Realist Analysis of the Relationship Between Logic and Experience (A)
ABSTRACT: I undertake to explain how the well known laws of formal logic--Barbara Syllogism, modus ponens, etc.--relate to experience by developing Edmund Husserl's critique of Formalism and Psychologism in logical theory and then briefly explaining his positive views of the laws of logic. His view rests upon his understanding of the proposition as a complex, intentional property. The laws of formal logic are, on his view (and mine), statements about the truth values of propositions as determined by their formal character and relationships alone. The laws thus understood explain how algorithms set up to mirror them can accomplish what they do to advance knowledge, even though they operate purely mechanically. Further, they explain the proper sense in which formal laws "govern," and may guide, processes of actual thinking. Husserl's theory is a realist theory in the sense that, on his interpretation, the laws of pure or formal logic hold true regardless of what any individual, culture or species may or may not think, or even if no thinking ever occurs.
By "logic" I shall understand the intellectual and practical contents of academic courses under the heading of "Logic," and that would take in the contents of the textbooks used and lectures given in such courses. So we wish here to inquire about the truths taught or the knowledge imparted in such courses, textbooks and lectures. I presume everyone will agree that they do convey some truths and impart some knowledge, which, of course, must also be in the possession of those who would qualify to teach such courses.
By "experience" I shall understand the flow of mental events that make up ordinary life. I do not mean, of course, what is happening around one, or the processes occurring in one's blood or liver, but one's life in the midst of what is happening around one: the taking in in thought, feeling and action, of what is happening around, or, for that matter, within one. Experience will therefore include events or acts of thinking, inferring, believing and perceiving, and these are the parts of experience which logic might be thought especially relevant to, if it is to be relevant at all.
Two Major Questions
Two intriguing and difficult questions arise with reference to logic and experience thus understood. They are questions that arose quite early in the historical path of philosophy, and that continue without generally received solutions up to today.
1. Is the truth or knowledge imparted by logic derived from experience?
2. Does the truth or knowledge imparted by logic apply to (guide or govern) experience?
If we say "No" to the first question, we are faced with the further question of what the truth or knowledge imparted by logic is derived from. That is, what is the justification of those truths that allow them to be treated as knowledge? And of course a number of answers to this further question have been advanced, especially in the 19th and 20th Centuries. And if we say "Yes" to the first question, we need an explanation of precisely how that knowledge is derived from experience.
With reference to the second question, our options are to say that the knowledge content of logic (as explained) does not apply to (guide or govern) experience at all; or we can say that it does, in which latter case we need to explain in what sense and exactly how it guides or governs experience--which will be a peculiarly trying task if we have already denied that logical knowledge is not derived from experience.
'Laws' of Logic
Before going on, however, let me say a little more about "logic," for it might be thought that a reference to "the content of academic courses in "logic" is too imprecise nowadays to pick out anything at all. I am sympathetic with that point, for it refers to a rather deplorable state of affairs in academia, one which actually results, I think, from the intellectual failure to deal in a convincing manner--or at all--with the topic of this collection of papers: namely, the relation between logic and experience. But it may be that we can narrow down the "content" referred to in such a way that few will any longer doubt what we are talking about--always a perilous hope in philosophy. It is difficult to imagine any course in "logic," even today, that does not try to impart truth and knowledge about the relationships of implication and contradiction as they are sometimes found to obtain between thoughts (and beliefs) or statements and propositions, or that fails to inform its students about the distinction between valid and invalid arguments, together with some techniques for distinguishing the one type of argument from the other. And so, instead of referring to the content, in general, of academic courses under the heading of "logic," we can restrict the content to precisely such specific matters as those just mentioned, and go on to raise our two questions.
We might even speak of laws of logic, and have in mind some of the clearest cases only, such as modus ponens, or the Barbara syllogism, or the standard list of "rules" for the logic of propositions and quantificational logic that form parts of most systems of "natural deduction" usually taught. We could then refer to "laws of logic" and pose our two questions specifically about them:
1a. Are laws of logic derived from experience? And if so how?
2a. How do laws of logic apply to (guide, govern) experiences--if they do?
Real Human Concerns
Now we should recognize that these questions raise issues of real human concern. Does logic (laws of logic) inform anyone about some important domain of objective reality, and is it of any use in helping us think better, i.e., in ways such that statements we make and beliefs we form are (more likely to be) true? Does it even allow us to attack others more effectively? In short, what is the use of logic?
Logic as a required course of studies has all but disappeared from university curricula. Whereas up to the 50's and 60's most philosophy departments had several large classes in formal logic every semester--because such a course was thought essential to academic preparation for life, and therefore was made a requirement for degree programs--now most departments have only one or two such classes each semester, and these are very sparsely attended, because training in formal logic is not regarded as essential to educational goals.
I hope it is obvious how answers to our two questions relate to such a major shift in educational policy. But the controversies about the relevance of logic to education and life are by no means new, and they have been pretty steadily engaged at least from the time of the Renaissance reaction against the syllogism up to the present. More often than not, the controversy has involved distinguishing between kinds of "logic"--for example, between formal, transcendental, informal, and inductive--and pitting them one against the other in various respects. The most recent installment has seen the replacement of "formal" by "symbolic" logic, and the opposition of "symbolic logic" to a logic of "ordinary language" and most recently to "narrative"logic.1
In every case, however, "logic" has something to do with necessary structures or moves in thought or discourse (perhaps life as well), and "symbolic" (formal) logic is often attacked because of its presumed inadequacy to express the necessary structures that govern actual discourse and real life. (Ryle, later Wittgenstein, Toulmin, MacIntyre, etc.)2 It is seen as largely irrelevant to "real life." This point of view has even led State Legislatures to mandate course in something called "Critical Thinking," which supposedly enables the student to become a better thinker (and better active agent) without having to master the presumed irrelevances of formal or symbolic logic.3
Here we must confine our topic within the broad ranging issues intimated by the above remarks. Our aim shall be to present a Realist answer to questions 1a and 2a. Though it is an answer which, I believe, can stand on its own feet without historical support of any kind, I shall present it in the form of an explanation of Edmund Husserl's theory of formal logic. This will enable us to tie into an already existing body of thought and literature that gives Realism in formal logic what could be taken as its best possible exposition.
Husserl developed his Realist--or "Absolutist," as he sometimes called it, (Husserl, 1970, pp. 158-9)4--theory of logic, with its own impressive answers to questions 1a and 2a, through a decade-long critical interchange with two other theories or philosophical interpretations of logic. These were Formalism and Psychologism.5 The main point of Formalism in the late 19th and early 20th Century was to think of the laws of logic as "laws" of an algorithm or system of written symbols that were formed and transformed according to rules which considered only the shapes and relative spatial positions of the symbols. The most well-known algorithmic system in Husserl's day was the "Boole/Schröder Algebra," given definitive expression in Schröder's Vorlesungen über die Algebra der Logik. This was the primary text with reference to which Husserl developed his understanding and critique of Formalism.6 Of course since Schröder's day we have had a number of other presentations of "formal" systems, most notably Whitehead and Russell's Principia Mathematica--though neither of them were Formalist in the philosophy of logic.
The algorithmic technique has certain indispensable advantages for scientific thought and research, of which Husserl, as a mathematician, was very well aware.7 It is simply impossible for the human mind to hold together in thought anything like the enormous complexity of the various fields of human inquiry, including logic itself, which nevertheless, and as a matter of fact, is easily mastered through a well-developed algorithm. So, very far from attacking and rejecting formal/symbolic techniques, Husserl insisted upon their necessity.
But that is not the end of the story. For the questions remain: Why do such algorithms work? and What is it that enables them to do what they do in providing knowledge of various domains of reality? It cannot be chance or blind hit-and-miss that results in algorithms (mathematical or logical) which are effective for the aims of advancing knowledge and enabling us to come to grips with a reality that exists independently of what we do or do not think about it. It is a curious fact that even outstandingly creative mastery of an algorithm does not require understanding of why it is able to accomplish for knowledge what it does, and may even hinder such understanding. "One can be an outstanding technician in logic, while being a very mediocre philosopher of logic, and again, one can be an outstanding mathematician, while being a very mediocre philosopher of mathematics. (Boole provides an outstanding example of both.)" (Husserl, 1994, p. 570) And no field shows this more clearly than mathematics, where successful application of formal techniques routinely outruns their rational justification.
What Husserl called a logic in the 1890's, when he was working through his position on Formalism, was an account of why successful techniques for obtaining knowledge work.8 Such an account had to be based upon direct insight into the nature of the technique in question (the organization of the symbols and transformations, for example) and its relationship to the subject matter it is used to grasp. In other words, one had to gain insight into the essence of the technique in question, as well as insight into how that technique was essentially correlated to the subject matter of the knowledge domain concerned.
In particular, in operating an algorithm (mathematical or logical) one indeed applies rules of symbol manipulation that refer only to the spatial properties and positions of the symbols. In operations, the symbols are "uninterpreted." But there is a point to the operations only because a certain correlation between the symbol formations and transformations, on the one hand, and the structures of concepts and truths about objects, on the other, is presupposed in how the algorithm is set up. The symbols can be and should be "uninterpreted" in operations, but not in the way they are set up or organized for operations.
The symbolic formula are in fact, according to Husserl, stand-ins for very general descriptions of kinds of concepts and propositions--that is, descriptions that do not require reference to any specific subject matter of the kinds of concepts and propositions in question. For example, such a description might mention a conjunction or disjunction or any propositions. That is what it is for them (the formula) to be formal in the classical logical sense of "form," which is not just a matter of the rules of manipulation referring only to the spatial characteristics and positions of the symbols.
Husserl's understanding of symbolic formula in logic is very close to the view expressed by Tarski with specific reference to the "logic of propositions," and, indeed, was very likely historically influential upon it:
"Just as the arithmetical theorems of universal character state something about the properties of arbitrary numbers, the laws of the sentential calculus assert something, so one may say, about the properties of arbitrary sentences. The fact that in these laws only such variables occur as stand for quite arbitrary sentences is characteristic of the sentential calculus and is decisive for its great generality and the scope of its applicability." (Tarski, 1965, p. 38)
Of course for Husserl the reason why one can say this of sentences is because of their correlation with thoughts (propositions). It is simply not true that the logical algorithm is in general arbitrary, though it is conventional. One can, within limits, change the "rules" of an algorithm, but one cannot change the laws of logic, which are grounded not in the symbols but in the formal structures of concepts and propositions, which in their nature allow us to know by inference, and possibly by calculation, what we could never master for knowledge in any other way.
Given the appropriate correlations between the algorithm, the formal structure of thoughts (concepts, propositions) and the corresponding realities, Husserl's view was that: "A truly fruitful formal logic constitutes itself from the outset as a logic of signs. When sufficiently developed, it will form one of the most important parts of logic in general (as the art of knowledge). The task of logic is the same here as elsewhere: to take possession of the natural modes of procedure [including algorithms] in the judging mind; to test them, and to provide insight into their value for knowledge; in order finally to be able to determine with precision their limits, extent, and significance, and to be able to formulate relevant general rules on that basis." (Husserl, 1994, pp. 50-51)
As for the logical calculus, then, it is "...a calculus of pure deduction; but it is not its logic. In it we have its logic just as little as the arithmetica universalis, which spans the whole domain of numbers, is a logic of that domain. Of the deductive mental processes involved, we discover just as little in the one case as in the other. Accordingly, the 'laws' of the calculus are also nothing less than they are the norms of all 'valid thinking', or, more precisely, of inference conforming to pure implications." (Husserl, 1994, p. 57)
Husserl's position is that to take the "laws" of the algorithm to be laws of logic is to make a huge mistake, a "category" mistake, and one that bars our way to understanding how those very 'laws' of the algorithm relate to the laws of logic, and to understanding what explains their amazing utility in our coming to apprehend the various fields of reality in itself that are at issues in scientific and other inquiries. Such understanding is precisely what Husserl will attempt to provide in his own positive theory of logic, including his theory of algorithms. The relations between the symbols of the algorithm--expressed in the "formation and transformation rules"--are not themselves logical relations or logical laws, and their utility can only be explain by distinguishing them from and correctly relating them to properly logical laws.9
Now Psychologism in logic has standardly positioned itself by opposition to Formalism, both during Husserl's early career and later in the history of thought. (Willard, 1984, pp. 177 & 202) It opposed Formalism largely because of how Formalism, as a point of pride, distanced itself from the actual events and process of human thinking. Psychologism could not agree that the "laws" of an algorithm, taken by themselves, could deal with actual thinking or life--a familiar story, and one with which Husserl, as we have seen, agreed. His interpretation and critique of Psychologism was worked out in the middle 1890s and given definitive expression in the Logical Investigations of 1900-1901, especially in volume I, "Prolegomena to Pure Logic."
The heart of Psychologism in logic is its claim that what the laws of logic are about, what they are true of, are regularities governing the course of individual thoughts and beliefs in the individual human mind. Modus ponens, for example, might be read as a generalization to the effect that, given belief that p and that if p then q, belief that q will follow in the course of the relevant mental life. If belief that q does not, in a given case, occur, it is only because other causal conditions are in play in that particular case, so that some other psychological law has taken over the course of experience. Thus it is natural to say, on this view, that logic is simply one chapter in the book of psychology. In the discussions of the "Prolegomena" Husserl considers, for example, the principle of non-contradiction (as A is not non-A) and the principle of identity (as A is A) in their psychologistic interpretation (Chapter 5 of the "Prolegomena"). They are presented in terms of what it is impossible or possible for the human mind actually to think and believe. The law of non-contradiction is read as stating that it is impossible for us consciously to affirm (believe) that A is B and that A is not B simultaneously, or believe simultaneously both a proposition and its denial.
He also considers an interpretation, due to G. Heymans, of the laws of syllogism as parallel to the laws of chemistry. Quoting Heymans:
"Just as the chemical formula 2H2 + O2 = 2H2O only expresses the general fact that, in suitable circumstances, two volumes of Hydrogen combine with one volume of Oxygen to form two volumes of water, so the logical formula
MaX + MaY = YiX + XiY merely express the fact that, in suitable circumstances, two universal affirmative judgments with a common subject, produce two new particular judgments in consciousness." (Husserl, 1970, pp. 131-132)
Of course for this to happen all disturbing influences must be excluded and one must be "rational." But the basic idea of Psychologism is just that the familiar laws of logic are empirical laws governing the actual course of mental events, and that they are derived inductively from observations of such events.
Probably there has never been given a more thorough hammering of a philosophical position than that which Husserl gave to Psychologism in the "Prolegomena," showing it to be false by its false consequences and to be groundless by identifying and refuting the premisses from which it is derived. Here I will summarize the refutation under three main points that concern the nature of laws of logic viz-a-viz empirical laws of psychology.
First, the laws of logic are exact or rigorous, while the laws of psychology are vague, and hold only under assumption of an indeterminate background of conditions. It would make no sense, Husserl thinks, to ask under what empirical conditions a law of logic is true. Of course which law of logic applies in a given case of thought or talk is an appropriate matter of inquiry.
Second, the laws of logic are known to be true by insight into the types of concepts and propositions involved and how truth values behave with reference to those types. No one thinks of proposing to examine four more cases of modus ponens to see if they might have true p and if p then q, but a false q, or looking to see if the factual conditions of thought might permit the q to be false.
Third, the laws of logic have no factual import. They would remain true if no minds existed. The laws of psychology do have factual import, at least insofar as we have evidence for them. For that evidence would have to consist in the actual regularities that have been observed to occur in the course of real mental events. Laws of psychology are 'laws' of the factual human mind.
Summarizing--and far from doing justice to his elaborate critique--Husserl shows that the laws of logic cannot be psychological laws because laws in the two fields are radically different in kind. The very sense of the laws in the two fields is radically different.10
Now as a historical aside of considerable significance for the current scene, it is noteworthy that after the "linguistic turn" in 20th Century philosophy, as it is sometimes called, nearly all of the main issues discussed by the philosophers of the late 1800s, having to do with algorithms and thought, or with laws of psychology and laws of logic, were dug up and reexamined, but now in terms of language instead of consciousness or experience. Issues of "logic and experience" became issues of "logic and language." The distance between "a formalized language" and "ordinary discourse" was emphasized (or deemphasized), and attempts were made to treat the laws of logic as (somehow) laws of language use--of what we could or could not say.11 Still more recently, attempts to treat thought processes as brain processes have seemed to necessitate (or permit) treatment of the laws of logic as causal laws of brain events.
Husserl's Realist Theory of the Laws of Logic
We seem, then, to face something of a dilemma. If we favor a close association of logic with psychology, then the rigor of the laws of logic and their independence of how we actually think is hard to understand. But if we favor formalism, how can the laws of logic apply to actual thinking and ordinary uses of language, which they surely must.
What, then, is Husserl's own theory of the laws of logic, and how does it answer questions 1a and 2a in such a way as to avoid the problems or errors of Formalism and Psychologism, and yet do justice to what is sound in each of them? And what are the important points in the positions of Formalism and Psychologism that we must allow for?
Algorithms do as a matter of fact allow us to deal effectively with reality, and, in some cases at least, to expand the scope of genuine thinking, not just calculating. It is possible to show an actual line of thought to have been valid or invalid by putting it into algorithmic formulas. Also, it is possible to dispense with genuine thinking and to nonetheless arrive at valid conclusions and true judgments about a corresponding reality. Justice must be done to this fact.
As for Psychologism, logical relationships do show up within events or acts of actual thought and discourse. One may contradict himself, for example. To deny this is to take a position that, for many thinkers, has amounted to denying any significant connection between logic and experience. But if we do not deny it, how are we to do justice to the obvious connection between the laws of logic and actual thinking?
The centerpiece of Husserl's interpretation of the laws of logic (of pure logic) is his understanding of the proposition. A proposition, according to him is a thought-that.... But it is a thought-that in the sense in which many people can have strictly the same thought-that, or one person can have the same thought-that on many occasions. It is therefore a one-in-the-many, a universal, an abstract object. It does not exist at a place and a time, though it may be present in events of thinking which are temporally located and are part of the life stream of a person who is spatially located.
Propositions are not beliefs, though they combine with belief and the other propositional attitudes in the experiences of human beings. However, beliefs, etc. do not, on Husserl's view, have propositions as their objects. The objects of beliefs are precisely the same as what the propositions are about or of. The relationship between a propositions and a belief whenever they are concretely combined in an act of thought is co-instantiation. A proposition is a quality of the same act as is the belief. During one main segment of Husserl's career (especially in the Vth "Investigation") the proposition is called the "matter" of the act and the attitude is its "quality." But both are qualities in the usual sense: qualities of acts of thoughts. Propositions become objects of mental acts only in special acts of reflection (such as ordinary logical thinking) or in cases where one is, precisely, thinking about propositions--as one does in pure logical theory. (Husserl, 1970, p. 332)
With the exception of the point just made, Husserl's view of propositions (and concepts) was shared, with minor variations, by many other outstanding logicians of the 19th and 20th Centuries: Bolzano, Frege, Russell and the early Wittgenstein, but also, I think, by Lotze and F. H. Bradley. Thus, that propositions have two truth values, that their truth values are determined by their internal structures ("truth conditions"), that the truth values of other propositions have necessary relations to them, which are also a function of the "forms" of the propositions in question. And so forth. Of course there were many variations of detail among all these thinkers.12
The form of a proposition (or inference or argument) was understood by Husserl to be its internal structure--the arrangement of "constants" and "variables"--described without regard to the particular individuals, properties or relations the proposition or inference is actually about. That is, without regard to its subject matter. What we call "Modus ponens,""DeMorgan's Laws," or the "Barbara Syllogism" are actually very general descriptions of certain classes of truth-preserving moves. Logical constants and variables are simply qualitative variations within the overarching quality: proposition. They are ways propositions can differ or be the same, but ways not specified by reference to what the propositions are about, their specific subject matter, and in that sense they are "formal" and therefore "pure."
The task of "pure" or strictly "formal"logic,13 on Husserl's view, is to identify certain simple propositions about propositions, whose truth can be grasped by reflection upon propositions generally, and which can provide intuitively justified axioms and rules of inference for deriving all true propositions about propositions that are true or false in virtue of their form, and about the logical relationships between propositions. In accomplishing this task it has to be very careful to avoid circularity. Husserl says:
"Pure logic ... has the extraordinary difficult task of analytically ascending to such axioms as are indispensable starting-points for deduction, and are also irreducible to one another without a direct or a reflective circle, and then constructing and arranging a deduction for the theorems of logic--of which the rules of the syllogism form a small part--so that at each step, not only the premisses, but also the principles of our deductive transitions, are either among our axioms, or among our previously proved theorems." (Husserl, 1970, p. 177) One sees here--points of philosophical interpretation aside--a very familiar program of logical research which, some have said, was closed out by the discoveries of Kurt Gödel.
So what Pure Logic, and the laws of formal logic, deal with are what Husserl calls "Ideal" entities. The Ideal is the type of being that universals have, which is characterized as being without temporal determination. (Husserl, 1970, pp. 109-110) That is, no universal (including concepts and propositions) is before, after or simultaneously with anything else. And any knowledge we have of them must come from direct, intuitive inspection of them (as with non-contradiction, modus ponens or Barbara Syllogism, to take cases from logic) or from pure deductions from such direct knowledge.
Accordingly we cannot ignore, as "the psychologistic logicians" do, "the fundamental, essential, never-to-be-bridged distinction between ideal and real laws, between normative and causal regulation, between logical and real necessity, between logical and real grounds. No conceivable gradation could mediate between the ideal and the real." (Husserl, 1970, p. 104) The clearing up of the issues around Psychologism depends "on a correct discernment of the most fundamental of epistemological distinctions, the distinction between the real and the ideal, or the correct discernment of all the distinctions into which this distinction can be analyzed." (Husserl, 1970, p. 193)
But we must "stay on guard against misinterpreting the opposition between Ideal and real as lack of relation." (Husserl, 1994, p. 204) The relation of the proposition or concept to the real flow of mental (or linguistic) events is secured by the fact that the proposition is instanced as a quality of corresponding events. And as a quality of whatever real events of thought there may be that instance it, whatever properties and relationships that quality (the proposition) may have will transfer, in an appropriate manner, to the real events.
Thus if a tone A is lower in the scale than E, that implies that all particular soundings of A will be lower than any particular soundings of E. But of course it is possible that there should be no particular soundings of these tones at all. And it is possible that there have been some soundings of one and no soundings of the other. The truth that A is lower in the scale than E has no implications for the actual existence of A or E. It only implies that any sounding of A that would occur would be lower than any sounding of E that would occur.
A similar point can be made with regard to numbers. A number N is greater than a number M. That implies that any concrete group of number N will be larger than any concrete group of number M. But of course there may never be such groups, or there may be one but not the other.
And now to Pure logic. There is perhaps a law of Pure logic according to which some proposition P implies a propositions Q. That does necessitate that any concrete flow of thoughts or beliefs which moves from thoughts that P to thoughts that Q will not move from true thoughts or beliefs to false ones. But it does not imply that there will ever be any actual thoughts or beliefs that P or that Q--real events in the flow of psychic life--and it does not imply that if one thinks or believes that P they will, much less will of necessity, also think or believe that Q. As Husserl graphically says, "No psychological law drives the judging subject under the yoke of logical laws." (Husserl, 1970, p. 119) All that the logical law guarantees in concrete thinking is the particular distribution of truth-values across the propositions instanced in the thinking that the logical law dictates for propositions as such, whether ever instanced or not.
This clearly is a major point about the relationship between the laws of logic and experience. Those laws do not tell you how you have to think, but they certainly tell you how you can think if you would think coherently and consistently. They cannot force you by an unconscious power to follow in your actual thinking a course of thought that will only let you go from truth to more truth, but anyone who consciously chooses to follow such a course of actual thought can be sure they are doing so by subjecting their thinking to the patterns laid out by the laws of formal logic. This is not an insignificant relationship between the laws of logic and experience, and surely it is one that would be very important for any field of study or practice.
But that is not the only connection between "experience" and logic for Husserl. In a certain manner we must "experience" propositions, their parts, and their relations before we can understand the laws of formal logic and know that they are true. Husserl's view is that one can only come to know what the primitive terms of Pure logic refer to by engaging in "the descriptive-psychological illumination of the origin of logical concepts." (Husserl, 1994, p. 199; cp. 251) That is, to understand what the basic terms of logic refer to or mean within the laws of logic--terms like "proposition,""true,""false,""or,""if...then,""An A,""All A's,"--you must view their referents directly, or you simply won't know what the laws of logic are about. And you do this by fixing upon them intuitively as they are present in your own acts of thought-that. "The laws of pure logic are truths rooted in the concept of truth, and in concepts essentially related to this concept." (Husserl, 1970, p. 192)
Now this may help clarify a few further points about Formalism and how its algorithms relate to experience. We do, after all, experience algorithms when we work with them, and they somehow guide our experience of our world. The symbols of the algorithm and the operations upon them are set up to run parallel to the structures of propositions that make up theories about domains of reality. The propositions of the theory are rigorously correlated to the "facts" of the domain, and that is how logical deduction permits us to master the domain far beyond the limits imposed upon us by perception or intuition. Most of what we know about any given domain is known by inference.
But that too is not quite true. For as our powers of perception and intuition are limited, so are our powers of genuine inference based on direct insight into logical connections. There is a soon-reached limit as to what we can hold before our minds in thought. The parallelism between the algorithm and the truths of the domain is the only thing that can deliver us from those limits. This is a huge issue for Husserl. Contrary to what is generally believed, knowledge for him is rarely intuitive. Wesenschau, though utterly essential, is a vanishingly small part of knowledge as a whole. This is why he says early on, and never later retracts it, that "A truly fruitful formal logic constitutes itself from the outset as a logic of signs." (Husserl, 1994, p. 50; cp. 17) The formal disciplines are ones "in which veritably towering thought-piles, and thought-combinations intertwined in a thousand ways, are moved about with the most sovereign freedom, and are spawned in every increasing intricacy by our researches." (Husserl, 1970, p. 201) Our ability to do this is due to "symbolic processes from which the intuitive element, as well as all true understanding and inner evidence are absent, but which are rendered secure because a general proof of the efficiency of the method has been once and for all guaranteed." (Ibid; see also p. 202 and Husserl, 1994, p. 51)
So we can summarize Husserl's realist or absolutist interpretation of the relationship between the laws of formal logic and experience as follows. The laws of formal logic are laws expressing the necessary truth values of propositions, insofar as those truth values are determined merely by the forms of the propositions involved. Propositions are, however, on occasion instanced in concrete acts of thought as properties of those acts: intentional properties, properties of specific ofness and aboutness. The laws of formal logic carry over to concrete thinking because what they are true of (propositions with their truth values) is embedded in those acts, though not in any way dependent upon them. This theory is realist or absolutist because, according to it, the laws of logic do not in any way depend for their meaning or truth upon any mental fact, and especially upon how a particular individual, culture or species may or may not actually think about anything.
The Psychologistic point done justice to: the laws of formal logic do apply to experiences of thought, belief, statement, in the sense that they tell you how truth values must distribute themselves across propositions formally described. Hence a particular thought, belief, or statement may formally contradict or imply another.14 In this sense they might be said to "govern" thinking, but they do not determine what thinking actually happens, and, particularly, they do not force people to think in conformity with them. Finally, the meanings of the basic terms of pure logic can be clarified as to their precise meaning only by intuitive, reflective awareness of propositions instantiated in our own experience. I think it is Husserl's view that this type of reflection is necessary if we are ever to understand what the laws of pure logic say, and if we are to verify the truth of the underived laws of pure logic, from which all the rest must be deduced.
The Formalistic point done justice to: One can arrive at knowledge of a domain by utilizing processes which do not involve thinking about that domain, much less insight into the matters concerned. The logical algorithm provides such processes, though it is not the only one. (Husserl, 1970, pp. 201-204) "Reduction of insight to mechanism in our thought-processes leads to an indirect mastery over those endlessly winding paths of thought that admit of no direct mastery." (Husserl, 1970, p. 201)
The Four Strata in All Scientific Research
One of the most illuminating passages for an understanding of Husserl's Realist theory of logic, with its peculiar answers to the question about the relationship between logic and experience, is '48 of the "Prolegomena." (Husserl, 1970, pp. 185-186)15 In this passage Husserl discusses what he calls "The Fundamental Distinctions" involved in all scientific knowledge. It turns out there are four interrelated strata of structures and their elements in all scientifically organized fields of knowledge.
- The strata of facts or states of affairs. This is the domain of reality to be mastered by the field of knowledge.
- The strata of propositions and concepts expressing the objective matters in 1. These are the truths about the facts or states of affairs in question, which make up any adequate theory about them. For example, certain states of affairs concerning numbers (e.g., very large ones) have never yet been thought by anyone. Yet they exist, and there are true propositions about them with logical relations holding between them, relations that fall under laws of logic with which we are now familiar.
- The strata of "cognitive experiences, in which science is subjectively realized, a psychological pattern of connection among the presentations, judgments, insights, surmises, questions etc., in which research is carried out, in which a theory already discovered receives its insightful thinking out." (Husserl, 1970, p. 185)
- The strata of algorithmic symbols and operations in which the elements of 2 can be encoded to allow 3 to grasp 1.
Now in fact Husserl does not list 4 as on a par with 1-3, no doubt because he thought of 4 as merely an instrument of 3. But his understanding of formal logic as fundamentally a theory of algorithms makes it clear that 4 is extremely important, and must be properly understood if we are to grasp his theory of logic and how it does justice both to what is important about Formalism and to what is important about Psychologism.
"Logic without Metaphysics"
Now I conclude by considering what I take to be one of the most likely objections to this theory of logic from the contemporary perspective. The objection is associated with the idea of "Logic without Metaphysics." Any theory of logic must, it has been assumed in recent decades, be non-committal on ontological issues. No doubt it is true that in order to have a respectable theory of logic one need not first have elaborated a general theory of reality. But the theories which take this line of an ontologically uncommitted logic do nevertheless assign a specific subject matter to "logicians' truths." That is unavoidable. Usually today, as we have indicated, it will be linguistic, either formal or 'ordinary'. The alternative to some substantive degree of ontological commitment would be to say that logicians' truths are about nothing at all, or that individual logicians can make their truths to be about anything they please, or that there are no logician's truths, and that logic is not a field of knowledge.
Now I don't think any of these alternatives are ultimately sustainable, and in any case those who take them will have to account for the facts that algorithms do, in obvious ways, allow us to master domains to knowledge and reality, and that the laws of formal logic do govern actual thinking and speaking in a certain way, and can be used to guide it, though it need not guide it.
The idea that one can speak about symbols and language in a philosophically innocent way is simply an illusion that, at one time, perhaps was necessary to allow people to continue to do philosophy while totally rejecting its past. But it is an illusion to think one can do logical analysis of language without a presupposed ontology of language itself. I have tried to show precisely why it is an illusion in an earlier paper of mine. (Willard, 1983)
The objection to the heavy ontological commitments of Husserl's theory of logic (and mind) can, however, be translated into objections to the particular ontological commitments this theory makes: for example, Platonism, truth, objective facts and states of affairs, etc. etc. Here is not the place to try to defend these, though they of course must be defended someplace. But the objection of heavy ontological commitments as such is, I think, not an objection at all, but a recommendation. This stands out when one looks at the works of others who have tried to avoid it. If one does avoids it, one simply cannot have a theory of formal logic in the sense we have been trying to talk about it in this paper. You have to be able to explain how whatever it is you think the laws of logic do or what they are about hooks up with algorithms and what they do, on the one hand, and actual events of thought and discourse on the other.
Wittgenstein, for example, whether the first or the second, simply has no theory of formal logic. He does not have an account (analysis, interpretation) of the mental event or act, and, specifically, of the sense perceptible word or sentence or utterance (type or token), and how it is to be integrated with the "rules of use" and "form of life" existing in a society where a language is spoken, on the one hand, and the particular behaviors of thought and action in the individual, on the other. He simply has no account of all this, not even the beginnings of one.
A similar point is to be made of Quine's "Web of Belief" (including as a central component the laws of logic), the physical organism and the social context. And a similar point is to be made of Heidegger, who, quite intentionally, spurns the very project of an analysis of acts of consciousness and regards formal logic as of vanishingly small philosophical interest.
It is interesting--perhaps it will be infuriating to some--to observe that, in this respect at least, all three of these philosophers turn out to be speculative, not analytic philosophers, each in his own way operating from a set of a priori assumptions or conclusions about the essence of language, and moving to general inclusive views of mind and reality. They operate from certain general points about what thought, language, logic and reality must be, and they never fill in the blanks. Husserl does try to fill in the blanks, and provide a clear picture of how the laws of logic fit into mind, scientific techniques and reality.
Now I make this remark only as an observation, not a criticism. It may be we can do nothing more than the three philosophers mentioned do. I think that in this regard Husserl is at least more forthcoming about what he is doing. It is virtually impossible to elicit from the others, by contrast, any account of the relation between formal (or other!) logic and experience.
- See Fisher, 1987, and Toulmin, 1958. Return to text.
- See Ryle, 1954, chapter VIII, and Strawson, 1952, chapters 1 and 2. Return to text.
- I have developed this point at length in Willard, 1997. Return to text.
- All references to Husserl's Logical Investigations will be to the English translation by J. N. Findlay, Husserl, 1970. Return to text.
- I have developed both these tendencies at great length in Willard, 1984, pp.136-166. Return to text
- The extensive writings in which Husserl painstakingly elaborated his critique of Formalism are not well know. Most of them are now published in English translation in Husserl, 1994, pp. 20-138 and 197-206. Return to text
- On the logical superiority of a method of mere operation on sense-perceptible signs, see Husserl, 1970b, pp. 241-243. Return to text
- See Husserl, 1994, pp. 49-51. Return to text
- See Willard, 1984, pp. 136-143 for further discussion of these points. Return to text
- For a much fuller exposition of these points see Willard, 1984, pp. 143-166. Return to text.
- For further discussion of this "turn" and its problems for a philosophy of logic, see Willard, 1989. Return to text.
- I have carefully specified the (very largely) common view of the proposition among logical theorists of the early 20th Century in Willard, 1984, pp. 180-186. See also Willard, 1972. Return to text.
- The use of "formal logic" as equivalent to "symbolic logic" is a mid-Twentieth Century usage. Frege and Russell, for example, never understood "formal" to mean "symbolic." For more on this and Carnap's role in the change see Willard, 1997. Return to text.
- The following passage is very helpful on Husserl's view of how the pure laws apply to individual mental events: "The distinction between the psychological mode of treatment, whose terms function as class-terms for mental states, and the objective or ideal mode of treatment where the same terms stand for ideal genera and species, is not a subsidiary, or a merely subjective distinction. It determines the difference between essentially distinct sciences. Pure logic and arithmetic, as sciences dealing with the ideal singulars belonging to certain genera (or of what is founded a priori in the ideal essence of these genera) are separated from psychology, which deals with the individual singulars belonging to certain empirical classes." (Husserl, 1970, pp. 184-185) Return to text.
- See also '' 61 and 62 of the "Prolegomena," and Husserl, 1994, pp. 378-381, as well as Willard, 1984, 194ff. Return to text.
Fisher, Walter R., 1987, Human Communication as Narration: Toward a Philosophy of Reason, Value, and Action, University of South Carolina Press, 201.
Husserl, Edmund: 1970, Logical Investigations, Humanities Press, New York, pp. xvii, 877. First edition in two volumes, 1900-1901, 877. Husserl, Edmund: 1970b, Philosophie der Arithmetik: 1890-1901, "Husserliana XII," Martinus Nijhoff, Den Haag, pp. xxvix, 585. First edition of Philosophie der Arithmetik, 1891.
Husserl, Edmund: 1994, Early Writings in the Philosophy of Logic and Mathematics, translated by Dallas Willard, Kluwer Academic Publishers, Dordrecht, pp. xlviii, 505.
Ryle, Gilbert, Dilemmas, Cambridge University Press, London, 1954, 129.
Strawson, P. F., Introduction to Logical Theory, Methuen & Co. LTD, London, 1952, 263.
Tarski, Alfred, Introduction to Logic and to the Methodology of Deductive Sciences, Oxford University Press, New York, 1965, 252.
Toulmin, Stephen, The Uses of Argument, Cambridge University Press, Cambridge, Eng., 1958, 264.
Willard, Dallas: 1972, "The Paradox of Logical Psychologism: Husserl's Way Out,"American Philosophical Quarterly, IX, #1 (January 1972), pp. 94-100.
Willard, Dallas: 1983, "Why Semantic Ascent Fails,"Metaphilosophy, XIV, #3-4, (July/October 1983), pp. 276-290.
Willard, Dallas: 1984, Logic and the Objectivity of Knowledge, Ohio University Press, Athens, OH., pp. xv, 277.
Willard, Dallas: 1989, "The Case Against Quine's Case for Psychologism,"Perspectives on Psychologism, edited by Mark Notturno, E. J. Brill, New York, pp. 286-295.
Willard, Dallas: 1997, "Degradation of Logical Form,"Axiomathes, VIII, #1-3, (December 1997), pp. 31-52.