Insight Chapter 10
Archival Number: A410
Author: Lonergan, B.
pt 279, l. - 12 (ts 1): ts has `What does it have to weigh, if one is to pronounce a "Yes" or a "No"?' Ms B changed `it' to `evidence' (by hand) but left remainder of sentence as is in ms A.
pt 280, l. 6 (ts 1): ts has `section' for `chapter'
pt 282, l. 2 (ts 3): ts has `syllogism'
pt 282, l. 9 (ts 3): ts has `... field. Such structures or procedures can, of course, be discovered and formulated by introspective analysis. But they exist and operate prior to such analysis and, in general, they do not operate any better after it is achieved.
In the present case the requisite link may be named the notion of knowing change, for if "something happened," then at least one change has occurred. Just as one might way that the notion or structure or procedure of knowing a thing consists in grasping an intelligible unity-identity-whole in data as individual, so the notion or structure or procedure of knowing change consists in grasping the same identity at different times in different individual data.
Conceivably, our man on returning home might have formulated the major premise, if this is the same home and if present data differ from remembered data, then something has happened. In fact, he did not formulate any such premise. He simply experienced present data, remembered different data, understood identity by direct insight, and by reflective insight grasped the virtually unconditioned. What was that grasp? If you wish to experience it, make a concrete judgment of fact: "certainly, I am reading a book." If you wish to analyse it, take your judgment as the conditioned, your data as the fulfilling conditions, and an immanent, operative structure
pt 282, par. `The general form': run into preceding par. in ts
pt 282, l. - 20 (ts 4): ts has `our man' for `the weary worker'
pt 282, l. - 18 (ts 4): ts has `insight' for `insights'
pt 283, l. - 10 (ts 5): ts has `Since any fire there might have been was extinguished, that judgment ...'
pt 283, l. - 6 (ts 5): ts began this par. (crossed out): `The basic element in the answer lies in a distinction between two types of further question'
pt 284, l. - 18 (ts 5): ts began this par. (crossed out): `Hence, the link between the conditioned and its conditions is a law operative in cognitional process'
pt 285, l. - 18 (ts 5): ts does not have `the' before `conditioned'
pt 286, l. 9 (ts 7): ts has `unless he learns to be more wary from mistakes and minor ineptitudes, he ...'
pt 286, l. 16 (ts 7): ts has `is' for `are'
pt 286, l. - 15 (ts 7): ts has `tested' for `executed'
pt 286, l. - 12 (ts 7): ts does not have `So'
pt 288, l. 12 (ts 9): ts: `For there to be a second thing or a second ideal frequency ...'
pt 288, l. - 20 (ts 9): ts has `... to generalize. The whole problem is to prevent them from generalizing rashly. There is ...'
pt 289, l. 6 (ts 9): ts has `of their proper use are so stringent that only exceptionally are they satisfied. The suspicion with which men greet analogies and generalizations is accordingly well founded. proper use can become so stringent proper use ...'
pt 289, subheading (ts 10): ts has `5. Common Sense.'
pt 289, l. 13 (ts 10): ts has `the' for `that'
pt 289, l. 16 (ts 10): ts does not have `Though some repetition will be involved'
pt 289, l. - 16 (ts 10): ts had `The remote source of common-sense judgments'; changed by hand to `The proximate ground and source of ...'
pt 289, l. - 13 (ts 10): ts had `The proximate source'; changed by hand to `The remote source'
pt 289, l. - 5 (ts 10): the words `If I may repeat myself' are added by hand
pt 290, l. 1 (ts 10): ts has `prevent' for `obstruct'
pt 290, l. 8 (ts 10): ts has colon after `art'
pt 290, l. 18 (ts 10): ts has` presupposes and improves'
pt 290, l. 21 (ts 10): `remote' is added by hand
pt 294, l. 16 (ts 13): ts had `As has been argued in the sections on Image and Truth and on Description and Explanation'; changed by hand to `As has been argued in earlier chapters'
pt 294, l. 19 (ts 14): ts has `immediate conjugates'
pt 294, l. - 16 (ts 14): ts has `mediated conjugates'
pt 294, l. - 14 (ts 14): ts has `from the empirical residue of the individual, the incidental, the non-systematically divergent, the unassignability of the continuum. The latter ...'
pt 295, l. - 15 (ts 14): ts: `operate it'
pt 296, par. Inversely (ts 15): run into previous paragraph
pt 296, par. On the other hand (ts 15): run into previous
pt 296, l. 11 (ts 15): ts has `as well' for `equally'
pt 298, par. But if: run into previous
pt 299, l. 18 (ts 17): ts has `sub-sections'
pt 299, subheading (ts 18): was `6. Probability of Judgment.' Changed in ts
pt 299, l. - 10 (ts 18): ts has `in the statistical phase' for `in studying statistical method'
pt 299, l. - 1 (ts 18): ts had the start of another paragraph, crossed out: `The point of the probable judgment is that it probably is true. Its grounds are not merely negative. It is not enough that our knowledge be incomplete and that reflective understanding fails to reach the virtually unconditioned for, were they the only requirements, a mere guess would be a probable judgment. But guessing is probable only in the statistical sense of non-systematic divergence; a good guesser regularly hits things off, not by the rational process of judgment, but by the non-rational process of venturing beyond the evidence'
pt 301, l. 7 (ts 19): ts has `don't' for `do not'
pt 301, l. - 21 (ts 19): ts has `sub-section' for `section'
pt 301, l. - 3 (ts 20): ts has `Automatically' for `Further'
pt 302, l. 1 (ts 20): ts has `and a certain amount of dabbling with gravitation. The more concrete aspects of these allied matters cannot be investigated without introducing further concrete aspects. The more speculative elements demand coherent speculation in the investigation of the further concrete aspects amount of dabbling ...'
pt 302, l. 2 (ts 20): ts has `Automatically further questions arise.'
pt 302, l. 3 (ts 20): ts has `gravitation, which in turn give rise to further questions.'
pt 302, l. 3 (ts 20): ts has `But' written in margin, to appear before `What is far more significant ...'
pt 302, l. 5 (ts 20): ts has `procedures which give relevance to enormous ranges of further questions.'
pt 302, l. - 4 (ts 21): ts: `to the establishment'
pt 302, l. - 1 (ts 21): ts does not have `non-scientific'
pt 303, l. 7 (ts 21): ts does not have `one may'
pt 303, l. - 20 (ts 21): ts has `... limit, so that, at the very time radical proposals for revision become again p ossible, the open minds of scientists are becoming closed. As Max Planck put it: "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." Scientific Autobiography and Other Papers, New York 1949.'
pt 303, l. - 7 (ts 21): ts has `principle of exclusion' for `canon of selection'
pt 304, l. 15 (ts 22): ts had: `what will be named the terminal categories'; `terminal' is changed by hand to `explanatory'; ms B had `terminal' and changed it by hand to `elements or'
pt 304, l. 20 (ts 22): ts: `... limit. While our argument was based upon the immanent tendency of the process itself to a limit, still we had to acknowledge that the limits reached were only provisional, that they merely put us on a platform whence the need for renewed efforts became apparent. Our argument ...'
pt 304, l. - 12 (ts 22): ts has `is increasingly'
pt 304, sec. 7 (ts 23): ts has a different introduction to this section (down to 305, par. Thus, if A ... Handwritten in left margin: `made a little neater in revision'. Ts reads:
Since analytic propositions and principles rest upon an analysis, we must begin from a series of distinctions.
First, a proposition is the content either of an act of conceiving, defining, thinking, considering, supposing, or else of an act of judging. Hence we distinguish between formal terms of meaning and full terms of meaning. Both are propositions, but the formal term of meaning is what you merely think about or consider, while the full terms of meaning is what you also affirm or deny.
Secondly, distinguish partial terms of meaning and rules of meaning. By partial terms of meaning are meant the elements within formal or full terms of meaning. In the proposition, The man is cold, "man" has a determinate meaning and "cold" has a determinate meaning; what they mean are named partial terms of meaning. Further, there are definite rules connecting partial terms of meaning with formal or full terms of meaning. When one combines the partial meanings, "the," "man," "is," and "cold," into the sentence, The man is cold, one obtains a formal or full term of meaning that is determined, not only by the elements, but also by the manner in which the elements combine to make sense. An analysis of that "manner in which elements generally may combine to make sense," would yield a set of rules of meaning.
Thirdly, we advert to a special case of the virtually unconditioned when the meaning of a proposition is its own justification and guarantee. The proposition itself provides the conditioned. The definitions of its partial terms provide the fulfilling conditions. And the rules of meaning provide the link between the conditions and the conditioned. Such propositions are termed analytic.
pt 304, l. - 16 (ts 23): ts has `opposite' for `converse'
pt 304, l. - 14 (ts 23): ts has `that rest' for `resting'
pt 306, l. 5 (ts 24): ts has ` of its terms'
pt 305, l. - 12 (ts 23): The following appears, crossed out, in ts (at the paragraph Now, since ...):
Now the question arises whether the analytic proposition is a mere object of thought or a judgment and a first step is to remove a confusion. The analysis of the analytic proposition reveals a virtually unconditioned that readily enough may be grasped by reflective understanding. There necessarily follows upon that grasp the judgment, This proposition is analytic. To affirm that a proposition is analytic is to affirm that it is self-justifying within the order of meaning. But the question is whether that order of meaning is formal or full, whether it is what is meant in the sense of considering, or what is meant in the sense of affirming.
Before attempting an answer let us note that analytic propositions can be produced more or less at will and indefinitely. Partial terms of meaning are a vast multitude and further partial terms can be provided by the art of defining. Rules of meaning provide a principle for selecting the partial terms that combine into analytic propositions. If the task requires some ingenuity, still that ingenuity can
pt 305, l. - 12 (ts 24): ts has `Fourthly' for `Now'
pt 306, l. 5 (ts 24): ts has `its' for `the same'
pt 306, l. - 18 (ts 24): ts has `... are mere tautologies.'
pt 306, l. - 14 (ts 24): ts: `...depend upon principles, that principles ...'
pt 307, l. 4 (ts 25): ts has `serial' for `serially'
pt 308, 1st par. (ts 25): par `Hence' is run into preceding
pt 308, l. 3 (ts 25): ts: `the' for `each'
pt 308, l. 18 (ts 26): ts has `depends'
pt 308, l. - 3 (ts 26): The following appears, crossed out, at this point:
For this reason we have intercalated between analytic propositions and analytic principles the intermediate class of provisional analytic principles. In the genesis of an empirical science, previous results provide norms and rules that guide further investigation and influence its conclusions. Absolutely, such norms and rules are subject to revision. But such revision would follow only if one reopened the inquiries that led to them. Hence, when one is dealing with other matters, such previous results are unquestioned
an empirical science, only one issue can be raised at a time; still several theoretical issues are relevant to the exact, experimental determination of any one. Hence empirical method heads for explanatory system because, without system, it is impossible to determine when any given correlation will be verified accurately, when some divergence from the correlation is to be expected, what is the source of that divergence, and how great the divergence will be
For this reason we have introduced the mitigated class of provisional, analytic principles. They are analytic propositions inasmuch as they rest on definitions. They are provisional analytic principles inasmuch as their terms, as defined, occur in probable, factual judgments. Their presence in empirical inquiry may be illustated by a simple example. What was H2O, not merely as an empirical conclusion, but also as a definition; what merely approximated to that formula automatically was pronounced to contain impurities. Still such a pronouncement was not absolute, and so it it was possible to reach the revised position that distinguishes between ordinary water, conforming to the formula, and heavy water, conforming to a different formula.
pt 310, ll. - 2 and - 1 (ts 28): ts lacks `or isomorphism' (bis)
ts 311, l. 4 (ts 28): ts has, crossed out, at this point the following:
Let us begin by recalling what has been said on higher viewpoints. Successive mathematical fields are reached inasmuch as symbolic representations of operations in the prior field provide the images in which are grasped the rules that govern and so define operations in the subsequent field. Terms in either field are the materials on which one operates or the products resulting from operations, where materials and products are not essentially different since inverse operations make it possible to take the materials as products and some products as materials.
ts 311, l. 4 (ts 29): ts has `Secondly, then, we have ...'
ts 311, l. 15 (ts 29): ts does not have `In the light of our general analysis of knowledge'
ts 311, l. 18 (ts 29): Crossed out at this point:
Two answers are offered. The first will be named psychological, for it is cast in terms of insights and reflection. The second will be named conceptual, for it attempts to lay down rules that characterize the mathematical series.
The psychological answer runs as follows.
In any mathematical department, terms are related by operations, and operations are governed by rules; but the rules are the expression of clusters of insights, and the clusters of insights stand in a psychological series. There is a laborious process named "learning mathematics." It consits in gradually acquiring the insights that are necessary to understand mathematical problems, to follow mathematical arguments, to work out mathematical solutions. That acquisition of insights involves a succession of higher viewpoints. But each higher viewpoint is related to previous, lower viewpoints. As was argued in a previous section, the symbolic representation of operations in the lower field provides the images in which intelligence grasps the new idea of the set of rules governing operations in the higher field. Hence, though the successive departments of the mathematical series are discontinuous from a logical standpoint, for they suppose different definitions and postulates, still they are continuous from a psychological viewpoint, for one gets the idea of the later in working at the earlier. Such psychological continuity defines the mathematical series. It settles which formalizations are mathematical and which are not.
However, on this psychological solution, only the competent mathematician can judge. Just as common sense judgments are the province of men of common sense, just as the probability of an empirical theory can be estimated only by the man familiar with that branch of inquiry, just as one relies on men of experience, on experts, on specialists in their respective fields, so in determining what is mathematics one has to appeal to the mathematician. The grounds for this position are quite general. Other judgments depend on judgments that settle which insights are correct. But which insights are correct can be settled only by the familiarity and mastery that stands as a limit to the self-correcting process in which previous insights give rise to further questions, and further questions give rise to complementing insights. As in other fields, so too in mathematics it is the man who has been through the self-correcting process of learning that possesses the familiarity and intellectual mastery on which judgment has to rest.
[More was left out here (see A 381). What follows, containing what is in pt, is from another typing.]
pt 311, l. - 5 (ts 53): ts has `From the viewpoint of the mathematician, this conjunction commonly is viewed as dynamic.'
pt 312, l. 17 (ts 54): ts has `the whole regions'
pt 312, l. 17 (ts 54): ts has `... occur. Finally, besides this preference for the general, the complete, the ideal, the development of mathematical thought also is restricted by its relevance to the material element'
pt 313, l. 10 (ts 55): ts: `that is attained'
pt 313, l. - 18 (ts 56): ts has Let us now revert to our question. On the one hand, the basic propositions of mathematics differ from the free analytic propositions that may be constructed by defining terms as one pleases and by combining terms into sentences in accord with whatever syntactical rules one pleases. On the other hand, though mathematics differs from the provisional analytic principles of the empirical sciences, still its fields of relations can be isomorphic with theirs.