. The point (ts 18): Before this paragraph a start on another paragraph is crossed out: Moreover, to look for a detailed exposition would be to miss the point of what we are trying to say. We have formulated a notion of emergent probability and briefly considered aspects of its significance
pt 126, l. 5ff. (ts 20): an earlier attempt at the first in the series is crossed out: 1. The significance of every prior situation resides in the possibilities it contains and the probabilities it assigns its possibilities. The principal possibilities it contains are the schemes that could emerge in that situation; and these possibilities mainly rest on the actual functioning of earlier, conditioning schemes
pt 126, l. -20 (ts 20): ts: is assured
pt 127, l. -8 (ts 20); ts: `breakdown'
pt 127, l. -10 (ts 21): ts: `... time intervals might result in no more than a longer survival of inert, elementary routines and more numerous fresh starts leading to further break-downs. might not be efficacious. ...'
pt 129, l. 14 (ts 22): ts had: `...a mere coincidence that can be traced back to earlier coincidences. From the earlier coincidences ...' This is changed by hand to what appears in pt.
pt 129, l. -13, -12 (ts 22): ts has semicolons after necessarily and positions
pt 130, l. 12 (ts 23): ts had `... a geometrization of nature was the key tool ...' Changed by hand.
pt 130, l. -18 (ts 23): ts has: `... are not too happy. They can be traced. Their profound influence can be followed in Descartes, in Hobbes, Locke, Berkeley, and Hume Their influence ...'
pt 130, l. -9 (ts 23): ts has `... and, consequently, that the Galilean law corresponds, not to our abstract classical law, but rather to what we have named a scheme of recurrence the Galilean law stands ...'
pt 131, l. 3 (ts 23): ts has ether
pt 132, l. 3 (ts 24): ts has, crossed out, the following before section on Darwin:
Closely related to mechanism, though distinguishable from it by its most austere formulation, there is a deductivist view of the universe of our experience. Natural laws are mathematical equations. Let us postulate, then, complete knowledge of all these equations and, as well, a perhaps super-human dexterity in their manipulation. Then, complete information on any single world situation would include the determination of all boundary conditions could be translated into a determination of all required boundary conditions, and the postulated dexterity would insure the consequent deduction of any other world situation.
The essential contention of this view, it would seem, lies in its affirmation that one world situation can be deduced from another without any consideration of intervening situations
The divergence between such deductivism and emergent probability seems to me to lie in the affirmation that one world situation can be deduced from another without any
pt 132, l. 9 (ts 25): ts has: `For, in the first place, Darwin explains. He tells ...' changed by hand.
pt 132, l. -14 (ts 25): ts: `... and he obtains his conclusions by appealing to what he names chance variations by appealing to the natural selection ...'
pt 133, l. 3 (ts 25): ts: `Natural selection is the work of nature, which gives a longer life expectancy and so more frequent litters to the type that are better equipped the work of nature, ...'
pt 133, l. -19 (ts 26): comma after environment in ts; also after won
pt 133, l. -1 (ts 26): The following paragraphs appear, crossed out, at this point:
Further, the probability of the survival of a given type will depend upon two main factors. On the one hand, there is the range of sets of alternative schemes within which the type of animal or plant could function successfully. On the other hand, there is the field of opportunities offered by environment for the functioning of one or more of the alternative sets. There are, of course, further and more complex aspects of the matter but, perhaps, they can be included in one manner or another under the foregoing formulations. Thus, for instance, potentialities for evasion, flight, or self-defence might be added to the schemes in which the animal could function, while competing and predatory animals would be considered as restrictions upon the favorableness of an environment for a given type.
However, if it is true that living things are involved in schemes of recurrence, one must not confuse the probabilities of emergence and survival of these schemes with the distinct probabilities of emergence and survival of combinations of variations. The former probabilities of schemes regard combinations of events. The latter probabilities of variations regard, not events, but potentialities for events. No doubt, the two are closely related, for potentialities for events are significant only if the events sometimes occur. Still, even the closest relationship, so far from proving identity, supposes distinction.
pt 134, par. However (ts 27): This paragraph does not appear in ts. Rather, there is the following paragraph:
Darwinism would indicate the necessity of such a further development. Accordingly, if a satisfactory notion of the thing can be reached, there will arise the following questions. Are things potential components for ranges of schemes of recurrence? Are they variable in these potentialities? Are such variations of potentiality capable of transmission? Is there a series of combinations of transmissible variations of potentiality? Are there the appropriate, successive schedules of probabilities for the emergence and the survival of the series of combinations of transmissible variations of potentiality? Finally, if these questions can be answered affirmatively, can those affirmations rest on general, methodological grounds?
pt 134, § 3.4 is completely rewritten by hand in ts. Replaced are the following pages (28-31):
3.4 Nineteenth century physicists were prone to regard Darwinism as the triumph, in the field of biology, of their own mechanistic view of world order. So far from suspecting that a new type of scientific explanation had been introduced, they took it for granted that Darwin's chance variations were but another name for mechanical processes too complex to be stated in detail.
In this fashion the crisis in the world view, immanent in scientific methodology, was postponed from the nineteenth century to the twentieth. It fell, not to biology, but to the invasion of physics itself by Relativity and by Quantum Mechanics, to force a radical revision of scientific outlook. Moreover, since the immediate result of a crisis in that the old thesis gives way, not at once to a higher synthesis, but rather to a set of merely contradictory antitheses, contemporary opinion tends to be content to replace determinism by indeterminism and mechanistic imagery by some symbolicism.
3.41 Inasmuch as indeterminism arises before imagery as such is attacked, the tendency is to replace one picture of the universe by another. There had been the picture of a vast aggregate of very small knobs, each centered at a point-instant and each subjected to a set of forces; moreover, it was believed that, in principle, the coordinates of position and the magnitude and direction of the forces were determinable to n decimal places with n as large as anyone pleased. There recently has risen an antithetical picture of a vast aggregate of, say, wavicles that can be located only approximately and that respond to accretions of energy, now in one manner, and now in another.
The canon of parsimony makes short work of both pictures. The scientist can affirm what he can verify. Directly in experience he can verify experiential conjugates. Indirectly, in combinations of experiences, he can verify pure conjugates. But there is no rhyme or reason to the view that either in experiences or in combinations of experiences he will ever verify pictures of what is too small to be seen. The only way in which a picture can be verified is to see or hear, taste or touch or smell, precisely what is imagined. Such verification is not possible in the realm of the sub-atomic. Therefore, pictures of the sub-atomic lie outside the realm of possible empirical science and must be left to artists and journalists.
3.42 However, one can admit this application of the canon of parsimony and still affirm an indeterminism, not indeed of pictures of the infra-sensible, but of the data that actually are sensed. Geometrical images endeavor to take on the properties of geometrical concepts; the image of a point has magnitude but the concomitant concept denies it magnitude; the image of a line has breadth, but the concomitant concept denies it breadth. By dint of imagining ever smaller points and ever thinner lines, the geometer generates in himself the illusion that his images possess the accuracy of his concepts and, moreover, when he turns his mind to physics, he fancies a universe with positions and forces accurate to any number of decimal places. Still, while the principle of excluded middle would necessitate the conclusion that every next decimal place must be occupied by a 0, or a 1, or a 2, etc., it remains that human senses, no matter how delicate the instruments that extend their range, must eventually meet their Waterloo and be forced to answer that further decimal places are indeterminate.
To take another instance, what to me is just a bug, to an entomologist is an animal that falls with neat precision under a series of differentiations. Both of us look at the bug, but I see only a slight fraction of what he accurately observes. He could point out to me, one by one, the features that I do not notice. In each case I could be brought to see the aspect or quality to which he draws my attention. Still, he would not have gone very far before I would begin to forget my earlier lessons and fail to distinguish between features already noticed and features under present scrutiny. In other words, the observation of data is not a mere matter of looking. To become a trained observer in any field, one must acquire a range of conceptual categories that both guide seeing systematically through a series of centers of attention and, as well, hold in synthesis the exact set of aspects that successively fall under observation. Now, if this is so, there arises an obvious extrapolation. Future scientific development will bring ever fuller and more accurate categories of classification and description, and so future observations will stand to present observations by trained scientists, as their present observations stand to the looking without noticing of mere laymen. It follows that, at every stage of scientific development, data have no more than an incomplete determinacy and, beyond that determinacy, there lies an indeterminacy.
Now, I believe the foregoing contentions to be, in the main, correct. But it would seem that some distinction has to be drawn between the indeterminate and the determinable. For, while neither is actually determined, still the indeterminate cannot be determined, and the determinable is what can be determined.
Moreover, there may be assumed to be a series of future stages of scientific development, and in each of these stages except the last, if there is a last, there will be data, not actually determined yet determinable. For in the next stage with its better instruments and its fuller complement of more accurate categories, more decimal places will be settled and more data will meet with effective attention.
At once it follows that, in any stage of scientific development except the last, one cannot draw the line between the indeterminate, which cannot be determined, and the determinable, that can and will be determined. Around the luminous area of determined data, there is a penumbra of determinable data; and only around that penumbra of unknown extent, is there the full darkness of the indeterminate.
Further, at each stage of scientific development, scientific intelligence abstracts from the data to which it does not advert. In so far as these data are determinable, the abstraction is an oversight that will be corrected in later stages of development. But in so far as these data are indeterminate, they never can influence scientific understanding, and so must be counted among the merely empirical residue of data from which intelligence always abstracts. In other words, the indeterminate is also insignificant. Beyond the decimal places that today are settled,
3.43 However, while I would not object to a claim that there exists an irreducible haziness to data, I think considerable care must be exercised in drawing inferences from this fact.
First of all, this haziness cannot affect the content of any science at any time. To establish laws, it is enough to show that they satisfy actual observations and actual measurements. To refute laws, there is no use appealing to observations and measurements that never can be made. One has to produce the evidence, and the evidence always consists in the determinate content of actual observations and actual measurements.
Secondly, this haziness is not surprising to anyone that grasps abstraction to be not impoverishing but enriching. If one supposed that laws relate sensible contents, one would be confronted with the dilemma either of denying the haziness of data to save the precision of the laws or else of denying the precision of the laws to save the haziness of the data. But, in fact, laws relate, not sensible contents, but abstract conjugates that implicitly are defined by the laws themselves. For laws are reached and are verified, not in data, but in combinations of combinations of combinations of data; and the meaning of the law is, not the concrete combinatory structure, but only its abstract pattern. Thus, every law is a general formula; to move from the law to the concrete, there must be added further information assigning particular numerical values to specific variables; the haziness of data implies that this further information cannot be completely accurate; but this defect of accuracy in the further information does not necessarily impugn the validity of the law; for the law can be the completely accurate limit on which all actual observations and measurements converge.
Thirdly, it follows that the shift from the old thesis of determinism to the mere antithesis of indeterminism rests on an unconscious assumption that abstraction is impoverishing. For, as we have just seen, the haziness of data does not necessitate any denial of the complete accuracy of classical laws in the abstract, where, however, abstraction is supposed to be enriching. But, as we have also seen, when abstraction is supposed to be impoverishing, then laws relate denuded replicas of aspects contained in data. The meaning of the law is not constituted ultimately by understood relations implicitly defining conceptual terms and, inversely, conceptual terms fixing intelligible relations. The meaning of the law includes a reference to a totality of instances, where each instance is a part or component or aspect in the sensibly given. On that showing, the law is concrete so that either laws must be inaccurate or else data must be as determinate as concepts.
Fourthly, the notion of enriching abstraction does, of course, raise a problem on the nature of objectivity. If the meaning of laws is constituted by understood relations implicitly defining terms, one cannot say that this meaning is objective in the sense that it is something out there to be looked at with one's eyes. Still, within the present context, it is not the notion of enriching abstraction but the development of science itself that creates this problem of objectivity; and, again within the limits of empirical science, an answer to the problem is supplied by the canon of parsimony. For the simple-minded notion that the objective is what is out there to be looked at, constitutes the vulnerable point both in Galileo's primary qualities and in Newton's true motion. Galileo maintained colors and sounds and the like to be merely subjective; he affirmed as real and objective the geometrical dimensions of matter in motion. Again, Newton considered movements relative to observable bodies to be apparent and movements relative to absolute space to be true. Still, operating within the field of empirical science, Einstein decided to treat given extensions and durations in the same fashion as Galileo treated colors and sounds; and when he did so, he reached a space and time that, whatever their objectivity, are not "obviously out there to be looked at." Finally, as there is a canon of complete explanation to cover the Einsteinian procedure, so also there is a canon of parsimony to account for the validity of abstract laws. As the scientist is not entitled to affirm what he cannot verify, so he is entitled to affirm what he can verify; but classical laws are verifiable, for verification consists, not in your layman taking a good look, but in scientists interpreting the combinations of combinations of combinations of thousands of particular results attested by trained observers.
Fifthly, there follows a judgment on the view that classical laws are mere macroscopic approximations to microscopic realities. Obviously, there is no objection to such an account of some classical laws, such as the formula relating the volume, pressure, and temperature of a gas
Fifthly, there follows a judgment on the view that all classical laws are mere macroscopic approximations to microscopic realities. Just as the formula relating the volume, pressure, and temperature of a gas is a statistical result of random movements, so also, some would claim, the law of inertia draws a merely ideal line about which moving bodies oscillate at random but imperceptibly. Now, clearly, if the oscillations are quite imperceptible, they are unverifiable; and if they are unverifiable, they can be affirmed not by scientists but only by journalists and poets. Again, if classical laws are verifiable, what more can be needed or wanted for their validity? There is no scientific need, but only an extra-scientific itch for an image of what really is going on "out there."