Husserl’s Critique of ‘Extensional’ Logic: ‘A Logic That Does Not Understand Itself’
This article first appeared in Idealistic Studies, Vol. IX, #2, May 1979. Numbers within "<>'s" indicate page numbers in that volume.
In Part II of Husserl's "great last work," as the Crisis is sometimes called, we find two passages in which he comments upon what he took to be an important and utter failure on the part of "die modernen Logistiker"--or, as Carr well translates it, "modern mathematical logicians." At the end of subsection 36 he says:
"The supposedly completely self-sufficient logic which modern mathematical logicians think they are able to develop, even calling it a truly scientific philosophy, namely, as the universal, a priori, fundamental science for all objective sciences, is nothing but naivete. Its self-evidence lacks scientific grounding in the universal life-world a priori, which it always presupposes in the form of things taken for granted, which are never scientifically, universally formulated, never put in the general form proper to a science of essence. Only when this radical, fundamental science exists can such a logic itself become a science. Before this it hangs in mid-air, without support, and is, as it has been up to now, so very naive that it is not even aware of the task which attaches to every objective logic, every a priori science in the usual sense, namely, that of discovering how this logic itself is to be grounded, hence no longer 'logically,' but by being traced back to the universal prelogical a priori through which everything logical, the total edifice of objective theory in all its methodological forms, demonstrates its legitimate sense and from which, then, all logic itself must receive its norms."
And later in the Crisis Husserl comments upon how the knowledge gained by phenomenological reflection can protect the accomplishments of ordinary or "objective" science from misunderstandings. He remarks that such misunderstandings "...are to be observed in abundance, for example, in the influence of naturalistic epistemology and in the idolization of a logic that does not understand itself." (italics added)
These are strong words, But I wish to point out that this theme of a lack <144> of self-understanding--and even of self-deception--on the part of logic and logicians is no mere afterthought on the part of the later Husserl. Rather, it is one dealt with in detail in the early writings of Husserl. In his review of Volume I of Schröder's Vorlesungen Ueber Die Algebra Der Logik, which appeared in the Göttingische Gelehrete Anzeigen for 1891, Husserl refers to Schröder's definition of deductive logic by means of the property of Folgerichtigkeit. He quotes Schröder's remark that "...deductive...logic concerns itself with the laws of valid thinking"; and he concludes that "...the presentation of such a logic of deduction is the goal which the author [Schröder] posits for himself" (GGA, p. 244). But then Husserl quickly adds: "Or 'intends to posit', I should more precisely say; for one can hardly deceive himself more about his true goals than the author here does. And I will go into the details of the evidence of this deception, since it is characteristic of the whole of extensional logic" (loc. cit.).
Related to the self-deception alleged of extensional logic about its general goals in developing a calculus is its related confusion about the relationship between a calculus and a language--and especially the confusion involved in its insistence that the calculus is a better language than the natural languages. This confusion emerged in Schröder's book with his theory of names. In the development of the calculus he thought it necessary "...to discover...the most rational system of designation for the naming of all objects and for the expression of all processes of thought" (italics added). Indeed he sought "...to vindicate that system as a necessary one." After quoting these words, Husserl remarks that "Schröder "...has once again fundamentally deceived himself about his own goals" (GGA, p. 259). The function of a calculus, and the symbols within it, simply is essentially different from the function of a language and the symbols within it--as Wittgenstein was to rediscover some four or five decades later. Husserl states (with appropriate elaborations): "It is above all certain that the logical calculus is only a calculus, and absolutely is not a language" (loc. cit.).
It is this theme of a failure on the part of logicians to understand exactly what it is that they do and do not do that I wish to develop from within some of Husserl's early writings. And I shall extend this theme, in my concluding remarks, to some contemporary works in logic. I have chosen to restrict my remarks here to Husserl's early writings because it is in these writings, if I am correct, that Husserl best lays out in detail the grounds of the need for a type of thinking about, and inquiry into, logic to which most formal (and especially "mathematical") logicians seem totally oblivious. The positive theory or philosophy of logic which Husserl develops in his <145> later works, such as Logical Investigations, Formal and Transcendental Logic, and Experience and Judgment, simply goes begging for hearers because there is no felt need for it. Especially among Anglo-Saxon logicians, it is looked upon as a subvariety of European philosophical florae which is astonishing and otiose. Logic, and that currently most interesting part of it called "formal semantics,' is done upon the assumption of clarity about certain fundamental questions having to do with the basic nature of the subject matter and the mode of logical studies. It is this assumption which Husserl rejects, and rejects because of confusions which he shows to exist in the writings of those engaged in logical studies.1
Although Husserl's reasons for rejecting the assumed clarity appear most forcibly in his works published from 1891-1900, my hope is to show the profound relevance of his negative critique of the "extensionalist" logic2 of that day to the logical studies of our own time. Perhaps this may have the effect of causing his constructive remarks in the philosophy of logic to be read, and to be read with the thought that they well might contain elements (at least) of a solution to problems as yet unresolved--and as yet unsuspected in some quarters--in the theory of logic.
It will aid our exposition of Husserl's critique of the "extensional" logic if we first say what, a this point in his career, he took a logic to be. He is, it seems to me, fairly clear about this matter from 1887 on, although his view certainly is immensely deepened and filled out in detail as his research progresses through the years. Husserl holds a logic to be a practical discipline, a theory about how one does something. The question which we must answer is: What is the particular "doing" here in question?
In the "Introduction" to the 1887 essay, "On the Concept of Number: Psychological Analyses," Husserl speaks of modern logic coming, "...in contrast to the older logic, to understand its true task to be that of a practical discipline (that of a Kunstlehre of judging correctly), and...to seek, as one of its principal goals, a general theory of the methods of science."3 The context of this statement makes it clear, I believe, that the view of logic here ascribed to "modern" logic is in fact Husserl's own. The same view of logic--though no doubt then held with a more profound grasp of it ramifications--is restated, elaborated, and defended in Logical Investigations (1900), Volume I, chapters two and three. There we find logic referred to by the Fichtean/Bolzanian term "Wissenschaftslehre"--a term later explicitly used by Carnap, and then replaced by him with the term <146>"Wissenschaftslogik" as being "more exact."4 In using this term Husserl answers our question above: The making of knowledge (Wissenschaft) is the Kunst or activity--the "doing"--of which logic is the theory. Logic concerns itself with a certain "natural"5 and familiar type of coming-to-know: with the kind of progressive and interconnected thought and knowing which is most fully exemplified in scientific inquiry. Its task is to understand, to appraise, and to guide such epistemic progressions.
With regard to this, it is certain that most "extensionalist" logicians, from Schröder to Carnap, would agree; although there is much confusion and disagreement as to the precise details of exactly what, then, is being done by logic and how it is to be done. In the "Foreword" of his Vorlesungen Schröder holds the algebra of logic to be alone "...capable of giving the laws of valid thought the most rigorous, concise, and comprehensive formulation." And on page 1 of that book he states that "Logic...concerns itself with all of those rules the following of which furthers knowledge of the truth." Again on page 64, as already quoted above, Schröder speaks of the logical task of finding a system of names "for the expression of all processes of thought" (italics added in both quotations). And, indeed, no matter how "formalistic" the logician may be, it is always the case that he expects the results of his work to apply to actual thought, and especially to scientific thought. This is no less true if he also has a view about the nature of his work which would make it (really or apparently) impossible or problematic for his results to so apply--which, as we shall see, is largely true of the "extensionalist" logic criticized by Husserl.
Now the general form of Husserl's critique can be stated in quite simple terms. There is a certain natural process of thought in which coming to know-on-the-basis-of-other-truths-known consists. A logic, as we have just seen, must be a theory of that process, from its simplest to its most complex forms. The extensionalist "logic," as we shall see below, is not a theory of that process; and yet it takes itself to be so. Hence, it is caught in "self-deception.""...Man kann sich kaum mehr über die eigenen Ziele täuschen" (GGA, p 244). We have, precisely, "a logic which does not understand itself."
Taking for granted, then, that a logic must somehow be a theory of the process of coming to know, or of inference,6 we turn to the task of exhibiting Husserl's reasons for believing that an "extensionalist" logic could not in fact be such a theory. I shall develop what I take to be his two major reasons for believing this, and shall do so by explaining points made in his two 1891 papers: his review of Schröder already referred to above and his "The Deductive Calculus and the Logic of Contents"7 (hereafter referred to <147> as VWP). I shall quote from these papers at lengths greater than would normally be justified, for they are little known and not easily accessible. The "extensionalist logic" and the "calculus" which will be referred to in the following is always, in the first instance, the system advanced by Schröder in his Vorlesungen, which Husserl called "the most superior extensional calculus of our time" (VWP, p. 170).
I. It is in the nature of a calculus or "algebra"--"extensionalist" or not--that it cannot be a logic, cannot give the laws of epistemic progression or valid thought.
(A) For what is a calculus?
"The specific function of the calculus consists in its being a method for the symbolic derivation of conclusions within a certain sphere of knowledge. Thus it is an art which, through an appropriate symbolizing of concepts, substitutes a calculational process--i.e., a rule-governed process of transposing and replacing signs with signs--for the process of actual inferring; and then, by means of the correlation of symbols and concepts established at the outset, it derives the desired judgment from the resultant end-formulae" (GGA , p. 259).
Thus, it is clear that calculation and deduction, which is perhaps the most essential feature involved in natural epistemic progression, are not only distinguishable, they are also separable. Husserl repeatedly emphasizes the fact that calculation and deduction are eidetically different processes. For example,
"But is calculation deduction? Not at all. Calculation is a blind procedure with symbols, following mechanically reiterative rules for the transposition and transformation of the signs in the respective algorithm. Also, the "setting up of an equivalent" [within the algorithm] of a problem is no deduction, just as little as is the final move in a deduction proceeding symbolically, viz., the interpretation of the resultant end-formula. The symbolic procedure replaces and thereby spares us many pure deductions, but is itself no deduction (GGA, p. 246)... Calculation is not deduction. Rather, it is a superficial (äusserliches) surrogate of deduction." (GGA, p. 247)
The justification of these remarks is easily seen if one will reflectively carry out a simple derivation within the logic of propositions, such as the following:
1. (D $ E) e -F
2. F v (G $ H)
3. D / E / w D e G
4. (D e E) $ (E e D)
5. D e E
6. D e (D $ E)
7. D e -F
8. (F v G) $ (F v H)
9. F v G
10. --F v G
11. -F e G
12. D e G
3, Mat. Equivalence
6, 1, Hyp. Sylg.
9, Doub. Neg.
10, Mat. Implication
7, 11, Hyp. Sylg.
In the passage from one line to the next no inference occurs at all. Possibly an inference does occur at some point in cases where the premisses symbolized are statements which one in fact believes, and where one also believes that the calculational rules employed run parallel to the logical implications of premisses to which they are applied. But that is not necessary to a calculation, nor is calculation necessary for insightful inference to occur. There is, perhaps, no need to go further into the descriptive details of the two types of processes at this point.
(B) But not only is calculation no deduction, the logical calculus is not a theory or account of deduction-not even of formal deduction. The "laws" of the calculus are not, nor do they express, the "laws" of valid thought. "Far removed from being a theory of pure deduction, it [the calculus] is rather a device for making such deduction superfluous" (GGA, p. 247).
"The logical calculus is, thus, a calculus of pure deduction, but not its logic.... Accordingly, the "laws" of the calculus are nothing less than they are the norms of "valid thinking" or, more precisely, of inference conforming to pure implications. Those laws are not rules to which everyone does and must conform, so far as one infers correctly. Rather, they are only rules which one can follow on any occasion, with full confidence of a correct result. In the light of this, they may well be suited for testing the result of any pure deduction; but whether the deduction itself was a correct one, that is something which they cannot decide. The mere multiplicity of algorithmic methods, the materially and formally quite different ways taken in solving the same problem--cf. here only the methods of Boole, Jevons, and Schröder, among others--teaches us that in the algorithmic formulae we in no wise find mirrored the canon for the deductive activities involved in knowing. Let the praxis of deducing draw ever so much use from such methods--and it is certainly very dubious whether it does--the logical theory of deduction remains where it was. It is, indeed, not even touched upon." (GGA, pp. 247-48)
(C) But, further, the calculus is not, nor does it provide, its own logic. In working the calculus, a certain progression of thoughts and experiences occurs, and this progression includes the actual operation of applying the laws to the appropriate symbols, as well as the reading of deductive problems into the symbols and reading them back out again at the end of the calculation. But the calculus does not itself provide a theory of this calculative process, much less a theory of its relationship to epistemic progression in general.
"Certainly here, as in the case of any calculatory discipline, those difficult questions about the essence and logical justification of the calculative method are unavoidable. All the more so, as it is upon the answering of these questions that the epistemic status of results from such disciplines is first and foremost dependent. If the "algebra of logic" were, instead of being a dexterous technique, at least a theoretically grounded, special method in logic, then it would have to give us some clarification of these questions. But the logic of this algebraic calculus does not fall within the mental horizon of the investigator who takes the calculus to just be deductive logic: especially since, in fact, the mental operations upon which the calculus is based do not themselves belong within that domain of pure deduction which it exclusively governs (GGA, p. 247).
It is, no doubt, this simple unclarity about itself, about the essence of its own procedure and of its relations to the other activities involved in epistemic progression, which opens the door to that "self-deception" of extensional logic to which Husserl alludes. He is, even at this early stage, very much the phenomenologist, in the basic, methodological sense of the term. He attempts to see what is the case in the use of a calculus, and to contrast this with what natural epistemic progression may be seen to be. And in all of this he regards himself, not as an enemy of the logical calculus, but as its <150> friend, who would show its true essence and use by correctly relating it to "the facts themselves." He warns that one must avoid "taking offence at the facts themselves (an der Sache selbst)9 in virtue of offence taken at the author's [Schröder's] inexact mode of speaking" (GGA, p. 270). For this might lead to a simple dismissal of the calculus, when, if rightly understood, it could be of great logical and philosophical interest. Indeed, he thinks that such dismissal has actually happened:
"In fact, the logic of the logical calculus is still very much in a bad way. Among its representatives there is not the slightest clarity either about the boundaries of this discipline, or about its relationship to deductive logic, on the one hand, or to arithmetic on the other. The logical considerations upon which the techniques are built are mostly of a kind that do not stand up to the most cursory examination. And now it is just the calculus which steps forward with the grand claim of being a wholly reformed logic, which is--for the first time--"exact." Hence, it is quite understandable that precisely the more scientific logicians tend, for the most part, to reject it (VWP, p. 169n).
Returning, now, to the conception of logic as the theory of epistemic progression, we may sum up this first major line of Husserl's criticism of "extensional" logic as follows: extensional logic presents a calculus as if it were a logic. By contrast, the calculus (and calculation) neither is epistemic progression nor a theory about it. Moreover, the extensional logic provides no account of its own calculus or algebra, and does not clarify the relationship of that calculus to epistemic progression or to the theory thereof. On the other hand, a complete logic would, of necessity, give such an account. Use of a calculus could be an element in epistemic progression, and a complete account of the latter would involve an account of the possibility of such use. (It is perhaps worth noting that no widely acceptable account of the role of calculi in epistemic progression has been developed to date. Indeed, I am unsure as to what extent one can safely say that such accounts even exist, whether acceptable or not.)
II. The extensionalistic interpretation of the algebra or calculus of logic (A) does not convert it into a logic, or (B) even into a truly logical calculus.
(A) Under the extensionalistic interpretation, the variables in the schemata of the calculus are, as is well-known, understood to range over classes of things or the "extensions" of concepts. It was widely assumed in Husserl's time that only by this interpretation of the variables could one obtain a logical calculus. Husserl acknowledges the existence of this assumption or "prejudice"10 as he calls it; and he even attempts in one place11 to <151> reconstruct a line of reasoning which lends plausibility to it. But the assumption is after all, he thinks, false--a mere prejudice. And he shows it to be false by constructing several nonextensional calculi which can perform the same logical tasks as the extensional calculus.12 But even if the extensionalistic interpretation were the only way to get a logical calculus, it would still be only a calculus, not a logic--and not even a logic of that or any other calculus. Hence, all of the above criticisms of it as a logic still apply despite its pretensions.
(B) But given the extensional interpretation, the algebra is not even a "truly logical calculus," in Husserl's view. That is to say, the calculus thus interpreted does not express the types of judgments and interconnections of judgments which actually are found in natural epistemic progressions. These progressions do not go from statements or judgments about classes to other statements or judgments about classes, according to Husserl. Instead of referring to classes, judgments in the "natural movement of thought" refer to "conceptual objects" alone. This is a view which Husserl finds "strongly emphasized by J. S. Mill" (VWP, p. 178);13 and while he admits that the forms of judgment "...which have been chosen by Boole, Jevons, C. S. Peirce, Schröder, and others" do not refer to conceptual objects, he insists that "...their selection [of other forms] rests more upon the contingencies of the historical development of logic in England than it does upon the facts themselves (an der Sache selbst)" (VWP, p. 177).
To interpret the judgment in terms of "conceptual objects" is to understand it to refer to objects--not to classes thereof--and to refer only by means of the concepts under which those objects fall. The two fundamental logical forms (the forms showing up in "natural" thought) are, according to Husserl: "Provided something is an S, it is a P" and "There is not a non-P which is S." He holds that
"In these we have the precise typical expression of all universal judgments. In so far as the remaining forms do present universal judgments, they must also, therefore, be counted as one of these. And this is easily shown from only attending to the genuine subjects and predicates of these remaining forms"14 (VWP, p. 177).
Husserl takes the first of these two forms just mentioned as most primitive, and develops his nonextensionalistic "calculus of conceptual objects" upon it alone. Precisely in virtue of this choice, he thinks, his calculus is "a truly logical calculus." For all judgments bear, not on classes, nor on conceptual contents, but rather purely and simply upon conceptual objects" (VWP, p. 178). His calculus, therefore, mirrors the structure of natural epistemic progression, although, of course, it too is not a logic--a theory of such progression. <152> Nor is calculation in even his "direct and authentic logical calculus" (VWP, p. 184) identical with natural epistemic progression.
Husserl willingly concedes that the class calculus, though less of a true logical calculus than the calculus of conceptual objects, is not without its justification. It transforms all universal judgments into equivalent judgments about classes, and is
"...not in the least disconcerted by the fact that in so doing it removes itself from the movement of the initial thinking, and often very considerably so. And it does this with complete justification, provided only that it no longer makes a claim to stand for (1) a logic of deduction, instead of (2) a mere technique thereof (VWP, p. 176).
In Husserl's view, nothing has contributed so much to the widespread neglect of the calculus as failure to hold distinct "...these two [just mentioned] goals, so essentially different, on the part of those who have invented and advocated the calculus" (loc. cit.).
On the class or extensional interpretation, therefore, the calculus remains at an unelucidated distance from natural epistemic progression; and only by confusion or self-deception can it lay claim to be a logic, or even a truly logical calculus. Husserl's further elaboration of the "natural" judgment, and in particular his claim that there is no such thing as a purely extensional judgment--that extensions cannot be given without contents and that even explicit class judgments are in fact judgments about conceptual objects (GGA, p. 257; VWP, p. 178n)--are, of course, philosophically interesting and important; but they are not necessary to carry the particular point at issue in this second main line of criticism of "extensional logic." The two lines of criticism taken together surely constitute an overwhelming demonstration that such a "logic" is no logic at all and leaves all main points in the theory of epistemic progression untouched. To insist that such a "logic" is a logic may well be some form of self-deception, and at best must involve a failure, for whatever reasons, to see the facts of the case.
Husserl's concern with the status of the discipline of logic, and with the relationship of that discipline's subject matter to knowledge and knowing in general, intensely engaged him throughout the 1890s. In 1900 Husserl speaks of the logic of his time as being not the "...completed science, but... the provisionally pretended one, the one still in progress, whose methods, doctrines, in short everything, are still in doubt."15 He despairingly refers to the differences expressed in the works of <153> Hamilton, Bolzano, Mill, Beneke, and, from his own time, Erdmann, Drobisch, Wundt, Bergmann, Schuppe, Brentano, Sigwart, and Ueberweg. Now ask, he says, "whether one then has a single science, or only a single name." His view is that "...one might settle for the latter, if there were not occasionally some more comprehensive groups of common themes; but in respect of the doctrine, and even the problems, no two logicians reach a tolerable understanding among themselves" (loc. cit).
I wish now to turn, for the concluding part of my remarks, to the logic of our own times, to see to what extent Husserl's charge of a lack of self understanding and lack of objectively cognitive ("scientific") character might apply to it. It is no doubt true that current logic is not "extensionalistic" or "algebraic" in precisely the same manner as was the logic which he criticized. And yet it is quite true that the general style of logic which he criticized has been the strongest current in logic from 1900 to the present. It also seems quite true that our current logic regards itself as giving an analysis or account, in some essential respects, of what we have above called "epistemic progression," especially when that logic is taken to include syntax, semantics, and pragmatics. So, in the light of what current logic is and claims to do, it is appropriate to ask whether or not such a logic understands itself.
We shall not restrict ourselves, at this point, to extensionalistic calculi, but will consider the responses of representatives of outstanding tendencies in logic to two general questions about the discipline of logic:
(A) What basic type or types of entity are mentioned in the logician's statements?
(B) What type or types of evidence does the logician have for his claims made as a logician?
Consideration of leading answers to these questions should indicate the extent to which the logic of our time can or cannot correctly claim to be a "logic" in the sense of a theory of epistemic progression. It also should give some indication of the extent to which we can now claim to have a logic which is objectively cognitive or "scientific" in character.
The Frege/Church View. On Frege's view17 the basic type of entity which is mentioned in the logician's statements is the Gedanke. There is no simple English equivalent for this term. Although the term "thought" is commonly used to translate it, the term "proposition"--for all of its obscurities--very likely would come closest to conveying what Frege had in mind to the current English reader. As he describes the Gedanke, it is not subject to spatial or temporal relations or sensuous determinations of any sort; nor is it a part or aspect of, or in any way dependent for its existence or <154> character upon, anything which is sensible or located in space or time. Specifically, there is no essential connection between the Gedanke and linguistic and mental acts or entities. But while the realm of the Gedanke is an immaterial "third realm," as Frege puts it, it nonetheless can be "expressed" by sentences and can be nonsensibly "grasped" or "entertained" by minds, as well as be judged to be true or false. More essentially, it is somehow subject to truth and falsity, stands in the standard logical relations of implication, contradiction, etc., and is always complex, composed of various sorts of elements--e.g., concepts and logical connectives--depending upon the degree of its complexity.
Stress should be laid upon the special mode of cognition by which, for Frege, the Gedanke is apprehended. This, perhaps more than anything else, will mark his view of logic in an age with strongly empiricist proclivities. Certainly he does not have an analysis of this mode, and frequently indicates an awareness of inadequacy in this respect. But this does not shake his conviction that there is such a mode of cognition, and that logicians and others use it constantly, regardless of whether they also adhere to an epistemology which brands such cognition as impossible or absurd. Alonzo Church expresses Frege's attitude on this point, as well as his own, in saying that "The preference of (say) seeing over understanding as a method of observation seems to me capricious. For just as an opaque body may be seen, so a concept may be understood or grasped. And the parallel between the two cases is indeed rather close."18
P. F. Strawson. According to Strawson, the subject of "logical appraisal" is the statement, or, more generally, discourse.19 Obviously a statement will not have that independence of human thought and discourse which the Fregian Gedanke had. Strawson maintains that "...rules about words lie behind all statements of logical appraisal."20 Like the Gedanke, on the other hand, the statement is said to be subject to truth, falsity, and logical relations, and is not identical with any sentence or other material, sense-perceptible entity. The following passage formulates several of these points:
"Earlier, I paraphrased 'seeing that two statements are inconsistent' as 'seeing that they cannot both be true together.' And it is clear that that of which we can say that it is true or false is also that of which we can say that it is consistent with another of its kind.... [W]e cannot identify that which is true or false [the statement] with the sentence used in making it; for the same sentence can be used to make quite different statements, some of them true and some of them false.... The sentence may have a single meaning which is precisely what ... allows it <155> to be used to make quite different statements. So it will not do to identify the statement either with the sentence or with the meaning of the sentence."21
Strawson then proceeds to stress that a statement is to be identified "by reference to the words used, but also by reference to the circumstances in which they are used, and, sometimes, to the identity of the person using them." This suggests that a statement is some sort of action or event, a particular, not a universal or abstract entity. It involves words somehow, but involves more than words. This sort of action would be quite complex, containing--among other things--subactions of reference and predication, and having what seems, from the latter quotation, to be "internal" relations to the "circumstances" in which it is made.
It is difficult to obtain much more than this from Strawson by way of a response to our question (A). It seems that, like Frege, he does not suppose that statements are given in simple sense perception, as are ink marks and sounds. But, unlike Frege, he does not seem concerned about an account of how we do get our information about "statements."Perhaps he regards this information as in the domain of "privileged access": information which we simply have, in virtue of knowing how to talk, and to account for which is neither possible nor called for. But it is not clear that this is what Strawson holds. Many details in his view of exactly what sort of thing or event a "statement" is are simply left open to conjecture by what he has said in his publications. In one of his later publications, where he speaks of "propositions" instead of "statements," he lists first, among the questions of philosophical logic, the question: "What exactly, is a proposition?"22 But neither here nor in his other publications do we find any more clear or elaborate answer to this question than the one embodied in the passages cited above.
W. V. 0. Quine. Quine also speaks in the language of "statements" in many of his writings. But when, in his Methods of Logic, for example, he holds "individual events of statement utterance" to be those things which admit of truth and falsity,23 he does not mean what Strawson means by "statement." In a later book his response to (A) becomes clear in the following passages. First, right after rejection of Fregian "third realm" propositions, he attempts to place his own position in contrast to the "Oxford" answer to (A):
"Some philosophers, commendably diffident about positing propositions in this bold [Fregian] sense, have taken refuge in the word "statement." The opening question of this chapter illustrates this evasive use. My inveterate use of "statement" in earlier books does not; I there <156> used the word merely to refer to declarative sentences, and said so. Later I gave up the word in the face of the growing tendency at Oxford to use the word for acts that we perform in uttering declarative sentences."24
This passage, then, attempts to hold the logical subject matter free from abstract entities of the Fregian sort as well as from concrete entities of the Strawsonian sort, which involve internal relations with the speaker and his circumstances. However, a second quotation is required to bring Quine's position on (A) more fully before us:
"Having now recognized in a general way that what are true are sentences, we must turn to certain refinements. What are best seen as primarily true or false are not sentences but events of utterance. If a man utters the words 'It is raining' in the rain, or the words 'I am hungry' while hungry, his verbal performance counts as true. Obviously one utterance of a sentence may be true and another utterance of the same sentence be false. Derivatively, we often speak also of inscriptions as true or false. Just as a sentence may admit of both a true and a false utterance, so also it may admit of both a true and a false inscription.... We speak yet more derivatively when we speak of sentences outright as true or false. This usage works all right for eternal sentences: sentences that stay forever true, or forever false, independently of any special circumstances under which they happen to be uttered or written.... In Peirce's terminology, utterances and inscriptions are tokens of the sentence or other linguistic expression concerned; and this linguistic expression is the type of those utterances and inscriptions. In Frege's terminology, truth and falsity are the two truth values. Succinctly, then, an eternal sentence is a sentence whose tokens all have the same truth value.... Let us now sum up our main conclusions. What are best regarded as true and false are not propositions but sentence tokens, or sentences if they are eternal.25
The main point of this passage is to deny that logic deals primarily with certain abstract entities of a kind other than Gedanken, namely, the Peircian type-sentence.26 Quine maintains that only one sort of thing is a sentence--is true or false--in an underivative sense. This is a certain subclass of sound sequences produced by human beings in certain ways. These are events: "events and utterance," or "verbal performances." The written sentence is here for Quine, as it was for Aristotle,27 derived from the spoken sentence; and the "sentence" as type is even more derivative, obtained from the spoken and the written sentence by some process of logical construction. Quine's answer to (A) is, therefore, that the basic sort of <157> entity mentioned by the logician at his trade is a certain type of sound sequence. Thus, logic deals with perfectly concrete, sense-perceptible entities. They are "physical phenomena,"28 and all of their interrelations, including the so-called "logical" ones, must finally reduce to relationships between physical organisms and their determinations--but especially, for Quine, between the conditioned responses of such organisms.29 Consequently, no special epistemology is called for to account for our grasp of sentences and their logical relations.
Hilary Putnam.The answers to (A) which we have sketched up to this point take truth and falsity as earmarks of the logician's subject matter,whatever it may be. However, many significant thinkers of recent years have assumed that classes--to which truth may hardly be ascribed without a very long explanation--are at least an indispensable part of what must be mentioned in response to (A). Putnam has recently published an essay30 in which he proceeds as though he shares this assumption. The essay does not purport to be a complete treatment of the philosophy of logic. Rather, as the author states, it is concerned "with the so-called ontological problem in the philosophy of logic and mathematics--that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist."31
The abstract entities in question turn out in very short order to be precisely and only classes. Just how they so turn out is not very clear from what is actually said in this essay; but Putnam indicates, at any rate, that he is one of those philosophers who "find something ridiculous in the theory that logic is about sentences" (p. 6). He does not give an explanation of why that theory is ridiculous beyond pointing out (very rightly) that words and sentences are no better suited to the nominalist's program than are classes themselves (pp. 10 f.). And--the nominalist's excepted--he scarcely alludes to alternative accounts of what "logic is about." He seems simply to think that that contemporary or "modern" interpretation of quantificational inference schemata, according to which they express properties of relations between classes, is sufficiently obvious without defense and without examination of alternatives to allow him safely to assume that the "abstract entities spoken of in logic" are classes or sets. Thus, one of the clearer cases of what he regards as a "logical principle" (p. 29) is "the general principle...: 'For all classes S, M, P: if all S are M and all M are P, then all S are P'" (p. 27). And so it is not surprising that he concludes that logic is indeed committed to the existence32 of these nonphysical33 entities, classes, or sets. A main part of his essay is then devoted to the attempt to show that physics also is so committed, and that it is rational to accept the existence of that to which both logic and physics are committed. As is characteristic of many <158> who give sets or classes an important philosophical role, Putnam does not provide any careful discussions of our knowledge of sets.
Looking back, now, at such fundamental differences as those between the four positions just sketched,34 the radical disagreements which are manifest empty the seeming agreement of logicians upon what Dewey called the "proximate subject matter"35 of logic of all rational significance. The following sequence of marks--or other sequences parallel in usage--might seem to indicate something about which all logicians have come to a certain agreement:
All A is B
All B is C
So: All A is C.
But in the light of the above we now see that logicians speaking with reference to these marks often are talking about utterly different things--categorially different things--than are other logicians speaking with reference to or by means of the same (kind of) set of marks. Aristotle's Prior Analytics and Mill's System of Logic, for example, or Quine's Methods and Church's Introduction, are in the declared intent of their authors about things of different ontological categories: things with radically different kinds of properties and relations, which require radically different modes of cognition. Cohen and Nagel rightly state:
"... there is a bewildering Babel of tongues as to what logic is about. The different schools, the traditional, the linguistic, the psychological, the epistemological, and the mathematical, speak different languages, and each regards the other as not really dealing with logic at all."36
The confusion is only augmented by the fact that the different languages used each employ signs of the same types as the others do. Much that passes for agreement is not agreement at all, but an unwillingness to raise questions, or else some concession to utility.37
The great developments in what is justly called "non-quantitative mathematics"38 during the last one hundred years have obscured what must surely be regarded as the continuing crisis in the foundations of formal logic. This crisis is most visible in the simple fact that among the best minds in the field there is radical, categorical disagreement upon what things are mentioned and analyzed in the field, and upon what their essential properties and relations are. Between some investigators the divergence is strong enough to warrant a parallel in imagination with, for example, theoreticians in music who are unable to agree upon whether they were theorizing about tones and their interrelations or black marks on staff lined paper.
This crisis is further evident when we consider current logical theory in <159> relation to question (B) above. We are then asking what, on current views, is the sort of rational basis which the logician has for the claims with which he fills his pages and hours? Is it the same sort as the mathematician or the mechanic or the lawyer has for his claims? Or is it different? And how is it different? In default of clear and thorough answers to such questions, the issue ultimately must become: does the logician have a rational basis for his claims?
In surveying the literature one notices that confusion and disagreement about (B) are far less obvious than that about (A). But this is only because (B) is hardly ever discussed at all by formal logicians. Perhaps confusion on (A) causes one to fail to see (B) as an issue. On the other hand, logicians are to be found (one hopes not often) who seem to suppose that, since they deal mainly with logically-true--or, more generally, logically-determinate--propositions, they also deal in L-true propositions. When one attempts to raise the issue of the evidence for logicians' truths, they think that one is concerned with the evidence for logical truths, and are puzzled at any suggestion that there is some issue not settled by the methods for ascertaining L-determinacy which logicians teach. But then there probably is no logician who would hold that the truths which he teaches are themselves L-determinate, once he has clearly faced the issue. Certainly logicians' lectures do not consist in uninterrupted tautologies and inconsistencies. But few logicians are at all reflective about the evidential basis of their quite L-indeterminate remarks. It is simply a fact that (B) does not receive from formal logicians the attention which it requires.
We shall not turn to the literature again to show that confusion and disagreement about (B) actually exist. The sketches of representative positions given above suffice to make that clear. But that such a condition is necessary follows from the diverse responses to (A) together with the manner in which (B) relates to (A). Simply put, if one logician says he is talking about something physical, while another says he is talking about something nonphysical, only a sufficient amount of confusion would allow them then to agree on the evidential basis of their claims. Categorially or merely essentially distinct types of objects call for distinct modes of cognition. Confusion and disagreement upon the objects of logical knowledge cannot but result in confusion or disagreement upon the nature of evidence in logic. Not only, then, do logicians intend to talk about radically different sorts of things, with the familiar schematic signs which show up in their books and on their blackboards, but the kind of evidence invoked for their claims differs radically from logician to logician.
Results of this survey of current views.One might suppose that, if <160> anything at all can evidence confusion in the elements and basic principles of a discipline, it would be radical or categorial disagreement between leading minds in the area on what that discipline studies--i.e., on what it is that one thinks about whenever he is actively engaged in knowing the truths of the discipline--and on what the kind of evidence is upon the basis of which the objects in question may come to be known and understood. And one might further think that nowhere would such confusion be as intolerable as in what has often stood as the science of science (Wissenschaftslehre or Wissenschaftslogik). Yet, in no discipline today do we have clearer evidence that such confusion exists than we do in logic itself. Only by refusing to look beyond the surface activity and the development of formal systems of one sort or another can we fail to see the confusion. There are serious grounds for questioning the status of logic as an objective and rational discipline.
Beyond this, it also seems clear that the various 'logics' which currently are most influential are very questionable as accounts of the essential elements in epistemic progression. Whatever might ultimately be made out from the various points of view about the relation of the various formal techniques to "natural thought," as Husserl called it, no clear and widely acceptable account of that relation is available; and, frankly, most logicians make no serious attempt at such an account. Quine, for example, really offers nothing in the way of a theory about the relationship between the formal techniques advanced by his various texts and the strings of sounds which, according to him, are the real bearers of truth and falsity, and which must be the final constituents of epistemic progression or of what he calls the "web of belief." And, it seems to me, he is much closer to dealing with this problem in a serious manner than other logicians mentioned above, possibly excepting Strawson.
If this is true, then within logical studies we stilltoday have "a logic that does not understand itself." We remain in a condition where, for example, the logic--and especially the formal methods--taught in our texts and courses is unintelligible in its theoretical underpinnings and in the details of its relationship to "natural thinking." It was, of course, precisely to make logic intelligible in these respects that Husserl developed his positive account of the science of logic in Logical Investigations and in his later works.39
- This assumption of clarity is, of course, a social--and psychological--fact, and as such has grounds other than the real or alleged confusions upon which Husserl focuses. There is no extant discipline of the Sociology of Logic (or of logicians), but such a discipline falls, in principle, within the Sociology of Knowledge, a subdivision of Social Psychology. Logicians are, after all, natural organisms functioning in the natural world; and it would be very interesting, no doubt, to inquire into the sociological grounds of the existence assumptions made by the practicing logicians of a given epoch, as well as into the grounds of their assumptions about what is methodologically clear and obvious or not. But Husserl's inquiry is not of this nature. For him it suffices to draw essential distinctions within, and to focus upon logical confusions relating to, the subject matter dealt with by the "extensionalist" logical theorists. And that is what we are interested in here. Yet for once it should be pointed out that it is important for the inquirer in any area to remember that his own beliefs about his subject matter are sociologically influenced. Only this realization, vividly present, can prevent one from ignorantly worshiping one or more of Bacon's Idols, convinced all the while of being guided by simple, clear-eyed perception of the truth. Return to text.
- For lack of a better term, I am referring to the general tendency in logic of which Husserl was first and last most critical as "extensional logic." While this appellation conforms to Husserl's usage and is historically justified, it should be pointed out that the tendency in question had two major elements, so far as Husserl's critique is concerned, and that these two elements are only contingently and historically, not essentially, connected. The first was the treatment of logic as something which could be a calculus, and of calculi as if they might be logics. The rejection of this treatment as a possibility is, I believe, the major point of his criticism in these early years, and certainly is what he has mainly in view in the Crisis statements quoted above. It runs parallel to his criticism, in volume I of the Logical Investigations, of "psychologistic logic," which took logic to be something which could be an empirical science (of certain types of mental facts). Both the extensionalistic arid the psychologistic logician errs on what logic could be, or on its very essence.
The second element in the general tendency which Husserl here criticizes is the view that logic is "really" a theory about the relations of classes or of the extensions of concepts. Many who held that logic could (and should) be treated as a calculus held that it could be so only if it were treated as a theory about classes (extensions) and their possible relationships. Thus the two elements of the general tendency were brought into historical connection. It is with the general tendency that Husserl is concerned, not just that element in it from which it gets the name "extensionalism." Return to text.
- Republished in Husserliana, Vol. XII, Philosophie Der Arithmetik, Nijhoff, 1970. the reference here is to p. 291; and see p. 47 of my English translation in Philosophia Mathematica, Vol. 9 (1972). (Unfortunately, the translation was extensively marred by the printer and there was no opportunity for corrections. It is to reappear in a volume, Husserl: Shorter Works, edited by Elliston and McCormik, to be published by Notre Dame Press in 1981.) See also p. xviii of Husserliana, Vol XVIII (1975), where Elmar Holenstein relates this view of logic as Kunstlehre back to Stumpf, Brentano, and Aristotle. Return to text.
- "Die Aufgabe der Wissenschaftslogik,"Einheitswissenschaft, Heft # 3, Verlag Gerold & Co., Wein, 1934, p. 5. Return to text. <162>
- On"natural" thinking, also referred to by Husserl as "actual thought," see especially pp. 176-77 of "Der Folgerungscalcul und die Inhaltslogik," in Vierteljahrsschrift für wissenschaftliche Philosophie, Vol. 15, # 2, 1891. Return to text
- I realize that some logicians will strongly assert that they have nothing to do with such processes. Yet they continue to apply the logical terms which they analyze--e.g., "inconsistent,""valid," etc.--to actual processes or events of thinking and speaking; and, for the most part, they continue to be paid by educational institutions which expect them to do something about the quality of such processes in students. Return to text
- See footnote # 5 above for bibliographical reference. Return to text
- "Voigt's'elementare Logik' und meine Darlegungen zur Logik des logischen Calcul,"Vierteljahrsschrift für wissenschaftliche Philosophie, Vol. 17, 1893, p. 1119n. Return to text
- This famous phenomenological slogan possibly derives from John Stuart Mill, who many times in his writings appeals to the facts or things themselves, as distinct from the manner in which they may be experienced, thought of, or spoken of by us. See, for example, section 1 of his chapter, "Of the Import of Propositions," in his A System of Logic. This was a chapter with which Husserl certainly was very familiar. It is true that the Gomperz edition of it uses the phrases "die Dinge selbst" and "die Thatsachen selbst" (p. 81 of Vol. I of John Stuart Mill's Gesammelte Werke, Leipzig, 1872), not the word "Sache." And Husserl did use the Gomperz edition. (See his note in subsection 5 of the second "Logical Investigation.") But he also read Mill and the other British Empiricists in the English, as is clear from subsections 13, 24, and elsewhere in the second "Logical Investigation." The terms "Sache" and "Sachverhalt" seem to have been favored by Stumpf, who was with Husserl at Halle for a number of years around 1890. Return to text
- See p. 112 of "A. Voigt's ... (etc.),"loc. cit., in footnote #8. Return to text.
- Ibid., p. 111n. Return to text.
- This is the entire point of VWP, referred to in footnote # 5. Return to text.
- No doubt the reference here is to A System of Logic, Bk. 1, Ch. V, "Of the Import of Propositions." See especially the last paragraph of subsection 2 and the second paragraph of subsection 4. Return to text.
- And see his remarks on the meaning of the common noun in natural language (GGA, pp. 251-52). Return to text.
- "Prolegomena to Pure Logic" (Vol. I of Logical Investigations), subsection 13. Return to text.
- Few things more clearly exhibit the contemporary obscurity in the foundations of logic than discussions of the relationships between syntactics, semantics, and pragmatics, and, especially, of whether pragmatic relations are "logical." Return to text.
- See the two papers, "Der Gedanke" and "Die Verneinung," in G. Frege, Logische Untersuchungen, ed. Günther Patzig (Gottingen: Vandenhoeck and Ruprecht, 1966), pp. 30-71, for texts corresponding to the description here given of Frege's view. An English translation of the former paper is in Mind, Volume 65 (1956), and one of the latter is in P. Geach and Max Black (eds.), Philosophical Writings of Gottlob Frege, (Oxford: Basil Blackwell, 1960). See also A. Church, Introduction to Mathematical Logic, (Princeton: Princeton University Press, 1956), pp. 23-31, where a view substantially the same as Frege's is advocated. Return to text.
- From"The Need for Abstract Entities in Semantic Analysis," in Copi and Gould (eds.), <163>Contemporary Readings in Logical Theory, (New York: Macmillan, 1967), p. 200. For further elaboration of the Gedanke-proposition response to question (A), see sections IV-VII of my paper, "The Paradox of Logical Psychologism: Husserl's Way Out,"American Philosophical Quarterly, IX (January, 1972). Return to text.
- Introduction to Logical Theory (London: Methuen and Co., 1952), pp. 1, 2, and 9. Return to text.
- Ibid., p. 12. Return to text.
- Ibid., p. 4. Return to text.
- Page 2 of P. F. Strawson (ed.), Philosophical Logic, (Oxford: The University Press, 1967). One notes that in the "Introduction" which he wrote for this volume Strawson does not touch upon attempts to answer the general question about the nature of propositions, but proceeds immediately to discuss the various classifications, properties, and relations of "propositions," without facing the general question. Of the readings which he selected to be contained in the anthology, only Frege's paper, "The Thought," referred to above, gives a direct answer to this general question. Return to text.
- Methods of Logic, rev. ed. (New York: Henry Holt and Co., 1959), p. xi. Return to text.
- Philosophy of Logic, (Englewood Cliffs: Prentice-Hall, 1970), p. 2. Return to text.
- Ibid., pp. 13-14. Return to text.
- This also is largely the point of the passage in Methods of Logic referred to above. However, examination of the literature of logic shows that the type-token distinction is not a clear one in the uses often made of it. Return to text.
- De Interpretatione, 16a, 3-4. Return to text.
- Word and Object, (New York: John Wiley and Sons, 1960), p. 5. Return to text.
- Ibid., p. 11. Return to text.
- Philosophy of Logic, (New York: Harper and Row, 1971). Return to text.
- Ibid., the "Preface." Return to text.
- Ibid., pp. 23, 32, and 56. Return to text.
- Ibid., pp. 15-16, 22-23, and 36. Return to text.
- These four do not, of course, cover all of the possibilities and other answers to (A) are actually given. One is classical psychologism, which holds the subject matter of logic to be mental events. Another is the current treatment of a proposition as a set of possible worlds. (See R. Stalnaker's "Propositions," in Issues in the Philosophy of Language, Yale University Press, 1976.) Return to text.
- In his Logic (1938) John Dewey remarked that "...contemporary logical theory is marked by an apparent paradox. There is general agreement as to its proximate subject-matter. With respect to this proximate subject-matter no period shows a more confident advance. Its<