A reading memo forCarnap's Logical Structure of the World (Pt. I Ch. A & Pt. II Ch. A)

Introduction

Quine (1969) apparently took Carnap (of the Aufbau) as viewing scientific statements as inherently intentional or denotational statements, i.e., already extensionally interpreted statements, i.e., statements that inherently talk about something language-external (as opposed to something that only pertains to the very language, such as its built-in inferential norms). Upon scrutiny, it should be clear that attributing this ordinary view of scientific statements to someone amounts to attributing to her a view of them such that they inherently make us ontologically committed, and committing, to the existence or reality of the language-external denotata,1 whenever we use these statements (as opposed to when we mention them, to borrow Quine's expression). To be more careful, I may have to avoid saying that Quine took Carnap's view of scientific statements in this way, if "taking" implies conscious choice. For, he too assumed this same conception of scientific statements, apparently without realizing that there was any choice here. (At least that is my interpretation at this point, after reading Quine (1969) and a handful of his earlier essays.) So, it seemed to me likely that he just assumed that when Carnap talked about "scientific statements," Carnap talked about what he understood as "scientific statements" (i.e., intentional or denotational statements), without realizing that in so doing he did so much as taking Carnap's view of them in one way rather than another.

However, according to Uebel (1992), Carnap (of the Aufbau) apparently said something that might make us question Quine's "take." According to Uebel, he preferred to reconstruct the language of science as

1 According to the online Merriam-Webster Dictionary article, the word "denotatum" is contrasted to "designatum" in that while the latter does not imply the actual existence of the object of "designation" (i.e., "designatum"), the former implies that of the "denoted" object ("denotatum"). This made me wonder if I had to use the word "designata" here, assuming that most scientists are ontological fallibilists. But, then, I thought that some unintended Gricean implicature may interrupt my intention, rendering the expression "designata" as if it implied that scientists talk about "objects" that they know do not exist. So, I ended up choosing the word "denotata" here.

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consisting only of what he called "structure descriptions," which (according to Uebel again) "may be viewed as a critical development of Hilbert's concept of implicit definitions" (Uebel, p. 32).2 When I read this part of Uebel (1992), it occurred to me that Carnap's project of the Aufbau may be in this respect more "esoteric" than Quine thought or could imagine (at least at the time of Quine, 1969). That is, I thought that Carnap's preference might be an indication that he was a sort of inferentialist-structuralist of scientific theories (as I am), who accurately distinguished scientific theoretical statements per se from their extensional interpretations, and accurately understood the former as not intentional but only intensional statements, i.e., as statements whose "meanings" consist only in their inferential entitlements/obligations, or, put alternatively, in the "positions" of their intensions in the totality of an abstract structure that is expressed by the whole theory. If so, the Aufbau view of scientific theoretical statements per se might be as "metaphysically abstinent" (to borrow Uebel's phrase) as its view of observation statements (i.e., statements about the phenomenal given).3 And, if so, this parallel metaphysical abstinence (toward both theoretical and observation statements) in turn may explain why or how he thought

2 In this "reading memo," long quotes will be "highlighted" by "shadow," to make it easy to see where the quotes start and end.3 Let me make two notes here. First, strictly speaking, I actually do not (yet) know if Carnap took observation statements (or protocol statements) as statements about the phenomenal given, and if so, exactly in what sense or what way he took them to be about the phenomenal given. But, based on the little I read of Uebel (1992) and the Aufbau, I assume that he took observation statements as, roughly speaking, "auto-psychological" or subjective reports of one's own phenomenal experiences, critically including reports of their relations. Secondly, I must emphasize that, while I share with this hypothetical "Carnap" the metaphysically abstinent conception of scientific theories (which is based on "his" intensionalism of scientific theories), I do not share "his" metaphysically abstinent conception of observation statement, which is based on "his" Machean conception of sense perception. Such a conception of perception Dewey would probably call "spectator-theoretic," and I reject such conception, joining Dewey in this. That is because I, as a sort of Gibsonian, think that the Machean conception is an ideological artifact. I'm currently writing a paper that criticizes this positivistic conception of perception, by calling it the standalone I/O conception of perception and action. If anyone is interested, please wait until I finish writing it up and put it on this website.

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that the Aufbau's project of reduction (of theoretical statements to observation statements) would be possible. Of course, such an explanation would bring up another interpretive problem, namely: If so, how then would Carnap explain the fact that we do use our scientific theories as bodies of extensionally interpreted statements, by applying them to our collective handling of external challenges? In short, how would he solve the "symbol-grounding" problem of scientific theories?

So, Uebel's remarks strongly enticed me to read the Part II, Chapter A (hereafter II-A) of the Aufbau, to check my (tentatively held) hypothesis and the related questions. And I read it, together with Part I, Chapter A (I-A),4 with two main questions in mind: (1)Was Carnap an intentionalist of scientific theories (as Quine was, and

"took" Carnap to be), or, was he an intensionalist (or inferentialist-structuralist) of them (as I am, and Uebel might suggest him to be)?

(2)If he was indeed such an intensionalist, how did he solve the "symbol-grounding" problem for his intensionalist conception of scientific theoretical statements?

A note on the artificiality of the text

As indicated above, this "reading memo" was originally started as a record of my personal history of developing a comparative understanding of the "structuralist" aspect of the Aufbau, in search of its similarities to and differences from my intensionalist or inferential-structuralist understanding of scientific theories. So, from the very beginning, its purpose was not just to present my final interpretation of the Aufbau (which I was sure would contain nothing new or valuable), but to present a record of how I come to that interpretation. I was thinking or hoping that such a record may be an effective tool to convey my own "esoteric" (naturalistic) philosophy to the contemporary readers. Partly due to this ulterior motive, this comparative effort led me to a number of long digressions, in order to make clear (to myself, as well as to readers) some detected differences, through which I ended up elucidating (or developing ----- I'm not sure which) my own idea about how science works. Or, more carefully put, it's an idea about how science may be thought to work, along the lines of my own (naturalistic) views of language, deductive inference, mathematics, and "we."

4 Part I Chapter B is a synopsis of the whole book. Honestly, I haven't read this Chapter very seriously yet. Nor have I read the rest of the book yet, at all.

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Apparently, this also helped me to further my critical reading of the I-A and II-A, which made me revise the present reading memo over and over again. As a result, it became a "rationally reconstructed" history of how I came to my final interpretation.

Texts below may contain some historical or pragmatic inconsistencies, due to this artificial "reconstruction" of the actual history. I tried to eliminate them as much as I could. But, I'm sure there are still many of them left unchecked. I hope that readers charitably interpret them. My intention with this "reconstruction" is not to make me look smarter than I am, but to make the present narrative more effective as a tool by which to help readers to "walk through" a certain "path."

Postscript (or précis) 1

To put a conclusion first, my initial expectation was, after all, a wishful projection of my own intensionalism to a few brief descriptions of the Aufbau. This became clear through the I-A.

More specifically, I eventually came to think that two things were revealed in the I-A. The first is Carnap's basic conception of his "problem space" (so to speak), which roughly consists of (i) his conception of perception and (ii) his conception of scientific statements. The second is the objective of the Aufbau project. Notably, his conception of scientific statements entirely presupposes, and, thus, is confined by, his traditional empiricistic conception of language-world relation. His conception of the objective in turn presupposes ----- not only in the sense of being confined by, but also in the sense of being motivated or required by ----- his "problem space."

Very briefly, the objective is to develop a "constructional system." (I explain how I now understand this shortly, in this précis 1.) Also briefly, his conception of perception is essentially that of Machean positivism, according to which what our sense perceptions directly provide us with are only subjective data of phenomenal experiences, not objective data about what the external world is like. (I hope that this suffices to convey all I have to say about his conception of perception, at least for this reading memo.) His conception of scientific statements (or rather, of the language-world relation on which it is based) is both extensional-representational (as opposed to pragmatistic) and atomistic-foundational

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(as opposed to relational-structural).5 This means that he after all takes scientific statements to be inherently intentional, i.e., already interpreted, statements that are true or false of the "objective" world,6 where that world is understood to consist of "objects" of multiple orders of generality/specificity and/or complexity/simplicity.7

Of course, this traditional-empiricistic conception of scientific statements is at least prima facie incompatible with the Machean conception of perception described above, if we commit ourselves to Quine's first

5 These contrasts drawn here (extensional-representational vs. pragmatistic and atomistic-foundational vs. relational-structural) presuppose a view of views of the language-world relation, which I'm afraid to be "esoteric." This view may be broken down to four interrelated theses, for the sake of exposition: 1. To understand the language-world relation from the standpoint of

representationalism is to understand it exclusively from the point of view of its language-entry side, i.e., exclusively in terms of what causes us (who are purely passive, receptive agents, in this picture) to form a linguistically formulated belief about the world.

Such stance can be more than reasonably called a "spectator theory" of propositional belief-formation, borrowing Dewey's phrase.

2. This representationalist/spectator-theoretic stance forces us to "analyze" the language-world relation (and, so, both relata, the language and the world) in the atomist-foundationalist manner, at least insofar as we are confined to the mechanistic conception of the natural (in particular, that of causation).

Much of the history of "analytic" philosophy, in the midst of which the Aufbau is composed, seems to me to be dominated by this basic orientation, without the key players' awareness of being thus dominated or limited by something. (When I occasionally claim to be a naturalist in this reading memo, my naturalism is not to be confused with this traditional, atomistic-foundationalistic and mechanistic-causalistic sort of naturalism.)

3. By contrast, to understand this same relation from the standpoint of pragmatism is ----- or may be profitably understood as ----- to understand it primarily from the point of view of the language-exist side, i.e., primarily in terms of what effects are created to the world as a result of our forming a linguistically formulated belief about the world. (It is only primarily, not exclusively, because it's just impossible to understand this relation without considering the language-entry side.)

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"cardinal tenet of empiricism" (i.e., "whatever evidence there is for science is sensory evidence," Quine, 1969, p. 75), to which Carnap is committed no less than Quine is. One aspect of the objective of the Aufbau project (making a "constructional system") is to offer a solution to this paradoxical incompatibility of the traditional empiricism and the Machean positivism (without rejecting the "cardinal tenet").

But, in the I-A, the same objective is also depicted in its other aspect, as an attempt to demonstrate the unity of all sciences (except perhaps

I actually think that Peirce's maxim may be more profitably understood broadly in this basic orientation, rather than as a variation of a verification principle, which is clearly a product of the language-entry-obsessed ideology of representationalism.

4. To try to "analyze" this relation in the relationalist-structuralist manner eventually forces us to take this sort of pragmatist stance, at least if we think that the relationalist-structuralist understanding requires us to adopt the Putnamian thesis of social division of linguistic/epistemic labor and the Brandomian normative-pragmatic conception of rational discourse.

Actually, I do think this requirement is real. And, what I call in this memo an inferentialist-structuralist or intensionalist conception of scientific theories is virtually this: the relationalist-structuralist conception of the language-world relation augmented by the (what I take as) natural synthesis of the Putnamian socialism, Brandomian normative pragmatics, and Peircean pragmatism.

Although this total view is not explicitly stated anywhere in the present reading memo, in retrospect, it is presupposed at various occasions. So, I made it explicit here, for the readers' sake (as well as for my own sake of understanding my view better).6 Actually, Carnap occasionally uses the adjective "intersubjective" to refer to the apparently same world. At this point, I'm inclined to think that he makes no clear, systematic distinction in the Aufbau between the intersubejctive world, in the sense of a sort of the reification of our intersubjectively shared belief-system concerning what the "world" is like, on the one hand, and, on the other, the genuinely objective world, in the sense of the "world as it is in itself," i.e., what ought (according to our folk-theory of language that is built in our native languages) to "exist out there" independently of our shared intersubjective beliefs about this "world" and from its historical changes and cross-linguistic/cultural diversities. At this point (having read only the I-A and II-A), it may be at least not impossible to interpret Carnap here as actually making a

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mathematics) by way of demonstrating the unity of all the "object-domains" (or rather, "concept-domains" in this context) dealt with by different sciences (except perhaps mathematics). Demonstrating the latter unity (of "concept-domains" of all sciences) is also required by Carnap's "problem space." As he puts it in Sec. 13 (from his point of view): "any intersubjective, rational science presupposes this possibility" of, in effect, this demonstration by way of "reconstructing" all "concept-domains" from the most basic "concept-domain" of sense-data. Presumably, his rationale here is that otherwise all scientific discourses on the external world would lose (their claim to) their extensions, according to the first "cardinal tent of empiricism."8

His "constructional system" is thus one stone to kill two birds: it is a "rational reconstruction" of the multi-ordered structure of "concepts of the intersubjective world" (or "objects of the objective world," as he equivocates between them ----- see the footnotes 6 and 7) in such a way that the "reconstruction" renders the "concepts/objects" of domains other than the most basic one as mere "constructs" from the "concepts/objects" of the most basic domain, where the most basic domain is taken to be that of phenomenal sense experiences,9 so that

systematic distinction between them, and as attempting in the Aufbau a "rational reconstruction" strictly of the current intersubejctive world (of his time and culture), with strictest "metaphysical abstinence" from making any claims about the objective world and the relation between the intersubjective and the objective "worlds." But, my impression is that it seems unlikely.7 Due to Carnap's equivocation between the "intersubjective" and "objective" worlds (see the previous footnote), it is not clear if his project (in effect) implies to attribute the said multiplicity (of generality/specificity and complexity/simplicity of "objects") to the "intersubjective" world or to the "objective" world. Given the fact that he takes his project as "the reduction of 'reality' to the 'given'" (Sec. 3), it is likely that he thinks this multiple orders "exist" in or with the "objective" world. But, given the fact that the data from which he reconstructs this multiplicity consist of ways in which scientists talk/think about the world, it's hard for me to understand why he could possibly think that way.8 The unity of sciences may be aspired by Carnap for reasons other than this one. But, I just don't know enough about the history.9 The fact that he chose the phrase "rational reconstruction" here (at least in the "Preface to the second edition") rather than a straightforward word "description," might be doubly indicative. For,

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the "constructional system" solves the dual problems of the unity of science and the empiricism-positivism incompatibility.

-----

That's been what I have finally taken out of the I-A. (That is to say, I came to find expressions of all of the above in the I-A, after I had read both of the I-A and II-A, more than once, and come to understand the Aufbau in this way.)

As of now, I interpret the II-A as giving an overview of Carnap's "structuralist" strategy of how to solve his dual problems of the empiricism-positivism incompatibility and the demonstration of the unity of sciences (or scientific "concept domains"). That is to say, I now think that his concept of the "structure descriptions" is heavily motivated by his "problem space," as a means to solve his dual problems.

----- "Reading memo" for Sections of the I-A -----

Two main questions with which I started my reading are (repeated verbatim): (1)Was Carnap an intentionalist of scientific theories (as Quine was, and

"took" Carnap to be), or, was he an intensionalist (or inferentialist-structuralist) of them (as I am, and Uebel might suggest him to be)?

while this phrase primarily indicates his (at least post hoc) awareness of the gap between the real "genealogy of concepts" (how the structure of scientific, intersubjective concepts is acquired by individuals or have been developed by the humanity) and his "rationally reconstructed genealogy of concepts" (how such a structure may be reconstructed from an artificially restricted conceptual domain, in accordance with laws of logic, etc.), this awareness seems to naturally bring with it an awareness of another gap, between a merely intersubjective structure of concepts, only which can be said to be "rationally reconstructed," and an objective structure of objects (if such exists at all), about which it makes no sense for us to say that we "reconstruct" it. (By the way, if Carnap uses this phrase, "rational reconstruction" only in the second edition of the Aufbau, then, given what he says throughout the I-A about "object" and "concept," I'm inclined to suspect that he may not have this critical awareness about his project when he was executing it.)

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(2)If he was indeed such an intensionalist, how did he solve the "symbol-grounding" problem for his intensionalist conception of scientific theoretical statements?

(Sec. 1)1. Carnap says that the purpose of the Aufbau is to make a

"constructional system."2. He gives an initial rough explanation of a "constructional system," as

a system which (in short) gives a "genealogy of concepts". ----- So far, no hint is found for the affirmative answer to the question (1).

(Sec. 2) 1. Carnap further clarifies what he means by a "constructional system."

Most importantly (as I see it), he in effect says that (i) it is a system which reduces an "object" to other "objects" (loosely speaking), and (ii) an "object" is said to be thus reduced if all the statements about it are (systematically) "translated" into statements about these other "objects."10

2. It becomes clear that the answer to the question (1) is actually negative. It's revealed that he anticipated Quine's bifurcation of epistemology into the conceptual and doctrinal sides (presented in EN):

"A theory [he probably means an established body of knowledge] is axiomatized when all statements of the theory are arranged in the form of a deductive system whose basis is formed by the axioms, and when all concepts of the theory are arranged in the form of a constructional system whose basis is formed by the fundamental concepts." (Emphasis mine)

Carnap thus sees "axiomatization" as an atomist-foundationalist (or reductionist) "analysis" (of Euclidean sort, so to speak) rather than an inferentialist-structuralist "analysis" (of Hilbertian sort), aimed at the bifurcated reductions of (i) all the theoretical truths into axioms (qua basic doctrines) and (ii) all the theoretical concepts into "fundamental concepts" (only the latter of which is attempted in the Aufbau's "constructional system," as pointed out by Quine later). No one who understands the fact that an axiom-system is a deduction system in the intensionalist (or inferentialist-structuralist) way, or

10 Judging from what Carnap says in Sec. 14 (of the II-A), he would probably require me to add a qualifying phrase to this "translational" rendition of his notion of reduction here, to the effect: without any loss of scientific objectivity. I will have something to say on this preservation of "scientific objectivity," later, in my #4 comment on Sec. 14.

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understands Hilbertian notion of implicit definitions as intensional (or inferential-structural) definitions, would find such a foundationalist bifurcation in an axiomatization of a "theory."11 So, lacking this inferentialist-structuralist understanding of an axiom-system as a deduction system, most likely, Carnap (of the Aufbau) was as naïve as Quine (of EN) about the distinction between scientific-theoretical statements per se and their interpretations.

3. However, when I was reading this Section initially, I was still clinging to the hypothesis that Carnap's attitude to scientific statements might be somehow (in his own, non-intensionalist way) as metaphysically abstinent as his attitude to observation statements, because of the idea that such a reading might offer an explanation of his (otherwise hard-to-sympathize) conviction that the Aufbau reduction is possible.

Actually, in retrospect, I was way too biased by this idea. To be naïve about the distinction between scientific-theoretical statements per se (as intensional statements) and their extensional interpretations just is to take them as inherently ontologically committing/committed statements. (And, as I will realize shortly, Carnap has another way to convince himself of the possibility of the Aufbau reduction, namely, a tricky use of the verification principle.)

11 By the way, because of a related reason, I'm not so sure how seriously we should take Quine's use of this bifurcation in EN, either. Quine of EN does not seem to have a clue of the inferential-structural conception of axiomatic scientific theories. But, he is well known for his radical empiricism (according to which even classical mathematics is in a sense empirical science) and his (mysterious) semantic holism for empirical-theoretical statements (as opposed to observation statements). Given them, it seems to me that he cannot be seriously taken by this bifurcation of epistemology, even as it is applied to classical mathematics (such as done by Russell & Whitehead). After all, this bifurcation is a crystallization of the bottom-up order of semantic identification (starting from sub-sentential concept-meanings, then compositionally moving up to sentence-meanings and theory-meanings), which is precisely the target of his holistic criticism based on the top-down semantic orientation. But, if he is not serious, it's strange that he makes no explicit reservation about his merely "pedagogical" or "rhetorical" use of it in EN… This is a mystery for me. If this mystery is solved by someone already, I appreciate reference to the relevant literature.

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So, while I came to drop the question (1), I was led to a new question (3), and the question (2) was now modified into (4), accordingly:

(3) Was Carnap (the "structuralist" of scientific statements) metaphysically abstinent about scientific statements (although he was not an intensionalist of scientific theories)?

(4) If he was, (i) how did he manage to hold such an attitude to scientific statements without intensionalism, and (ii) how did he solve the "symbol-grounding" problem for his (somehow metaphysically abstinent) "structuralist" conception of scientific statements?

(Sec. 3) 1. Here, Carnap finally says something that indicates that even the

answer to the question (3) is negative, after all. Carnap says that "The present study is an attempt to apply the theory of relations to the task of analyzing reality,"

while by the latter "task" he means "the reduction of 'reality' to the 'given'."

This description of the "task" indicates the Machean-positivistic view of the science-sense gap, i.e., the view that while empirical sciences apparently teach us about what the "objective-external world" is like, our sensory perceptions provide us only with merely subjective-internal, phenomenal experiences. So, finally, Carnap seems to me to take scientific statements as inherently intentional statements, carrying full ontological commitment to the "reality" of what they are about.

2. Still, according to Uebel, he also says something later (in the II-A), which indicates that he takes scientific statements as "structural statements" in some sense. So, his conception of scientific statements must exhibit this mysterious mixture of intentionalism (taking them to be inherently about something language-external, and thus to be ontologically committed and committing) and "structuralism" ----- of some other sort than that of inferential-struturalism or intensionalism of scientific theories. (This mix was mysterious to me, as an intensionalist of scientific theories.)

3. So, now, my questions shifted again. The question (3) was now dropped, and those of (4-i) and (4-ii) were "dissolved." In their stead, I now faced questions of:

(5) What exactly is Carnap's "structuralist" conception of scientific statements like?

(6) How are the intentionalist aspect and the "structuralist" aspect of Carnap's conception rendered compatible?

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(7) Exactly what is Carnap's own rationale for developing this strange conception of scientific statements?

(Sec. 4) 1. Carnap reveals his purpose, or intended ramification, of actually

developing a "constructional system" of the sort he means for the entire (empirical) science: a demonstration of the unity of conceptual domains of all sciences (perhaps except for mathematics).

2. Carnap anticipates that, in making such a "constructional system" (for the entire science), some special method of "construction" called "logical complex" may be needed, instead of "mere summation."

3. He clarifies this distinction as one between a (mere) "whole" and a "logical complex."

"The whole is composed of its elements; they are its parts. An independent logical complex does not have this relation to its elements, but rather, it is characterized by the fact that all statements about it can be transformed into statements about its elements."

And, he gives an example of "synthetic geometry." "All statements about [synthetic geometrical] constructs are ultimately statements about the elements [i.e., points, lines, surfaces]."

Carnap sees in this "geometrical synthesis" an analogue of the "logical complex," a key method for his unificationist project (of demonstrating the unity of all domains of all sciences) and his positivistic project (of reducing the objective-external "reality" to the subjective-internal "given").

4. His analogy is especially appropriate, if the attempted "construction" or "reduction" were an inferentialist-structuralist "analysis." So, it again attracted me to the intensionalist interpretation of Carnap a bit, although I am pretty sure now that his use of this analogy is mere coincidence. Anyway, the analogy motivates this false reading because just as we make no definite reference in geometry, neither do we make any definite reference in theoretical physics, or so I dare to presume as an intensionalist (inferentialist-structuralist) of scientific theories.

I think that in geometry, as well as in theoretical physics, we only make indefinite, descriptive, and essentially conditional

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references, by way of quantification.12 Such indefinite references take place in forms like, e.g.,

"An A is (always) a B,"or, to put it in a way that makes explicit the quantificational pragmatics implicit in the original expression,

"For all x, if A(x), then B(x)."Here, both of A and B are axiomatic-theoretically identified (i.e., "implicitly defined," in Hilbert's sense) by the very theory of which the quantified statement is a theorem. I mean, it must be so as long as the "reference," which is carried out by way of the universal quantification and the temporarily reference-maintaining use of the variable x, is to be indefinite.13 Often, such quantified statements occur with a specification of the domain of quantification, e.g.,

12 In doing each of geometry and theoretical physics, we surely make (and take) definite references to numbers (of various sorts). In this "reading memo," I ignore this fact, although I think that to understand this fact, that is, to understand "what numbers are" (or, rather, how the phenomenon of making/taking number-reference works), is the single most fundamental problem for the kind of naturalistic (which means pragmatistic and intensionalistic, among other things) philosophies of mathematics and science, which I pursue. After all, that the present "memo" ended up offering a sketch of my naturalistic philosophy (just as you are about to see) was an unintended turn of event, and, as it happened, the sketch just focused on its aspects as naturalistic philosophies of language, logic (or deduction) and science. It leaves entirely untouched this fundamental math-science problem of the phenomenon of "numbers" (or numbers-in-use). I'm aware of this, and I intend to handle this problem in future writings.13 Someone may wonder if an indefinite reference is possible through existential quantification. To this understandable question, my answer is that, if we observe the pragmatics of our own axiomatic-deductive discourses carefully, it should become clear that in theoretical-deductive discourses, no "existential" quantification really occurs (at least in deductive-inferential contexts, as opposed to fictional-referential contexts that are embedded in a larger deductive-inferential context). What occurs in its stead (in deductive-inferential contexts) is exceptive quantification, so to speak, which carries only as much ontological import as universal quantification (about which, of course, deductive scientists have long agreed to take to carry no existential import). If anyone is interested in this opinion of mine, please see this (in English) or this (a summary of the former, in Japanese and English).

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"For all x in a domain D, if A(x), then B(x)."In such a case, the locally indefinite reference of the quantified variable x would carry an aspect of being a definite reference, at a relatively more global context, if the domain D is identified by some interpreted scientific theory or some folk-theory (or, if D is identified by a recursive definition as a class of "constructed" entities ----- but, this case is not immediately relevant to the current topic, so I omit its discussion in this "reading memo"). Only if D is axiomatic-theoretically identified (i.e., "implicitly defined") by another axiomatic theory could the "reference" of x be indefinite at that (more global) level, too.

5. An important point here is that, in my naturalistic view, this lack of definite reference is only observed with our scientific-theoretical, rigorously deductive discourses (or deliberations) that are carried out at an "abstract" level, independently of any specific extensional interpretation of theories. By contrast, in our daily physical talks about "things out there," we do make definite references all the time, by way of what may be called broadly-ostensive references (which include not only directly ostensive references such as made by demonstratives and the first/second-person pronouns, but also indirectly ostensive references made by all sorts of anaphoric expressions and definite descriptions).14 These are all essentially indexical references, through taking and making of which we commit one another to the existence of the referred-to "things out there."

Moreover, although I actually think that such daily "thing"-talks involve an aspect of theoretical transactions, I also think that the theories that are (tacitly) appealed to in such practical contexts are only folk-theories (of physics, biology, psychology, etc.), as opposed to axiomatically formulable scientific theories that afford us purely deductive discourses. By "folk-theories," I mean such theories that their major concepts (specifically, nominal as opposed to verbal ones) are (i) structured by what Silverstein called a referential hierarchy (Silverstein, 1987), and, for this reason, (ii) inherently intentional and ontology-laden. An upshot of this conception of "folk-theories" is that "we" just cannot talk about these folk-theoretically identified natural kinds purely deductively, i.e., independently of their (inherent) extensions, because of the theoretical connection between them and the inherently indexical natural-kind concept of "we." Indeed, by

14 How definite descriptions are involved in indirectly ostensive references is already explained, in its all essence, by Carnap. See my comment on Sec. 13.

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making and taking such folk-theoretical, ontology-laden statements, we constantly engage in the reproduction, and/or occasional revision, of the whole natural ontology (so to speak) that is build in our language, which (the natural ontology) includes what may be called the natural definition of the most inherently indexical natural kind, i.e., of what "we" are. At least, that is how I, as a sort of naturalist of language, think the phenomenon of language works (and how the phenomenon of "we" works, as well).

This kind of inherently ontology-laden pragmatics does not happen, by definition, with our use of scientific-theoretical concepts in purely deductive discourses on axiomatic scientific-theories (or on abstract structures that are defined or expressed by the axiomatic theories).

6. Another important point here is that, although purely deductive discourses (or deliberations) occur only in theoretical sciences, that does not mean that all scientific discourses are purely deductive in this sense. Consider what we do (or amount to doing) when we try to empirically test a scientific theory, and when we collectively, as a community or society, try to behave in ways informed by a scientific theory. At both scenes, what we try to do amounts to somehow trying to connect the scientific theory (which is inherently void of any intentionality) with our perceptions and actions ----- at the former scene of theory-testing, in the direction of "afference," and at the latter scene of theory-applying, in the direction of "efference" (metaphorically speaking). Now, in my opinion, we achieve this collective theory-world connecting, in each direction, through mediations by (i) an interpretation of the theory-in-use (through which the theory is conferred with some intentionality) and (ii) our folk-theories (of physics, biology, and, most critically, psychology of perception and action), which comprise the natural ontology of our language and are inseparably connected with the interpretation. Moreover, I take them to be scenes of language-entry and language-exit, not in the sense of scenes in which an individual language-user encodes her perception into a linguistic message and decodes a linguistic message into a piece of motor behavior. Rather, they are scenes of collective language-in and language-out, where linguistic/epistemic division of labor plays essential role.

For instance, even when I try to check Newton's laws of motion by conducting a simple experiment by myself, to be able to do so, I must prepare some measuring instruments devised by someone else, of which I have learned from someone else how to use, previously. Surely, it's possible for me to devise such instruments all by myself. But, to be able to do so, I must have

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learned from someone else some conventions of measurement (such as systems of units of weight, length, time, etc., and how they work), prior to the devising. Again, I might try to invent all such "conventions" by myself, to be sure, in order to prepare myself for the future devising of measuring instruments, with which I plan to test Newton's theory. To be able to do so, however, I must have learned from someone else the real number arithmetic, previously. Of course, I might try to invent it all by myself, too. But, then, to be able to do so, I must have had learned some language first. (I cannot imagine it's possible that someone invents real number arithmetic all by herself before she acquires any language.) And, even if I grant the possibility of all of these unthinkable solitary attempts (only for the sake of argument), I don't think it's possible at all that an individual being invents a whole language individually. It should be clear that the scene of theory-application is even harder to imagine to be carried out in solitude.

These scenes of collective language-entry and language-exit essentially comprise our making and taking of various speech acts to and from one another, which (those making and taking) involve perceptions and actions of the makers and takers of the speech acts, through and through. That is to say, while I'm suggesting here that these making/taking of speech acts form some causal-historical "chains" or "trees," I'm opposing the idea that the language-world interface only occurs at the "ends" of these "chains" or "trees" ----- as if our making/taking of speech acts remain "inside language" except at such "peripheries." Every moment of our making/taking of such a speech act is a moment of collective language-in/out.

So, after all, these scenes of collective language-in and language-out may be said to comprise individual language-in's and language-out's, although they are not scenes in which individual language-users mindlessly encode their perceptions into linguistic messages and decode linguistic messages into motor behaviors. For instance, if I take my temperature by reading a thermometer and decide to stay in bed today, it constitutes a scene of individual language-out which is theory-laden, in the sense that my rationale or deliberation that connects the temperature-reading to the behavior of remaining in bed involves theory-laden inferences (or material inferences, to borrow Sellars-Brandomian terminology). But, more importantly, notice that this scene already contains a tacit moment of individual language-in, at the moment of my perceiving the piece of (electric) gadget as a thermometer,

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which fact (the fact of my perceiving it as a thermometer) presupposes that I know what a thermometer is, in the sense of knowing what it is for and how to use it. This perception of mine constitutes an individual language-in, which is as much theory-laden as my individual language-out. The collective language-in and language-out (the collective theory-testing and theory-applying) comprise individual language-in's and language-out's in this theory-laden, pragmatic sense.

I'm suggesting here that these collective theory-testing (language-entry) and theory-applying (language-exit), consisting of individual language-entries and -exists of the theory-laden sort, are processes through which we collectively and historically achieve the (Quinean) holistic extension-assignments for our empirical scientific theories. (This does not apply to the intended extensional semantics of "foundational-axiomatic theories" for the foundations of classical mathematics. I think a very different consideration is needed for them.) Moreover, the extension-assignment is dynamical, for that matter, meaning that our individual, theory-laden language-entries and -exists are at the same time both our consumptions and reproductions/revisions of our interpretations of the theories involved ----- and, through which, of our natural ontology by which we live. After all, as far as the individual language-entries are concerned, their occurrence consists in combining of (i) the direct or indexical reference to something external and (ii) the inferential-structural identification of that something.

Many of these making/taking of speech acts (i.e., theory-laden, individual language-in's and -out's) fully deserve to be called scientific discourses, i.e., can be understood as making/taking of some scientific statements, in the sense that their making/taking are laden with some scientific-theories. (Many are even laden with the very theory being tested/applied collectively.) However, none of these statements are made/taken in the purely deductive manner of scientific-theoretical discourses, inasmuch as they are made/taken in the process of the collective theory-testing/applying. That is to say, these collective language-entry/exit scenes are such that, in them, our scientific theories (which are inherently intensional, without any ontology attached) and our folk-theories (which are inherently intentional, attached to the natural ontology of our language) are inter-connected seamlessly and dynamically, constantly

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reproducing/revising our natural ontology (and, with it, our "way or form of life"), thereby defining/redefining (implicitly but indexically) "what we are."

7. I now think that it would be hard to attribute to Carnap of the Aufbau (as well as Quine of EN) this naturalistic awareness or conception of the pragmatics of our institution of empirical science, in both sides of which (i.e., in the theory-testing and theory-applying scenes) the aforementioned sort of linguistic/epistemic division of labor is seen to play essential role. So, accordingly, neither of them is hard to see as being clear about the critical distinction between scientific theories per se and their interpretations (the latter of which are inseparably based on our folk-theories of various sorts, which comprise the natural ontology of our language).

Postscript (or précis) 2

As stated in the Postscript (or précis) 1, I now see the II-A as offering an overview of Carnap's basic "structuralist" strategy, of how to solve the problem of the empiricism-positivism incompatibility (in such a way that it would also demonstrate the unity of sciences).

In retrospect, the II-A can be divided into three blocks:Block 1 (Sec's 10 – 12): Carnap develops his concept of the "structure" of

a "relation," as a background on which to base his concept of a "purely structural definite description."

Block 2 (Sec's 13 – 15): Carnap develops and defends his thesis that, given a single domain of "objects" (or "concepts" ----- I omit this explication hereafter) that is handled by a single science, it ought to be in principle possible to develop a system of "purely structural definite descriptions" such that every occurrence of every "object" term in statements of that science can be simultaneously replaced by a "purely structural definite description."

Block 3 (Sec. 16): Carnap indicates his "structuralist" strategy to solve the dual problems of the empiricism-positivism incompatibility and the unity of science.

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----- "Reading memo" for Sections of II-A -----

My reading of the II-A was guided by the questions (5) through (7). Let me restate them here:

(5) What exactly is Carnap's "structuralist" conception of scientific statements like?

(6) How are the intentionalist aspect and the "structuralist" aspect of Carnap's conception rendered compatible?

(7) Exactly what is Carnap's own rationale for developing this strange conception of scientific statements?

The questions (5) and (6) were both solved as I came to understood the concept of "purely structural definite description." So, they will be finally answered through Block 2.

The answer to the question (7) lied in Carnap's "problem space," all along, in retrospect. But, it was also recapitulated in Block 3 (Sec. 16).

(Sec. 10) --- Block 11. Here in Section 10, Carnap declares:

"Science deals only with the description of structural properties of objects." (p. 19)

Let me call this Carnap's structuralist thesis (of scientific statements).

2. To gradually clarify the intended meaning of this thesis, he next makes a distinction between a "property description" and a "relation description":

"A property description makes individual or, in a sense, absolute, assertions while a relation description makes relative assertions." (p. 19)

This distinction does sound like a distinction made by an intensionalist of scientific theories.15 But ….

3. Carnap's distinction seems to miss two important points.

15 More specifically, it sounds to overlap with my intensionalist distinction between monadic and relational universals, which I present in the paper I mentioned in the footnote 3. But, while my distinction corresponds to what I call, in that paper, the fundamental Atomism of relatum and the fundamental Structuralism of relations, Carnap's distinction is drawn totally within the framework of the fundamental Atomism of relatum.

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First, his distinction pays attention only to the predicative part of the whole of a speech act of "description" or "assertion," ignoring the referential part, and, thereby revealing his lack of appreciation of the importance of the difference between definite (or indexical) references and indefinite (or fictional or hypothetical and structural-descriptive) references, for the proper understanding of Hilbert's concept of "implicit definition" (and of the notion of an axiom-system as a deduction system). (Here, I assume that any such speech act contains the referential and predicative parts, although the whole of the reference-and-predication unit may or may not be within the scope of a quantification.) To see his neglect of the referential part, considering two contrasting cases would be helpful: On the one hand, even a "relational" predicate can be used

to make an absolute assertion if the predicate is used (i) as interpreted and (ii) with referential expressions that definitely refer to the external relata. For instance, "a is taller than b" where "a" and "b" make definite references, makes an absolute assertion, as indicated by its symbolic form, Taller(a,b).

Carnap may object that this does not count as an "absolute assertion" by his standard. But, insofar as the notion of an n-ary relation is understood as a set of ordered n-tuples (as it is so understood by Carnap), I see no fundamental difference between an assertion of "Tall(a)" and that of "Taller(a,b)," as regards their "absoluteness."

And, even (non-relational or monadic) "property" predicates can make a relative assertion if (i) a number of them are used together, as (non-interpreted) theoretical predicates that are "implicitly defined" by an axiomatic theory, and, thereby, used as intensionally mutually interrelated by the theory, and if (ii) they are used with the same variable that indefinitely refers under the same quantification, in the scope of which all of its occurrences maintain its fictional or hypothetical reference. To re-use the same example above, "For all x, if A(x), then B(x)" where "A" and "B" denote "implicitly defined" theoretical concepts, makes a relative assertion.

Carnap may now object that my (Yasuda's) distinction between "absolute" and "relative" assertions here is what he shortly explains as the distinction between (mere) "relation description" (and "property description,"

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taken together), on the one hand, and "structure description," on the other. I may grant a point to this objection, to an extent. But, ultimately, there is a difference between Carnap's and my distinctions, which Carnap probably cannot see as long as he cannot see the fundamental epistemological difference between his notion of "purely structural definite description" (which is based on a questionable application of the verification principle, as I explain shortly) and the Hilbertian notion of implicit definition (as it is properly, intensionally understood).

Secondly, at least judging from the II-A, he seems to miss a structuralist possibility that a "property description" (i.e., a predication made by using a monadic predicate) might be a part of an absolute but structural description (a combination which would be an oxymoron to Carnap), which, if taken independently, looks as if it were an incomplete description or predication.16 A perfect example of an absolute but structural description is

any application of an axiomatically, purely deductively defined abstract-structural concept (of mathematics) to some "concrete" data-sets. For example, when we say that the "concrete" system ¿ is a commutative group, we are clearly not giving a meager "(monadic) property description" to a single referent, but giving a "structure description," in the most genuine sense of the term, to a certain "concrete" and inherently structured data-set (with which we are intuitively acquainted, in this case). Note that this "structure description" is fundamentally distinct from a "relation description" in Carnap's sense which presupposes the Cartesian product of otherwise "flat" domains of direct reference, say, D1×D2×⋯D n, of which the said "relation" is taken as a subset.

Actually, it's tempting to judge, from Carnap's text, that he even presupposes that a "relation" is a subset of

16 This is a point tightly related to Quine's semantic holism. (But, I suspect that even Quine did not fully understand this point, assuming that he was not aware of the obvious connection between his semantic holism and the Putnamian concept of the division of linguistic labor.) Moreover, I also think that this point has something to do with Ancient Greek, post-Platonic problem of relatives. (See this, for a related discussion, by me, of this possibility.)

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the Cartesian product of the same set (in the form of Dn). However, a good part of what he says about a "relation" seems to be generalizable to the notion of a "relation" as a subset of D1×D2×⋯D n where the componential sets are not necessarily the same. So, I charitably take his notion of a "relation" in this generalized sense.

An example of an "incomplete" description, i.e., a part of an absolute but structural description, is given when someone describes the color of the surface of something as, say, "red." Such a description, in my view, effectively ascribes to the surface a certain structural property that is indicated by, e.g., the color solid. In this case, she is in a sense (i) tacitly making a massively parallel definite references simultaneously, not just to the seen surface of the explicitly referred-to object but also to the seen surfaces of surrounding objects (or, in case the comparison is tacitly made against the past colors of the same object, to those past surfaces) and (ii) tacitly attributing to all of them certain structurally-mutually related (pseudo-monadic) properties. The explicitly made, superficially monadic ascription ----- of the (seemingly) monadic "property" of being "red" to the (current) surface of the object ----- is only an incomplete part of the whole structural-absolute description.

Another example of an "incomplete" description might help to clarify my naturalistic view of language. Every scene of individual language-in involves some "incomplete" descriptions because it is theory-laden in some ways. For instance, if I try to play with a small moving entity because I perceive it as a "cat" (thereby instituting a moment of an individual language-in), it constitutes an implicit "incomplete" description. Behind making (as well as taking, if ever) of such a natural-kind attribution (or identification), there lies a shared presupposition of certain natural ontology such that, to identify something as a "cat" amounts to locating that object at a certain juncture of that inherently structured ontology.

And, needless to say, to locate something at a juncture of the natural ontology includes to be disposed or ready to interact with that thing in certain ways rather than others. After all, natural kinds that are "implicitly defined" (in some sense) by "our" natural ontology are all theoretically (yet indexically) connected with the inherently indexical natural kind of "we," which

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connections comprise such pragmatic "information" of affordance/dual-affordance (restrictance? Impedence? I don't know the terminology) of the target kind, to "us."

So, a successful making and taking of such an "incomplete" description (explicit or implicit) presupposes a history of similar "incomplete" descriptions of various objects, having been made and taken in the speech community to which the current maker/taker of the description belong. In other words, such an "incomplete" description takes place as a part of the history of the massively parallel "incomplete" references-and-predications, which are nonetheless in a sense simultaneous. And, it is mostly through this sort of making and taking of "incomplete" descriptions that we take part in the natural history of language, which is the history of continuous reproduction/revision (as well as "consumption") of the natural ontology, including the aforementioned natural definition of what "we" are.

(Sec. 11) --- Block 11. Here he makes the most critical distinction for us to understand his

structuralist thesis, the one between (mere) "relation descriptions" and "structure descriptions."

"[Structure descriptions] do not even specify the relations themselves which hold between [individual elements of the range assumed in the given context]. In a structure description, only the structure of the relation is indicated, i.e., the totality of its formal properties. (A more precise definition of structure will be given later.)" (Emphasis by Carnap)

Notice that he connects the phrase "the structure of the relation" and "the totality of its formal properties" by "i.e." (in German [d. h.]). It seems to me now (after reading the II-A fully) that this "d.h." carries some convoluted (and problematic) dialectics behind Carnap's conception of the "structure of a relation." The parenthesized remark following the "d.h." sentence seems to indicate this dense dialectics. On his behalf, I may break it down thus: by this "d.h.," he (probably) actually means to say that the (complete) "structure of a relation" ought to be identifiable with the totality of its "formal properties" without loss of specificity, if we limit our demand of specificity to that of specificity-up-to-"scientific objectivity." (What I mean by this will be clear through the rest of the present reading memo.)

2. By "formal properties of a relation," he means:

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"those that can be formulated without reference to the meaning [inhaltlicher Sinn] of the relation and the type of objects between which it holds. They are the subject of the theory of relations." (p. 21)

And, after this abstract description, Carnap gives examples of such "formal properties of a relation" as symmetry, asymmetry, reflexivity, irreflexivity, transitivity, intransitivity, connectedness, etc.

These examples (which I assume come to from the Russelean theory of relations, though I haven't read anything by him on this theory) can be said to be Carnap's first elaboration of his initial abstract description of his notion of "formal properties of a relation." (He soon gives what amounts to his second elaboration of it, by way of the notion of an arrow diagram.) I think that this first elaboration is another indication that Carnap's conception of "formal properties of a relation" (and, so, his conception of the "structure of a relation" as well) is fundamentally epistemologically at odds with Hilbert's concept of implicit definitions (understood in the intensionalist sense). (The gap is already indirectly suggested by the fact that he conceives of a "relation" set-theoretically, such that an n-ary relation is a subset of the Cartesian product of n sets.) The key here is the pragmatics of our use of the equality symbol, =. In a logical, or "logistical" definition of any of the relation-theoretical "formal properties" (e.g., reflexivity, symmetry, transitivity, connectedness), our use of this symbol is ontologically committed/committing.17 By contrast, in implicitly defining a system of theoretical concepts by way of making/taking an axiom-setting ceremony (so to speak, borrowing Kripke's phrase of "naming ceremony"), our use of this symbol is entirely ontologically free-of-charge.18

17 I take all of these "formal properties" require a use of the equality symbol =. It's just that the critical, ontologically committing/committed use of this symbol that is essentially involved in our linguistic definition of such "properties" is often rendered redundant or anyhow unnecessary by the pragmatics of our use of the quantifiers and bound-variables. So, for instance, reflexivity is actually to be defined thus: R is reflexive on D just in case for all x , y∈D, if x= y, then R ( x , y ). Similarly, symmetry: R is symmetric on D just in case for all x , y∈D, even if x≠ y, if R ( x , y ), then R ( y , x ). Transitivity: R is transitive on D just in case for all x , y , z∈D even if x≠ y and y ≠ z, if R ( x , y ) and R ( y , z ), then R ( x , z ).18 To be more precise about my view on this topic, I must add that, when

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3. To illustrate the idea of the "structure of a relation" further, he introduces the notion of an arrow diagram, and with it, that of "isomorphism" (or "structural equivalence") between two "relations" of the same basic form (i.e., between two subsets of "isomorphic" Cartesian products).19

The latter notion (the "isomorphism" of "relations") is an anticipation of what he shortly (in the next Section) calls the "complete structure" of, or a "complete structure description" of, a "relation" (i.e., a subset of a Cartesian product). Given Carnap's identification (by the "d.h.") of the notion of "the structure of a relation" with that of "the totality of its formal properties," this arrow-diagram illustration amounts to his second elaboration of his abstract description of the notion of "formal properties of a relation," quoted above.

4. To be fair (or, to avoid being inadvertently unfair) to Carnap, let me take a note that he mentions something about "congruence" between two "isomorphic relations" and about "topological equivalence" between two arrow diagrams (or "relations"?). I could understand neither.

As for the "topological equivalence," I suppose that the notion of an arrow diagram all along abstracts from all "topologically irrelevant" specs like "distance between two points" and "angle between two arrows." If so, can there be any difference between "isomorphism" ("structural equivalence") and the "topological equivalence"?

we are making and taking some fictionally or hypothetically direct-referential statements under the scope (or reign, as it were) of a (categorical or exceptive) quantification, i.e., within a larger deductive-inferential context (of, e.g., making/taking an axiom-setting ceremony), our use of the symbol = there (in that embedded context) bears fictional or hypothetical ontological charge. If anyone is interested in this topic, I have written fragmentary essays on this topic in my blog, e.g., this, this, and this.19 Notice that, if his notion of the "isomorphism" of two "relations" requires the coincidence not only as to which pairs (or n-tuples) bear the "relation" in question but also as to which do not bear it, then, the question of such "isomorphism" does not even arise between "relations" of different basic forms, i.e., between a subset of a Cartesian product P and a subset of a Cartesian product Q where P and Q are not "isomorphic" (in the sense of being the products of the same number of component sets, say, P1 ,P2⋯Pn and Q1 ,Q2⋯Q n, where for each i, (1≤i ≤n), Pi and Qi are equinumerous).

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(Sec. 12) --- Block 11. Carnap here in effect says that an arrow diagram gives a "complete

structure description" of a "relation" (i.e., a subset of a Cartesian product).

2. He then clarifies what he means by the "completeness" of a "structure description" of a "relation" by appealing to the notions of "isomorphism" and "formal properties." He says that:

"If two relations have the same structure [i.e., are "isomorphic" or "structurally equivalent"], then they are equivalent in all formal properties. Thus, all formal properties of a relation are determined if its structure is [completely] described."

These remarks clearly tell that Carnap's concepts of "isomorphism" and the "completeness" of a "structure description" assume that for these concepts, not only the positive information (as to which n-tuples of the assumed Cartesian product belong to the "relation" in question) but also the negative information (as to which n-tuples do not) matter.

3. He then says something that expresses an assumption behind his conceptions of "formal properties" and a "complete structure description" of a "relation," which I think is critical for the rationale of his Aufbau project. He says:

"On the other hand, there is no general rule as to which formal properties suffice to determine the [complete] structure of a relation; it is the task of the theory of relations to investigate this question in detail."

Given the contrasting connective ("On the other hand"),20 one naturally expects that the connective would be followed by a remark that makes a contrast to the previous statement ("all formal properties of a relation are determined if its structure is [completely] described"), such as a remark rejecting its converse, i.e., to the effect of saying that:

The complete structure of a relation may not be determined even by all of its formal properties.

20 Actually, I later realized (after I wrote almost all of the present memo) that the original German text did not contain any phrase that corresponds to this English phrase, "On the other hand." But, given the context, I do think that Carnap draws a contrast here, which justifies the translator's inserting this contrasting phrase here. So, I leave my text here as it was before I realized this fact.

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Carnap's actual remark does not exactly sound to say this. But, I think that it sort of says this, with a distortion of impression due to his critical assumption that:

Although there is no a priori guarantee that all formal properties of a relation determine the complete structure of the relation, they ought to do so.

Because of this assumption, while the "task of the theory of relations" strictly includes the investigation of whether all formal properties of a relation (invariably) determine the complete structure of the relation, Carnap omits this fundamental question from his statement of its "task," and immediately mentions the next "task" that awaits right after establishing the (expected) affirmative answer to the first fundamental question. In other words, he mentions the more specific "task," presupposing the affirmative answer to the first question.

4. Carnap assumes the affirmative answer to the first question, i.e., assumes the truth of the aforementioned critical assumption, because it must be true for his structuralist thesis (mentioned above) to be true while the "structural properties" dealt with by science obviously pertain to infinite "relations" (i.e., subsets of Cartesian products of which some componential set is infinite). He says:

"It must be possible to give an exact definition of the concept of structure [of a relation] and to indicate the structure of a given relation without the aid of [arrow] diagrams" (emphasis mine)

because"an arrow diagram is … possible only if the number of members [of each componential set of the Cartesian product assumed by the relation] is finite."

His "must" (the italicized, i.e., emphasized word in the first quote above) can come from nowhere other than his structuralist thesis (and the obvious infinity of the domains that concern science), as explained above. A natural interpretive question here is where his assumption, or conviction, of his structuralist thesis comes from. (I will give my answer to this question in the rest of this "memo." But, briefly, I think it comes from his "problem space," i.e., from his dual problems of the empiricism-positivism incompatibility and the unity of science.)

It's nice that Carnap is aware of what it takes for his structuralist thesis to be true. But it's sad that he is too optimistic about this possibility, and too confident in claiming, right after remarking the necessity (for his thesis to be true) of

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this possibility's truth (by the phrase to the effect of "It must be possible …"), that

"But, in this context, it is quite permissible to use the arrow diagram for the purpose of illustration, since … it exhibits all the fundamental aspects of the general concept of structure."

Frankly, in my opinion (as an intensionalist of theoretical science), Carnap was deceived precisely by this arrow-diagram image of the concept of a "relation" (and its derivative concept, the relation-theoretic concept of a "formal property" of such a "relation"), despite the otherwise promising idea of his structural thesis.

5. Carnap admits that his structuralist thesis amounts to a formalist thesis, to the effect that:

"scientific statements speak only of forms, independently of [their materials, i.e.,] what their elements and their relations are."

Again, I perfectly agree to this formalist thesis, provided that (i) the thesis is held for scientific theoretical statements per se and (ii) the concept of "form" is intensionally (inferentialist-structurally) understood.

6. He rhetorically grants that such a thesis does sound paradoxical, if held for statements of empirical science, as opposed to statements of classical mathematics. (In his view, Russell and Whitehead showed that the same formalist thesis held true for statements of classical mathematics. And, he finds nothing paradoxical in this result.) His granting is rhetorical in that he presents this paradox as what he has already solved (and what he will soon show how to solve, in particular, in Sec. 14).

At first, the fact that he perceives Russell and Whitehead's work in this formalist/structuralist line puzzled me. So did the fact that Carnap does not find the formalist thesis being held for classical mathematics any paradoxical. Based on some secondary literature, I assumed that a core of their work was Peano arithmetic, which included a conspicuous definite reference to the initial element of the (number) sequence. Based on this assumption, I thought that Carnap's structuralist/formalist thesis, if it was to be applied to Peano arithmetic, must have demanded that this direct reference be replaced by some "purely structural definite description." It took me a while to digest what it means in this regard that his structuralism/formalism accepts a finite arrow diagram as a "purely structural description" of a "relation." This attitude

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would naturally render Peano arithmetic a "purely structural description" of a "relation" (or a system of "relations," perhaps), despite its involvement of the direct reference, despite the strange fact that all of models are isomorphic (in the set-theoretical sense), not only homomorphic. In other words, a description like "The element which is the successor of no element" would perfectly qualify as a "purely structural definite description" of the first element. For Carnap, the very notion of "structure" must have come from what Russell and Whitehead did for classical mathematics, indeed, from the theory of relations. (He explicitly says in Sec. 3 that the Aufbau project is "an attempt to apply the theory of relations to the task of analyzing reality.") And, so, there is no reason for, or point in, asking whether what their "rational reconstruction" of classical mathematical knowledge qualify as purely formal or structural. (I hope that my relating this initial puzzlement helps some readers to grasp the fundamental difference between their understanding of the concept of the "formal" or "structural" and my intensionalist (inferentialist-structurlist) understanding of this concept.)

From my point of view, as an intensionalist of axiomatic theories, Peano arithmetic is not a pure deduction system ----- at least it does not seem so prima facie. In other words, concepts of Peano arithmetic do not quite seem to me to be "implicitly defined" in Hilbert's sense. This is not only because of its direct reference to the initial element of the sequence but also because of the so-called "successor" function. It seems to me that their involvement in Peano arithmetic makes the pragmatics of both the equality symbol = and quantification there ontologically charged sort. However, my opinion on this may change if Peano arithmetic is shown to have an alternative axiomatic formulation in which no direct-referential symbol and no "successor" function occurs. But, honestly, I'm skeptical. In this regard, it seems suggestive that Peano arithmetic is categorical (in the sense that all of its models have the same cardinality of ℵ 0). I have a hunch that categoricity in this sense of an "axiomatic" theory is a sign that it's not a pure deduction system, formulated in the strictest abstinence from extensional or denotational semantics and in total freedom of ontological charge. It seems to me that the purely deductive concept of a "form" or a "structure" must be free of inherent cardinality. (But I cannot explain where my

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"must" come from briefly. Please allow me skip this in t his memo.) Anyway, for now, I just remain a skeptic of the possibility of the said reformulation.

(Sec. 13) --- Block 21. Carnap identifies two ways of "indicating the meaning [or

denotation] (Bedeutung) of object-name in a scientific statement" (emphasis mine): by ostensive definition and by definite description.

Here he nonchalantly accepts that such "indications of denotations" occur in scientific statements. This is the clearest evidence that his conception of scientific statements is not at all "metaphysically abstinent," after all. And, although it's not explicitly stated, this is a fact which makes one side of his problem of the incompatibility of empiricism (that science tells us something about the external world) and positivism (that sense says nothing about it).

2. He makes a good point about definite description. He says that "a definite description indicates the relation of the object in question to other objects" (emphasis mine) ----- which I take to mean that it achieves the "unequivocal circumscription" (i.e., definite reference) by appealing to some previously established definite reference ----- so that (i) the "problem of the determination of objects is only pushed back one more step with each definite description" and (ii) the problem "can be finally solved only through ostensive definitions" (all quotes from p. 24).

Here, a version of (Kripke's later notion of) "causal-historical chain of reference" is anticipated. This is fascinating. I do think this is generally how speech act of definite reference really works, in our daily thing" talks.

3. Carnap then foretells that he will argue for two things (both of which I later realize to be critical for his "structuralist" solution to his dual problems):

(A) "within any [single] object domain, a unique system of definite descriptions is in principle possible, even without the aid of ostensive definitions," and (B) "any intersubjective, rational science presupposes [the] possibility [of devising a unique system of definite descriptions without help of ostensive definition, for the totality of all objects of [all domains of empirical] knowledge]" (emphases mine).

As I hinted above (and will explain later), his argument for (A) will prove to rely on a questionable use of the verification principle. And,

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worse, his argument for of (B) will prove to be nothing more than a roundabout restatement of his "problem space."

(Sec. 14) --- Block 2Carnap offers an initial step toward the promised argument for (A) above. The initial step is given in an inexact form of an example, of "railroad diagram." I see at least four problems in this initial step.

1. The "object domain" of the example is the discrete, countable (or denumerable) one. Any illustration of the said "possibility" [of devising a unique system of definite descriptions without help of ostensive definition], based on this sort of "concrete" example, can be hardly expected to be applicable to scientific-theoretical conceptual domains, which are mostly nondenumerable.

2. He includes in his "structural inspection" (which presumably avoids any recourse to ostensive definition) the act of counting numbers (of dots between two intersections, or of lines meeting at an intersection). But, in order to count things, one has to ostensively identify the first object first, the second object second, and so on.

Notice that, at each time one moves on to the ostensive identification of the next object, one has to recourse to some increasingly presupposing act (linguistic or conscious-mental act) of reference-maintenance, i.e., of keeping track of the episodic memory of (i) which object was counted first, (ii) which one was counted secondly (so, as having been distinguished from the first one previously), (iii) which one was counted thirdly (so, as having been distinguished from both of the second and the first ones, previously, where the second one is recalled as having been distinguished from the first one, even more previously), (iv) which one was counted fourthly (so, as having been distinguished from all of the third, second, and first ones, previously, where the third one is recalled as having been distinguished from both the second and the first ones, even more previously, where the second one is recalled as having been distinguished from the first one, even yet further previouly) … and so on and so forth. After all, the act of counting involves the inherently metapragmaitc notion of next-ness relation, which is not a relational-structural notion from the point of view of the intenionalism of axiomatic theory.

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3. He seems to be totally oblivious of what may be called "symmetrical" data-situations. For a simplest example, suppose that the "railroad diagram" consists of one circular line, with no intersection. In that case, there are as many distinct ways of extension-assignment as there are dots (or "stations") ----- or so we think, most naturally. But, according to Carnap, they are "objectively" indistinguishable, and, hence, "objectively" there is only one way of extension-assignment here.

"Symmetry" (in any sense) may be surely hard to encounter in our daily perceptual experiences of particular or singular entities. But, "symmetry," if the notion is broadly taken, seems to be much commoner in theoretical exact sciences.

4. Finally, his claim that "within any object domain, a unique system of definite descriptions is in principle possible, even without the aid of ostensive definitions" is finally defended, at the most critical point, only by an appeal to a version of the verification principle:

"[Two locations for which we find no difference even after exhausting all available scientific relations] may be [still] subjectively different: I could be in one of these locations, but not in the other. But, this would not amount to an objective difference, since there would be in the other place a man just like myself who says, as I do: I'm here and not the other." (Emphases mine)

It is as if Carnap thinks that this "pragmatic" principle (in a poorly understood sense of "pragmatism," I dare to say) can be a good reason to accept Leibniz's principle of the identity of indiscernibles, in total rejection of the "objective differences" among only "subjectively" distinguishable "extension-assignments" (assuming that they can be called extension-assignments) to the "structure" of a "relation," such as those distinguishable only by means of situating oneself within the data-situation (thereby creating a "perspective" to it).

Needless to say, if we accept this strange application of the verification principle, then, that means that we deny the "objectivity" of the very notion of "symmetry." Moreover, it also means that we deny the "objectivity" of the fact that we do count things, i.e., we do keep track of episodic memory of increasingly presuppositional ostnsions (as outlined above). This is because, to keep track of such episodic memory is to keep track of the dynamic history of a sheer "subjective" difference between two otherwise indistinguishable group of

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objects: between objects that have been already counted and those that are as yet to count.

(Sec. 15) --- Block 21. Carnaps completes his argument for (A), by adding:

"Where such a [system of] definite description[s] is not unequivocally possible, the object domain must be enlarged or one must have recourse to other relations."

Presumably, this is so as to enrich the resources available for a system of definite descriptions for that domain. He apparently thinks that this kind of "resource-enrichment" can be performed indefinitely, which in principle assures that a system which purely structurally definite-decriptively specify all the objects of the domain can be eventually achieved.

2. But, he repeats the problematic use of the verification principle again:

"If all relations available to science have been used, and no difference between two given objects of an object domain has been discovered, then, as far as science is concerned, these objects are completely alike, even if they appear subjectively different. ([If two objects are finally thus scientifically indistinguishable], the two objects are not only to be envisaged as alike, but as identical in the strictest sense….)"

This completes his argument for (A).3. Carnap explicitly (if parenthetically) admits the apparent

paradoxicality of this conclusion, but leaves the question untouched. The parenthesized remarks is continued as:

"(… This is not the place to give a justification for this apparently paradoxical assertion.)"

4. Carnap then indicates some connection between his "purely structural definite descriptions" and Hilbert's implicit definitions.

"The purely structural definite descriptions … are closely related to the implicit definitions which Hilbert has used for his axiomatic geometry."

Uebel seems to think similarly, as mentioned at the outset of the present reading memo. To repeat it, he says that:

"Carnap's use of structural descriptions may be viewed as a critical development [of] Hilbert's concept of implicit definitions" (p. 32),

probably in part based on Carnap's own remark. But, I now disagree with both of them. I think that there is an epistemologically/ontologically fundamental difference between the pragmatics of Carnap's "structural descriptions" and that of

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Hilbert's implicit definitions, partly based on my (aforementioned) analysis of the different pragmatics of our use of the equality symbol, =, in them.

However, Uebel's interpretation is quite understandable not only because of Carnap's explicit remark, but also because of the genuine intricacy of the pragmatics of the equality = and quantification, involved in them.21

5. By the way, I'm puzzled by Carnap's strange claim about the notion of consistency (of an axiom-system):

It is "a formal-logical property which can be ascertained through purely logical considerations" (emphasis mine).

As far as I know, there are only two ways by which we can "ascertain" the consistency of an axiom-system. One is by way of demonstrating the existence of a model, and the other is by way of "formalizing" the axiom-system into a recursively defined syntactic sign-system known as a "formal (deduction) system" and by proving, as for the resulting "formal system," that it is impossible to construct a pair of "theorems" in the form "P" and "not-P." Neither method seems to me to remain within the limit of "purely logical consideration."

(Sec. 16) --- Block 31. Carnap sums up an implication of the possibility of (A) for someone

who wants to prove the unity of sciences:"… [E]ach object name which appears in a scientific statement can in principle … be replaced by a structural definite description of the object, together with an indication of the object domain to which the description refers" (emphasis mine).

The problem here (for the unificationist) is that, the actualization of the possibility of (A) only amounts to a sort of domain-restricted elimination of ostensive definitions. Seen from "outside" of the domain, the "purely structural" specification of an object in it may still require a background ostensive specification of the very domain, unless somehow this domain-specification is rendered unnecessary.

21 Actually, I may well be wrong, at least in detail, about the pragmatic difference between "formal definitions/descriptions of relations" (in Carnap's sense) and implicit definitions of axiomatic-theoretical terms (in Hilbert's sense), which I discussed in the aforementioned analysis. I'm still in the middle my research. I must study the pragmatics of our use of the "equality" symbol = in the so-called "theory of relations" more carefully, in comparison to the pragmatics our use of it in abstract-algebraic axiomatics.

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2. Carnap reminds readers of the purpose (or the intended effect) of actually making a "constructional system" for all the scientific conceptual domains: a demonstration of the unity of sciences. By this reminder, he indicates that the problematic need of the domain-specification will be rendered unnecessary, for the project of the Aufbau.

This argument still hides a problem. Even for the Aufbau project, the need of the domain-specification is not entirely eliminated because Carnap's "constructional system" only reduces many domains to one, not to zero. This single domain, which is supposed to be that of the sense-data, needs to be specified by the most problematic kind of ostensive definition. That this ostensive domain-specification is "given" to all of us, is a part of the Machean positivistic conception of sense perception, as the (notorious) "given." So, for Macheans like Carnap, the problematic nature of being left with this domain might be hard to see….

3. Carnap finally gives the promised argument for (B) above, that science presupposes the possibility of a "purely structural constructional system" (so to speak) for all the sciences. The argument goes as follows:

i. "[W]hatever does not belong to the structure [or form] but to the material (i.e., anything that can be pointed out in a concrete ostensive definition) is, in the final analysis, subjective."

ii. "[S]cience wants to speak about what is objective." In other words, Science presupposes that it speaks only about what is objective.

iii. Science presupposes that it speaks only about what belongs to the structure of form.

iv. Even if the "object-domain" of each specific science is turned into a system of "purely structural definite descriptions," if the specification of its "object-domain" is left without the "desubjectivization" (i.e., "structuralization" or "formalization"), the presupposition of science is not finally satisfied. (This follows from i. above.)

v. Science presupposes that the need of the domain-specification for each specific science can be eliminated.

vi. The only way to do this is by way of making a "constructional system," i.e., by way of "constructing" all scientific concepts from the most basic conceptual domain.

As mentioned above, this argument misses the fact that this method leaves one domain to the most problematic sort of ostensive

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definition.

Final comment: Carnap's attitude to scientific statements i.e., what he intends to rationally reconstruct, exhibits this ambivalence about "metaphysical abstinence." On the one hand, he may be said in a sense "metaphysically abstinent," in that he sees them to be (deep down) purely structural statements, in which no ostensive definition really occurs. But, on the other hand, he does see them intensional or denotational statements, containing (at least in its surface form) terms that fix their denotations by ostensive definitions. In this regard, his attitude is not at all "metaphysically abstinent." Problematically, he takes these incompatible attitudes to the same things, scientific statements. (Recall that, in my case, I take scientific theoretical statements per se as ontologically free-of-charge, and take their interpretations, or assigned denotations, to be ontologically charged, in the sense that making/taking of them make us ontologically committing and committed.) Without realizing his inconsistency, he tries to convince readers (as well as himself, I suppose) of the (self-contradictory) thesis that an ostensively defined reference (to what is "in the final analysis, subjective") can be replaced by a "purely structural/formal" reference (to "what is objective"). And, this effort ends up using the verification principle in the aforementioned problematic way.

In my diagnosis, his inability to see this inconsistency comes from the general inability, of his "time," to understand the pragmatics of (i) the deductive discourses (or deliberations), which are ontologically free-of-charge (except, in case of deductions in theoretical physics, for the commitment to the "existence" in some sense of numbers), and (ii) of the empirical theory-testing/applying (i.e., the collective language-entry/exist), through which we commit ourselves to the existence of instances of the theoretically defined concepts, as well as to the norms as to how we are to expect those instances to interact one another (in virtue of being the instances of those theoretical concepts).

References

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Quine, 1969, "Epistemology naturalized," in Ontological Relativity and Other Essays, New York: Columbia University Press, pp. 69-90.

Silverstein, M., 1987, "Cognitive implications of a referential hierarchy," in M. Hickmann (Ed.), Social and Functional Approaches to Language and Thought, Orlando: Academic Press, pp. 125-64.

Uebel, T.E., 1992, Overcoming Logical Positivism from Within: The Emergence of Neurath's Naturalism in the Vienna Circle's Protocol Sentence Debate, Amsterdam: Editions Rondopi.

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