Case Study Meaning And Definition Of Philosophy

Research philosophy is a vast topic and here we will not be discussing this topic in great details. In business and economics dissertations at Bachelor’s level, you are not expected to discuss research philosophy in a great level of depth, and about one page in methodology chapter devoted to research philosophy usually suffices. For a business dissertation at Master’s level you may need to provide more discussion of the philosophy of your study, but even there, about two pages of discussions has to be accepted as sufficient by your supervisor.

Discussion of research philosophy in your dissertation should include the following:

  1. You need to specify the research philosophy of your study. Your research philosophy can be pragmatism, positivism, realism or interpretivism as discussed below.
  2. The reasons behind philosophical classifications of the study need to be provided.
  3. You need to discuss the implications of your research philosophy on the research strategy in general and the choice of primary data collection methods in particular.

The Essence of Research Philosophy

Research philosophy deals with the source, nature and development of knowledge[1]. In simple terms, a research philosophy is belief about the ways in which data about a phenomenon should be collected, analysed and used.

Although the idea of knowledge creation may appear to be profound, you are engaged in knowledge creation as part of completing your dissertation. You will collect secondary and primary data and engage in data analysis to answer the research question and this answer marks the creation of new knowledge.

In essence, addressing research philosophy in your dissertation involves being aware and formulating your beliefs and assumptions.  As it is illustrated in figure below, the identification of the research philosophy is positioned at the outer layer of the ‘research onion, accordingly it is the first  topic to be clarified in research methodology chapter of your dissertation.

Research philosophy in the ‘research onion’[2]

Each stage of the research process is based on assumptions about the sources and the nature of knowledge. The research philosophy will reflect the author’s important assumptions and these assumptions serve as base for the research strategy. Generally, research philosophy has many branches related to a wide range of disciplines. Within the scope of business studies in particular there are four main research philosophies:

  1. Pragmatism
  2. Positivism
  3. Realism
  4. Interpretivism (Interpretivist)

The Choice of Research Philosophy

The choice of a specific research philosophy is impacted by practical implications. There are important philosophical differences between studies that focus on facts and numbers such as an analysis of the impact of foreign direct investment on the level of GDP growth and qualitative studies such as an analysis of leadership style on employee motivation in organizations.

The choice between positivist and interpretivist research philosophies or between quantitative and qualitative research methods has traditionally represented a major point of debate. However, the latest developments in the practice of conducting studies have increased the popularity of pragmatism and realism philosophies as well.

Moreover, as it is illustrated in table below, there are popular data collection methods associated with each research philosophy.

Pragmatism Positivism Realism Interpretivism
Popular data collection methodMixed or multiple

method designs,

quantitative and qualitative

Highly structured,

large samples,

measurement, quantitative, but can use qualitative

Methods chosen must fit the subject matter, quantitative or qualitativeSmall samples, in-depth

investigations, qualitative

 Research philosophies and data collection methods[3]

My e-book, The Ultimate Guide to Writing a Dissertation in Business Studies: a step by step assistance contains discussions of theory and application of research philosophy. The e-book also explains all stages of the research process starting from the selection of the research area to writing personal reflection. Important elements of dissertations such as research philosophy, research approach, research design, methods of data collection and data analysis are explained in this e-book in simple words.

John Dudovskiy

[1] Bajpai, N. (2011) “Business Research Methods” Pearson Education India

[2] Source: Saunders, M., Lewis, P. & Thornhill, A. (2012) “Research Methods for Business Students” 6th edition, Pearson Education Limited

[3] Table adapted from Saunders, M., Lewis, P. & Thornhill, A. (2012) “Research Methods for Business Students” 6th edition, Pearson Education Limited

This supplement collects together various definitions and descriptions of analysis that have been offered in the history of philosophy (including all the classic ones), to indicate the range of different conceptions and the issues that arise. (There are also some remarks on related topics such as analyticity, definition, and methodology more generally.) In most cases, abbreviated references are given; full details can be found in the Annotated Bibliography on Analysis, in the section mentioned in curly brackets after the relevant definition or description. Where there is more than passage quoted from a particular author, passages are numbered in chronological order of composition (as far as that can be determined).

  • it is not the same thing to take an argument in one’s hand and then to see and solve its faults, as it is to be able to meet it quickly while being subjected to questions; for what we know, we often do not know in a different context. Moreover, just as in other things speed or slowness is enhanced by training, so it is with arguments too, so that supposing we are unpractised, even though a point is clear to us, we are often too late for the right moment. Sometimes too it happens as with diagrams; for there we can sometimes analyse the figure, but not construct it again: so too in refutations, though we know on what the connexion of the argument depends, we still are at a loss to split the argument apart. (SR, 16, 175a20-30) {§2.4}

  • We must next explain how to reduce syllogisms to the figures previously described; this part of our inquiry still remains. For if we examine the means by which syllogisms are produced, and possess the ability to discover them, and can also analyse [analuoimen] the syllogisms when constructed into the figures previously described, our original undertaking will be completed. ((PrA, I, 32, 46b40-47a6; Tredennick tr. slightly modified) {§2.4}

  • Thus it is evident (1) that the types of syllogism which cannot be analysed in these figures [viz., second figure syllogisms into the third figure, and third figure syllogisms into the second figure] are the same as those which we saw could not be analysed into the first figure; and (2) that when syllogisms are reduced to the first figure these alone are established per impossibile.

    It is evident, then, from the foregoing account [taken as including the discussion prior to chapter 45] how syllogisms should be reduced; and also that the figures can be analysed into one another. (PrA, I, 45, 51a40-b5; Tredennick tr., substituting ‘analysed’ for ‘resolved’) {§2.4}

  • If it were impossible to prove truth from falsehood, it would be easy to make analyses [analuein]; for then the propositions would convert from necessity. Let A be something that is the case; and if A is the case, then these things are the case (things which I know to be the case—call them B). From the latter, then, I shall prove that the former is the case. (In mathematics conversion is more common because mathematicians assume nothing incidental—and in this too they differ from those who argue dialectically—but only definitions.) (PoA, I, 12, 78a6-13) {§2.4}

  • We deliberate not about ends but about means. For a doctor does not deliberate whether he shall heal, nor an orator whether he shall convince, nor a statesman whether he shall produce law and order, nor does any one else deliberate about his end. Having set the end, they consider how and by what means it is to be attained; and if it seems to be produced by several means they consider by which it is most easily and best produced, while if it is achieved by one only they consider how it will be achieved by this and by what means this will be achieved, till they come to the first cause, which in the order of discovery is last. For the person who deliberates seems to inquire and analyse in the way described as though he were analysing a geometrical construction (not all inquiry appears to be deliberation—for instance mathematical inquiries—but all deliberation is inquiry), and what is last in the order of analysis seems to be first in the order of becoming. And if we come on an impossibility, we give up the search, e.g. if we need money and this cannot be got; but if a thing appears possible we try to do it. (NE, III, 3, 1112b8-27) {§2.4}

  • The art of arranging a series of thoughts properly, either for discovering the truth when we do not know it, or for proving to others what we already know, can generally be called method.

    Hence there are two kinds of method, one for discovering the truth, which is known as analysis, or the method of resolution, and which can also be called the method of discovery. The other is for making the truth understood by others once it is found. This is known as synthesis, or the method of composition, and can also be called the method of instruction.

    Analysis does not usually deal with the entire body of a science, but is used only for resolving some issue. (LAT, 233-4) {§4.1}

  • Now analysis consists primarily in paying attention to what is known in the issue we want to resolve. The entire art is to derive from this examination many truths that can lead us to the knowledge we are seeking.

    Suppose we wondered whether the human soul is immortal, and to investigate it we set out to consider the nature of the soul. First we would notice that it is distinctive of the soul to think, and that it could doubt everything without being able to doubt whether it is thinking, since doubting is itself a thought. Next we would ask what thinking is. Since we would see nothing contained in the idea of thought that is contained in the idea of the extended substance called body, and since we could even deny of thought everything belonging to body - such as having length, width, and depth, having different parts, having a certain shape, being divisible, etc. - without thereby destroying the idea we have of thought, from this we would conclude that thought is not at all a mode of extended substance, because it is the nature of a mode not to be able to be conceived while the thing of which it is a mode is denied. From this we infer, in addition, that since thought is not a mode of extended substance, it must be the attribute of another substance. Hence thinking substance and extended substance are two really distinct substances. It follows from this that the destruction of one in no way brings about the destruction of the other, since even extended substance is not properly speaking destroyed, but all that happens in what we call destruction is nothing more than the change or dissolution of several parts of matter which exist forever in nature. Likewise it is quite easy to judge that in breaking all the gears of a clock no substance is destroyed, although we say that the clock is destroyed. This shows that since the soul is in no way divisible or composed of parts, it cannot perish, and consequently is immortal.

    This is what we call analysis or resolution. We should notice, first, that in this method - as in the one called composition - we should practice proceeding from what is better known to what is less known. For there is no true method which could dispense with this rule.

    Second, it nevertheless differs from the method of composition in that these known truths are taken from a particular examination of the thing we are investigating, and not from more general things as is done in the method of instruction. Thus in the example we presented, we did not begin by establishing these general maxims: that no substance perishes, properly speaking; that what is called destruction is only a dissolution of parts; that therefore what has no parts cannot be destroyed, etc. Instead we rose by stages to these general notions.

    Third, in analysis we introduce clear and evident maxims only to the extent that we need them, whereas in the other method we establish them first, as we will explain below.

    Fourth and finally, these two methods differ only as the route one takes in climbing a mountain from a valley differs from the route taken in descending from the mountain into the valley, or as the two ways differ that are used to prove that a person is descended from St. Louis. One way is to show that this person had a certain man for a father who was the son of a certain man, and that man was the son of another, and so on up to St. Louis. The other way is to begin with St. Louis and show that he had a certain child, and this child had others, thereby descending to the person in question. This example is all the more appropriate in this case, since it is certain that to trace an unknown genealogy, it is necessary to go from the son to the father, whereas to explain it after finding it, the most common method is to begin with the trunk to show the descendants. This is also what is usually done in the sciences where, after analysis is used to find some truth, the other method is employed to explain what has been found.

    This is the way to understand the nature of analysis as used by geometers. Here is what it consists in. Suppose a question is presented to them, such as whether it is true or false that something is a theorem, or whether a problem is possible or impossible; they assume what is at issue and examine what follows from that assumption. If in this examination they arrive at some clear truth from which the assumption follows necessarily, they conclude that the assumption is true. Then starting over from the end point, they demonstrate it by the other method which is called composition. But if they fall into some absurdity or impossibility as a necessary consequence of their assumption, they conclude from this that the assumption is false and impossible.

    This is what may be said in a general way about analysis, which consists more in judgment and mental skill than in particular rules. (LAT, 236-8) {§4.1}

  • It is advisable to stress the point that philosophy, as we understand it, is wholly independent of metaphysics, inasmuch as the analytic method is commonly supposed by its critics to have a metaphysical basis. Being misled by the associations of the word ‘analysis’, they assume that philosophical analysis is an activity of dissection; that it consists in ‘breaking up’ objects into their constituent parts, until the whole universe is ultimately exhibited as an aggregate of ‘bare particulars’, united by external relations. If this were really so, the most effective way of attacking the method would be to show that its basic presupposition was nonsensical. For to say that the universe was an aggregate of bare particulars would be as senseless as to say that it was Fire or Water or Experience. It is plain that no such possible observation would enable to veify such an assertion. But, so far as I know, this line of criticism is in fact never adopted. The critics content themselves with pointing out that few, if any, of the complex objects in the world are simply the sum of their parts. They have a structure, an organic unity, which distinguishes them, as genuine wholes, from mere aggregates. But the analyst, so it is said, is obliged by his atomistic metaphysics to regard an object consisting of parts a, b, c, and d, in a distinctive configuration as being simply a + b + c + d, and thus gives an entirely false account of its nature.

    If we follow the Gestalt psychologists, who of all men talk most constantly about genuine wholes, in defining such a whole as one in which the properties of every part depend to some extent on its position in the whole, then we may accept it as an empirical fact that there exist genuine, or organic, wholes. And if the analytic method involved a denial of this fact, it would indeed be a faulty method. But, actually, the validity of the analytic method is not dependent on any empirical, much less any metaphysical, presupposition about the nature of things. For the philosopher, as an analyst, is not directly concerned with the physical properties of things. He is concerned only with the way in which we speak about them.

    In other words, the propositions of philosophy are not factual, but linguistic in character – that is, they do not describe the behaviour of physical, or even mental, objects; they express definitions, or the formal consequences of definitions. Accordingly, we may say that philosophy is a department of logic. For we shall see that the characteristic mark of a purely logical inquiry is that it is concerned with the formal consequences of our definitions and not with questions of empirical fact.

    It follows that philosophy does not in any way compete with science. The difference in type between philosophical and scientific propositions is such that they cannot conceivably contradict one another. And this makes it clear that the possibility of philosophical analysis is independent of any empirical assumptions. That it is independent of any metaphysical assumptions should be even more obvious still. For it is absurd to suppose that the provision of definitions, and the study of their formal consequences, involves the nonsensical assertion that the world is composed of bare particulars, or any other metaphysical dogma.

    What has contributed as much as anything to the prevalent misunderstanding of the nature of philosophical analysis is the fact that propositions and questions which are really linguistic are often expressed in such a way that they appear to be factual. A striking instance of this is provided by the proposition that a material thing cannot be in two places at once. This looks like an empirical proposition, and is constantly invoked by those who desire to prove that it is possible for an empirical proposition to be logically certain. But a more critical inspection shows that it is not empirical at all, but linguistic. It simply records the fact that, as the result of certain verbal conventions, the proposition that two sense-contents occur in the same visual or tactual sense-field is incompatible with the proposition that they belong to the same material thing. And this is indeed a necessary fact. But it has not the least tendency to show that we have certain knowledge about the empirical properties of objects. For it is necessary only because we happen to use the relevant words in a particular way. There is no logical reason why we should not so alter our definitions that the sentence ‘A thing cannot be in two places at once’ comes to express a self-contradiction instead of a necessary truth. (1936, 75-7) {§6.7}

  • From our assertion that philosophy provides definitions, it must not be inferred that it is the function of the philosopher to compile a dictionary, in the ordinary sense. For the definitions which philosophy is required to provide are of a different kind from those which we expect to find in dictionaries. In a dictionary we look mainly for what may be called explicit definitions; in philosophy, for definitions in use. ...

    We define a symbol in use, not by saying that it is synonymous with some other symbol, but by showing how the sentences in which it significantly occurs can be translated into equivalent sentences, which contain neither the definiendum itself, nor any of its synonyms. A good illustration of this process is provided by Bertrand Russell’s so-called theory of descriptions, which is not a theory at all in the ordinary sense, but an indication of the way in which all phrases of the form ‘the so-and-so’ are to be defined. (Ibid., 80-1) {§6.7}

  • [A serious mistake in my account in Language, Truth and Logic] was my assumption that philosophical analysis consisted mainly in the provision of ‘definitions in use’. It is, indeed, true that what I describe as philosophical analysis is very largely a matter of exhibiting the inter-relationship of different types of propositions; but the cases in which this process actually yields a set of definitions are the exception rather than the rule. ...

    ... Thus, when Professor Moore suggests that to say that ‘existence is not a predicate’ may be a way of saying that ‘there is some very important difference between the way in which “exist” is used in such a sentence as “Tame tigers exist” and the way in which “growl” is used in “Tame tigers growl”’, he does not develop his point by giving rules for the translation of one set of sentences into another. What he does is to remark that whereas it makes good sense to say ‘All tame tigers growl’ or ‘Most tame tigers growl’ it would be nonsense to say ‘All tame tigers exist’ or ‘Most tame tigers exist’. Now this may seem a rather trivial point for him to make, but in fact it is philosophically illuminating. For it is precisely the assumption that existence is a predicate that gives plausibility to ‘the ontological argument’; and the ontological argument is supposed to demonstrate the existence of a God. Consequently Moore by pointing out a peculiarity in the use of the word ‘exist’ helps to protect us from a serious fallacy; so that his procedure, though different from that which Russell follows in his theory of descriptions, tends to achieve the same philosophical end. (1946, 31-3) {§6.7}

  • By intuition is meant the kind of intellectual sympathy by which one places oneself within an object in order to coincide with what is unique in it and consequently inexpressible. Analysis, on the contrary, is the operation which reduces the object to elements already known, that is, to elements common both to it and other objects. To analyse, therefore, is to express a thing as a function of something other than itself. All analysis is thus a translation, a development into symbols, a representation taken from successive points of view from which we note as many resemblances as possible between the new object which we are studying and others which we believe we know already. In its eternally unsatisfied desire to embrace the object around which it is compelled to turn, analysis multiplies without end the number of its points of view in order to complete its always incomplete representation, and ceaselessly varies its symbols that it may perfect the always imperfect translation. It goes on, therefore, to infinity. But intuition, if intuition is possible, is a simple act. (1903, 6-7) {§5.1}

  • [Analysis] operates always on the immobile, whilst intuition places itself in mobility, or, what comes to the same thing, in duration. There lies the very distinct line of demarcation between intuition and analysis. The real, the experienced and the concrete are recognised by the fact that they are variability itself, the element by the fact that it is invariable. And the element is invariable by definition, being a diagram, a simplified reconstruction, often a mere symbol, in any case a motionless view of the moving reality. (1903, 40-1) {§5.1}

  • Modern science is neither one nor simple. It rests, I freely admit, on ideas which in the end we find clear; but these ideas have gradually become clear through the use made of them; they owe most of their clearness to the light which the facts, and the applications to which they led, have by reflection shed on them - the clearness of a concept being scarcely anything more at bottom than the certainty, at last obtained, of manipulating the concept profitably. At its origin, more than one of these concepts must have appeared obscure, not easily reconcilable with the concepts already admitted into science, and indeed very near the borderline of absurdity. This means that science does not proceed by an orderly dovetailing together of concepts predestined to fit each other exactly. True and fruitful ideas are so many close contacts with currents of reality, which do not necessarily converge on the same point. However the concepts in which they lodge themselves manage somehow, by rubbing off each other's corners, to settle down well enough together. (1903, 74) {§5.1}

  • It is a very common and most ruinous superstition to suppose that analysis is no alteration, and that, whenever we distinguish, we have at once to do with divisible existence. It is an immense assumption to conclude, when a fact comes to us as a whole, that some parts of it may exist without any sort of regard for the rest. Such naive assurance of the outward reality of all mental distinctions, such touching confidence in the crudest identity of thought and existence, is worthy of the school which so loudly appeals to the name of Experience. ... If it is true in any sense (and I will not deny it) that thought in the end is the measure of things, yet at least this is false, that the divisions we make within a whole all answer to elements whose existence does not depend on the rest. It is wholly unjustifiable to take up a complex, to do any work we please upon it by analysis, and then simply predicate as an adjective of the given these results of our abstraction. These products were never there as such, and in saying, as we do, that as such they are there, we falsify the fact. You can not always apply in actual experience that coarse notion of the whole as the sum of its parts into which the school of ‘experience’ so delights to torture phenomena. If it is wrong in physiology to predicate the results, that are reached by dissection, simply and as such of the living body, it is here infinitely more wrong. The whole that is given to us is a continuous mass of perception and feeling; and to say of this whole, that any one element would be what it is there, when apart from the rest, is a very grave assertion. We might have supposed it not quite self-evident, and that it was possible to deny it without open absurdity. (PL, §64/ WLM, 77-8) {§5.6}

  • judgement is the differentiation of a complex whole, and hence always is analysis and synthesis in one. (AR, 149/WLM, 158) {§5.6}

  • At any moment my actual experience, however relational its contents, is in the end non-relational. No analysis into relations and terms can ever exhaust its nature or fail in the end to belie its essence. What analysis leaves for ever outstanding is no mere residue, but is a vital condition of the analysis itself. Everything which is got out into the form of an object implies still the felt background against which the object comes, and, further, the whole experience of both feeling and object is a non-relational immediate felt unity. The entire relational consciousness, in short, is experienced as falling within a direct awareness. This direct awareness is itself non-relational. It escapes from all attempts to exhibit it by analysis as one or more elements in a relational scheme, or as that scheme itself, or as a relation or relations, or as the sum or collection of any of these abstractions. And immediate experience not only escapes, but it serves as the basis on which the analysis is made. Itself is the vital element within which every analysis still moves, while, and so far as, and however much, that analysis transcends immediacy. (ETR, 176/WLM, 280-1) {§5.6}

  • I would rather now lay more stress on the logical vice of all Analysis and Abstraction – so far as that means taking any feature in the Whole of Things as ultimately real except in its union with the Whole. (Collected Works of F.H. Bradley: Selected Correspondence 1905-1924, Bristol, Thoemmes Press, 1999, 275)

  • Analysis and synthesis I take in the end to be two aspects of one principle … Every analysis proceeds from and on the basis of a unity ... The point before us is the question as to how, without separation in its existence, we can discriminate ideally in analysis. (ETR, 300)

  • Socratic method is a way of bringing our practices under rational control by expressing them explicitly in a form in which they can be confronted with objections and alternatives, a form in which they can be exhibited as the conclusions of inferences seeking to justify them on the basis of premises advanced as reasons, and as premises in further inferences exploring the consequences of accepting them. (2000, 56) {§6.9}

  • I think of analytic philosophy as having at its center a concern with semantic relations between what I will call ‘vocabularies’. … Its characteristic form of question is whether and in what way one can make sense of the meanings expressed by one kind of locution interms of the meanings expressed by another kind of locution. So, for instance, two early paradigmatic projects were to show that everything expressible in the vocabulary of number-theory, and again, everything expressible using definite descriptions, is expressible already in the vocabulary of first-order quantificational logic with identity.

    The nature of the key kind of semantic relation between vocabularies has been variously characterized during the history of analytic philosophy: as analysis, definition, paraphrase, translation, reduction of different sorts, truth-making, and various kinds of supervenience—to name just a few contenders. In each case, however, it is characteristic of classical analytic philosophy that logical vocabulary is accorded a privileged role in specifying these semantic relations. It has always been taken at least to be licit to appeal to logical vocabulary in elaborating the relation between analysandum and analysans—target vocabulary and base vocabulary—and, according to stronger versions of this thesis, that may be the only vocabulary it is licit to employ in that capacity. I will refer to this aspect of the analytic project as its commitment to ‘semantic logicism’. (2006, Lecture One, §1) {§6.9}

  • What I want to call the “classical project of analysis”, then, aims to exhibit the meanings expressed by various target vocabularies as intelligible by means of the logical elaboration of the meanings expressed by base vocabularies thought to be privileged in some important respects—epistemological, ontological, or semantic—relative to those others. This enterprise is visible in its purest form in what I have called the “core programs” of empiricism and naturalism, in their various forms. In my view the most significant conceptual development in this tradition—the biggest thing that ever happened to it—is the pragmatist challenge to it that was mounted during the middle years of the twentieth century. Generically, this movement of thought amounts to a displacement from the center of philosophical attention of the notion of meaning in favor of that of use: in suitably broad senses of those terms, replacing concern with semantics by concern with pragmatics. (Ibid., Lecture One, §2) {§6.9}

  • the analysis or, more precisely, quasi-analysis of an entity that is essentially an indivisible unit into several quasi-constituents means placing the entity in several kinship contexts on the basis of a kinship relation, where the unit remains undivided. (1928a, §71; English tr. by Rolf A. George slightly altered) {§6.7}

  • The logical analysis of a particular expression consists in the setting-up of a linguistic system and the placing of that expression in this system. (1936, 143) {§6.7}

  • That part of the work of philosophers which may be held to be scientific in its nature—excluding the empirical questions which can be referred to empirical science—consists of logical analysis. The aim of logical syntax is to provide a system of concepts, a language, by the help of which the results of logical analysis will be exactly formulable. Philosophy is to be replaced by the logic of science—that is to say, by the logical analysis of the concepts and sentences of the sciences, for the logic of science is nothing other than the logical syntax of the language of science. (1937, xiii) {§6.7}

  • The task of making more exact a vague or not quite exact concept used in everyday life or in an earlier stage of scientific or logical development, or rather of replacing it by a newly constructed, more exact concept, belongs among the most important tasks of logical analysis and logical construction. We call this the task of explicating, or of giving an explication for, the earlier concept … (1947, 8-9) {§6.7}

  • By the procedure of explication we mean the transformation of an inexact, prescientific concept, the explicandum, into a new exact concept, the explicatum. Although the explicandum cannot be given in exact terms, it should be made as clear as possible by informal explanations and examples. ...

    The term ‘explicatum’ has been suggested by the following two usages. Kant calls a judgement explicative if the predicate is obtained by analysis of the subject. Husserl, in speaking about the synthesis of identification between a confused, nonarticulated sense and a subsequently intended distinct, articulated sense, calls the latter the ‘Explikat’ of the former. (For both uses see Dictionary of philosophy [1942], ed. D. Runes, p. 105). What I mean by ‘explicandum’ and ‘explicatum’ is to some extent similar to what C.H. Langford calls ‘analysandum’ and ‘analysans’: “the analysis then states an appropriate relation of equivalence between the analysandum and the analysans” [Langford 1942, 323 {§6.4}]; he says that the motive of an analysis “is usually that of supplanting a relatively vague idea by a more precise one” (ibid., p. 329).

    (Perhaps the form ‘explicans’ might be considered instead of ‘explicatum’; however, I think that the analogy with the terms ‘definiendum’ and ‘definiens’ would not be useful because, if the explication consists in giving an explicit definition, then both the definiens and the definiendum in this definition express the explicatum, while the explicandum does not occur.) The procedure of explication is here understood in a wider sense than the procedures of analysis and clarification which Kant, Husserl, and Langford have in mind. The explicatum (in my sense) is in many cases the result of analysis of the explicandum (and this has motivated my choice of the terms); in other cases, however, it deviates deliberately from the explicandum but still takes its place in some way; this will become clear by the subsequent examples. (1950, 3) {§6.7}

  • Socrates was essentially the inventor of a method. ... His revolt against the study of nature was essentially a revolt against observation in favour of thought; and whereas mathematical method, as an example of thought, had already been discovered by his predecessors, his own discovery was that a similar method, for which he invented an appropriate technique, could be applied to ethical questions. This technique, as he himself recognized, depended on a principle which is of great importance to any theory of philosophical method: the principle that in a philosophical inquiry what we are trying to do is not to discover something of which until now we have been ignorant, but to know better something which in some sense we knew already; not to know it better in the sense of coming to know more about it, but to know it better in the sense of coming to know it in a different and better way—actually instead of potentially, or explicitly instead of implicitly, or in whatever terms the theory of knowledge chooses to express the difference: the difference itself has been a familiar fact ever since Socrates pointed it out. (1933, 10-11) {§5.6}

  • [The] work of disentangling and arranging questions, which ... I [call] analysis, may be alternatively described as the work of detecting presuppositions. ... The analysis which detects absolute presuppositions I call metaphysical analysis; but as regards procedure and the qualifications necessary to carry it out there is no difference whatever between metaphysical analysis and analysis pure and simple ... (1940, 39-40) {§5.6}

  • It is only by analysis that any one can ever come to know either that he is making any absolute presuppositions at all or what absolute presuppositions he is making.

    Such analysis may in certain cases proceed in the following manner. If the inquirer can find a person to experiment upon who is well trained in a certain type of scientific work, intelligent and earnest in his devotion to it, and unaccustomed to metaphysics, let him probe into various presuppositions that his ‘subject’ has been taught to make in the course of his scientific education, and invite him to justify each or alternatively to abandon it. If the ‘inquirer’ is skilful and the ‘subject’ the right kind of man, these invitations will be contemplated with equanimity, and even with interest, so long as relative presuppositions are concerned. But when an absolute presupposition is touched, the invitation wil be rejected, even with a certain degree of violence.

    The rejection is a symptom that the ‘subject’, co-operating with the work of analysis, has come to see that the presupposition he is being asked to justify or abandon is an absolute presupposition; and the violence with which it is expressed is a symptom that he feels the importance of this absolute presupposition for the kind of work to which he is devoted. This is what ... I called being ‘ticklish in one’s absolute presuppositions’; and the reader will see that this ticklishness is a sign of intellectual health combined with a low degree of analytical skill. A man who is ticklish in that way is a man who knows, ‘instinctively’ as they say, that absolute presuppositions do not need justification. (Ibid., 43-4) {§5.6}

  • metaphysical analysis, the discovery that certain presuppositions actually made are absolute presuppositions, is an integral part or an indispensable condition, you can put it whichever way you like, of all scientific work.(Ibid., 84) {§5.6}

  • [discussing his ‘Rule Four’: “We need a method if we are to investigate the truth of things”] … the human mind has within it a sort of spark of the divine, in which the first seeds of useful ways of thinking are sown, seeds which, however neglected and stifled by studies which impede them, often bear fruit of their own accord. This is our experience in the simplest of sciences, arithmetic and geometry: we are well aware that the geometers of antiquity employed a sort of analysis which they went on to apply to the solution of every problem, though they begrudged revealing it to posterity. At the present time a sort of arithmetic called ‘algebra’ is flourishing, and this is achieving for numbers what the ancients did for figures. (Rules for the Direction of the Mind, in PW, I, 16-17) {§4.2}

  • As for the method of demonstration, this divides into two varieties: the first proceeds by analysis and the second by synthesis.

    Analysis shows the true way by means of which the thing in question was discovered methodically and as it were a priori, so that if the reader is willing to follow it and give sufficient attention to all points, he will make the thing his own and understand it just as perfectly as if he had discovered it for himself. But this method contains nothing to compel belief in an argumentative or inattentive reader; for if he fails to attend even to the smallest point, he will not see the necessity of the conclusion. Moreover there are many truths which - although it is vital to be aware of them - this method often scarcely mentions, since they are transparently clear to anyone who gives them his attention.

    Synthesis, by contrast, employs a directly opposite method where the search is, as it were, a posteriori (though the proof itself is often more a priori than it is in the analytic method). It demonstrates the conclusion clearly and employs a long series of definitions, postulates, axioms, theorems and problems, so that if anyone denies one of the conclusions it can be shown at once that it is contained in what has gone before, and hence the reader, however argumentative or stubborn he may be, is compelled to give his assent. However, this method is not as satisfying as the method of analysis, nor does it engage the minds of those who are eager to learn, since it does not show how the thing in question was discovered.

    It was synthesis alone that the ancient geometers usually employed in their writings. But in my view this was not because they were utterly ignorant of analysis, but because they had such a high regard for it that they kept it to themselves like a sacred mystery.

    Now it is analysis which is the best and truest method of instruction, and it was this method alone which I employed in my Meditations. As for synthesis, which is undoubtedly what you are asking me to use here, it is a method which it may be very suitable to deploy in geometry as a follow-up to analysis, but it cannot so conveniently be applied to these metaphysical subjects.

    The difference is that the primary notions which are presupposed for the demonstration of geometrical truths are readily accepted by anyone, since they accord with the use of our senses. Hence there is no difficulty there, except in the proper deduction of the consequences, which can be done even by the less attentive, provided they remember what has gone before. Moreover, the breaking down of propositions to their smallest elements is specifically designed to enable them to be recited with ease so that the student recalls them whether he wants to or not.

    In metaphysics by contrast there is nothing which causes so much effort as making our perception of the primary notions clear and distinct. Admittedly, they are by their nature as evident as, or even more evident than, the primary notions which the geometers study; but they conflict with many preconceived opinions derived from the senses which we have got into the habit of holding from our earliest years, and so only those who really concentrate and meditate and withdraw their minds from corporeal things, so far as is possible, will achieve perfect knowledge of them. Indeed, if they were put forward in isolation, they could easily be denied by those who like to contradict just for the sake of it. (‘Second Set of Replies’, in PW, II, 110-11) {§4.2}

  • [In replying to the objections that Husserl had raised in his Philosophie der Arithmetik (1891) to Frege’s Grundlagen definitions] If words and combinations of words refer to [bedeuten] ideas, then for any two of them there are only two possibilities: either they designate the same idea or they designate different ideas. In the former case it is pointless to equate them by means of a definition: this is ‘an obvious circle’; in the latter case it is wrong. These are also the objections the author raises, one of them regularly. A definition is also incapable of analysing the sense, for the analysed sense just is not the original one. In using the word to be explained, I either think clearly everything I think when I use the defining expression: we then have the ‘obvious circle’; or the defining expression has a more richly articulated sense, in which case I do not think the same thing in using it as I do in using the word to be explained: the definition is then wrong. One would think that a definition was unobjectionable in the case where the word to be explained had as yet no sense at all, or where we were asked explicitly to regard its sense as non-existent so that it was first given a sense by the definition. But in the last case too, the author refutes the definition by reminding us of the difference between the ideas (p. 107). To evade all objections, one would accordingly have to create a new verbal root and form a word out of it. This reveals a split between psychological logicians and mathematicians. What matters to the former is the sense of the words, as well as the ideas which they fail to distinguish from the sense; whereas what matters to the latter is the thing itself: the Bedeutung of the words. The reproach that what is defined is not the concept but its extension actually affects all mathematical definitions. For the mathematician, it is no more right and no more wrong to define a conic as the line of intersection of a plane with the surface of a circular cone than to define it as a plane curve with an equation of the second degree in parallel coordinates. His choice of one or the other of these expressions or of some other one is guided solely by reasons of convenience and is made irrespective of the fact that the expressions have neither the same sense nor evoke the same ideas. I do not intend by this that a concept and its extension are one and the same, but that coincidence in extension is a necessary and sufficient criterion for the occurrence between concepts of the relation that corresponds to identity [Gleichheit] between objects. (RH, 319-20/FR, 225-6) {§6.2}

  • We come to definitions. Definitions proper must be distinguished from elucidations [Erläuterungen]. In the first stages of any discipline we cannot avoid the use of ordinary words. But these words are, for the most part, not really appropriate for scientific purposes, because they are not precise enough and fluctuate in their use. Science needs technical terms that have precise and fixed Bedeutungen, and in order to come to an understanding about these Bedeutungen and exclude possible misunderstandings, we provide elucidations. Of course in so doing we have again to use ordinary words, and these may display defects similar to those which the elucidations are intended to remove. So it seems that we shall then have to provide further elucidations. Theoretically one will never really achieve one’s goal in this way. In practice, however, we do manage to come to an understanding about the Bedeutungen of words. Of course we have to be able to count on a meeting of minds, on others’ guessing what we have in mind. But all this precedes the construction of a system and does not belong within a system. In constructing a system it must be assumed that the words have precise Bedeutungen and that we know what they are. (LM, 224/FR, 313) {§6.2}

  • We have ... to distinguish two quite different cases:

    1. We construct a sense out of its constituents and introduce an entirely new sign to express this sense. This may be called a ‘constructive definition’ [‘aufbauende Definition’], but we prefer to call it a ‘definition’ tout court.

    2. We have a simple sign with a long-established use. We believe that we can give a logical analysis [Zerlegung] of its sense, obtaining a complex expression which in our opinion has the same sense. We can only allow something as a constituent of a complex expression if it has a sense we recognize. The sense of the complex expression must be yielded by the way in which it is put together. That it agrees with the sense of the long established simple sign is not a matter for arbitrary stipluation, but can only be recognized by an immediate insight. No doubt we speak of a definition in this case too. It might be called an ‘analytic definition’ [‘zerlegende Definition’] to distinguish it from the first case. But it is better to eschew the word ‘definition’ altogether in this case, because what we should here like to call a definition is really to be regarded as an axiom. In this second case there remains no room for an arbitrary stipulation, because the simple sign already has a sense. Only a sign which as yet has no sense can have a sense arbitrarily assigned to it. So we shall stick to our original way of speaking and call only a constructive definition a definition. According to that a definition is an arbitrary stipulation which confers a sense on a simple sign which previously had none. This sense has, of course, to be expressed by a complex sign whose sense results from the way it is put together.

    Now we still have to consider the difficulty we come up against in giving a logical analysis when it is problematic whether this analysis is correct.

    Let us assume that A is the long-established sign (expression) whose sense we have attempted to analyse logically by constructing a complex expression that gives the analysis. Since we are not certain whether the analysis is successful, we are not prepared to present the complex expression as one which can be replaced by the simple sign A. If it is our intention to put forward a definition proper, we are not entitled to choose the sign A, which already has a sense, but we must choose a fresh sign B, say, which has the sense of the complex expression only in virtue of the definition. The question now is whether A and B have the same sense. But we can bypass this question altogether if we are constructing a new system from the bottom up; in that case we shall make no further use of the sign A – we shall only use B. We have introduced the sign B to take the place of the complex expression in question by arbitrary fiat and in this way we have conferred a sense on it. This is a definition in the proper sense, namely a constructive definition.

    If we have managed in this way to construct a system for mathematics without any need for the sign A, we can leave the matter there; there is no need at all to answer the question concerning the sense in which – whatever it may be – this sign had been used earlier. In this way we court no objections. However, it may be felt expedient to use sign A instead of sign B. But if we do this, we must treat it as an entirely new sign which had no sense prior to the definition. We must therefore explain that the sense in which this sign was used before the new system was constructed is no longer of any concern to us, that its sense is to be understood purely from the constructive definition that we have given. In constructing the new system we can take no account, logically speaking, of anything in mathematics that existed prior to the new system. Everything has to be made anew from the ground up. Even anything that we may have accomplished by our analytical activities is to be regarded only as preparatory work which does not itself make any appearance in the new system itself.

    Perhaps there still remains a certain unclarity. How is it possible, one may ask, that it should be doubtful whether a simple sign has the same sense as a complex expression if we know not only the sense of the simple sign, but can recognize the sense of the complex one from the way it is put together? The fact is that if we really do have a clear grasp of the sense of the simple sign, then it cannot be doubtful whether it agrees with the sense of the complex expression. If this is open to question although we can clearly recognize the sense of the complex expression from the way it is put together, then the reason must lie in the fact that we do not have a clear grasp of the sense of the simple sign, but that its outlines are confused as if we saw it through a mist. The effect of the logical analysis of which we spoke will then be precisely this – to articulate the sense clearly. Work of this kind is very useful; it does not, however, form part of the construction of the system, but must take place beforehand. Before the work of construction is begun, the building stones have to be carefully prepared so as to be usable; i.e. the words, signs, expressions, which are to be used, must have a clear sense, so far as a sense is not to be conferred on them in the system itself by means of a constructive definition.

    We stick then to our original conception: a definition is an arbitrary stipulation by which a new sign is introduced to take the place of a complex expression whose sense we know from the way it is put together. A sign which hitherto had no sense acquires the sense of a complex expression by definition. (LM, 227-9/FR, 317-8) {§6.2}

  • The analysis of an idea, as it used to be carried out, was, in fact, nothing else than ridding it of the form in which it had become familiar. To break an idea up into its original elements is to return to its moments, which at least do not have the form of the given idea, but rather constitute the immediate property of the self. This analysis, to be sure, only arrives at thoughts which are themselves familiar, fixed, and inert determinations. But what is thus separated and non-actual is an essential moment; for it is only because the concrete does divide itself, and make itself into something non-actual, that it is self-moving. The activity of dissolution is the power and work of the Understanding, the most astonishing and mightiest of powers, or rather the absolute power. The circle that remains self-enclosed and, like substance, holds its moments together, is an immediate relationship, one therefore which has nothing astonishing about it. But that an accident as such, detached from what circumscribes it, what is bound and is actual only in its context with others, should attain an existence of its own and a separate freedom—this is the tremendous power of the negative; it is the energy of thought, of the pure ‘I’. Death, if that is what we want to call this non-actuality, is of all things the most dreadful, and to hold fast what is dead requires the greatest strength. Lacking strength, Beauty hates the Understanding for asking of her what it cannot do. But the life of Spirit is not the life that shrinks from death and keeps itself untouched by devastation, but rather the life that endures it and maintains itself in it. It wins its truth only when, in utter dismemberment, it finds itself. It is this power, not as something positive, which closes its eyes to the negative, as when we say of something that it is nothing or is false, and then, having done with it, turn away and pass on to something else; on the contrary, Spirit is this power only by looking the negative in the face, and tarrying with it. This tarrying with the negative is the magical power that converts it into being. This power is identical with what we earlier called the Subject, which by giving determinateness an existence in its own element supersedes abstract immediacy, i.e. the immediacy which barely is, and thus is authentic substance: that being or immediacy whose mediation is not outside of it but which is this mediation itself. (PS, ‘Preface’, §32, 18-19)

    [Summary of above passage offered by J.N. Findlay] The analysis of an idea is the removal of its familiarity, its reduction to elements that are the true possessions of the thinking self. In such reduction the idea itself changes and renders itself unreal. The force which effects analysis is that of the Understanding, the most remarkable and absolute of powers, the power of the thinking self and also of death. It is above all marvellous that this thinking self should be able to isolate, and to look at apart, what can only exist as an aspect or ‘moment’ in a living whole. Thinking Spirit can, however, only grasp such a whole by first tearing it into parts, each of which it must look at separately for a while, before putting them back in the whole. The thinking self must destroy an immediate, existent unity in order to arrive at a unity which includes mediation, and is in fact mediation itself. (‘Analysis of the Text’, §32, in PS, 499) {§5.2}

  • every method by which we investigate the causes of things is either compositive, or resolutive, or partly compositive, partly resolutive. And the resolutive is usually called analytic, while the compositive is usually called synthetic. (Logica, ‘On Method’, §1, 289) {§4.1}

  • What philosophers seek to know. Philosophers seek scientific knowledge either simply or indefinitely, that is, they seek to knkow as much as they can when no definite question is proposed or the cause of some definite phenomenon or at least to discover something definite, such as what the cause of light is, or of heat, or gravity, of a figure which has been proposed, and similar things; or in what subject some proposed accident inheres; or which of many accidents is above all conducive to the production of some proposed effect; or in what way particular proposed causes ought to be conjoined in order to produce a definite effect. Because of the variety of the things sought for, sometimes the analytic method, sometimes the synthetic method, and sometimes both ought to be applied.

    The first part, by which principles are found, is purely analytic. Seeing that the causes of all singulars are composed from the causes of universals or simples, it is necessary for those who are looking simply for scientific knowledge, which consists of the knowledge of the causes of all things insofar as this can be achieved, to know the causes of universals or those accidents which are common to all bodies, that is, to every material thing, before they know the causes of singular things, that is, of the accidents by which one thing is distinguished from another. Again, before the causes of those things can be known, it is necessary to know which things are universals. But since universals are contained in the nature of singular things, they must be unearthed by reason, that is, by resolution. For example, let any conception or idea of a singular thing be proposed, say a square. The square is resolved into: plane, bounded by a certain number of lines equal to one another, and right angles. Therefore we have these universals or components of every material thing: line, plane (in which a surface is contained), being bounded, angle, rectitude, and equality. If anyone finds the causes or origin of these, he will put them together as the cause of the square. Again, if he proposes to himself the conception of gold, the ideas of being solid, visible, and heavy (that is, of tending to the center of the earth or of motion downwards) and many others more universal than gold itself, which can be resolved further until one arrives at the most universal, will come from this by resolution. And by this same method of resolving things into other things one will know what those things are, of which, when their causes are known what those things are, of which, when their causes are known and composed one by one, the causes of all singular things are known. We thus conclude that the method of investigating the universal notions of things is purely analytic. (Ibid., §§ 3-4, 291-5) {§4.1}

  • The method of scientific knowledge, civil as well as natural, [starting] from sense-experience and [going] to principles is analytic; while [starting] from principles is synthetic. (Ibid., §7, 301) {§4.1}

  • it is obvious that in the investigation of causes there is a need partly for the analytic method, partly for the synthetic method. The analytic method is needed for understanding the circumstances of the effect one by one; the synthetic method for putting together those things which, single in themselves, act as one. (Ibid., §10, 311) {§4.1}

  • that art of geometers which they call logistic is ... the method according to which by supposing that the thing asked about is true they come upon in reasoning either things known [to be true], from which they can prove the truth of the thing sought, or [they come upon] impossibilities, from which it can be understood that what was supposed [to be true] was false. (Ibid., §19, 329) {§4.1}

  • §1. MATHEMATICS ARRIVES AT ALL ITS DEFINITIONS SYNTHETICALLY, WHEREAS PHILOSOPHY ARRIVES AT ITS DEFINITIONS ANALYTICALLY

    There are two ways in which one can arrive at a general concept: either by the arbitrary combination of concepts, or by separating out that cognition which has been rendered distinct by means of analysis. Mathematics only ever draws up its definitions in the first way. For example, think arbitrarily of four straight lines bounding a plane surface so that the opposite sides are not parallel to each other. Let this figure be called a trapezium. The concept which I am defining is not given prior to the definition itself; on the contrary, it only comes into existence as a result of that definition. Whatever the concept of a cone may ordinarily signify, in mathematics, the concept is the product of the arbitrary representation of a right-angled triangle which is rotated on one of its sides. In this and in all other cases the definition obviously comes into being as a result of synthesis.

    The situation is entirely different in the case of philosophical definitions. In philosophy, the concept of a thing is always given, albeit confusedly or in an insufficiently determinate fashion. The concept has to be analysed; the characteristic marks which have been separated out and the concept which has been given have to be compared with each other in all kinds of contexts; and this abstract thought must be rendered complete and determinate. For example, everyone has a concept of time. But suppose that that concept has to be defined. The idea of time has to be examined in all kinds of relation if its characteristic marks which have been abstracted have to be combined together to see whether they yield an adequate concept; they have to be collated with each other to see whether one characteristic mark does not partly include another within itself. If, in this case, I had tried to arrive at a definition of time synthetically, it would have had to have been a happy coincidence indeed if the concept, thus reached synthetically, had been exactly the same as that which completely expresses the idea of time which is given to us. (IDP, 2:276-7/TP, 248-9) {§4.5}

  • The true method of metaphysics is basically the same as that introduced by Newton into natural science and which has been of such benefit to it. Newton’s method maintains that one ought, on the basis of certain experience and, if need be, with the help of geometry, to seek out the rules in accordance with which certain phenomena of nature occur. (IDP, 2:286/TP, 259) {§4.5}

  • What I am chiefly concerned to establish is this: in metaphysics one must proceed analytically throughout, for the business of metaphysics is actually the analysis of confused cognitions. If this procedure is compared with the procedure which is adopted by philosophers and which is currently in vogue in all schools of philosophy, one will be struck by how mistaken the practice of philosophers is. With them, the most abstracted concepts, at which the understanding naturally arrives last of all, constitute their starting point, and the reason is that the method of the mathematicians, which they wish to imitate throughout, is firmly fixed in their minds. This is why there is a strange difference to be found between metaphysics and all other sciences. In geometry and in the other branches of mathematics, one starts with what is easier and then one slowly advances to the more difficult operations. In metaphysics, one starts with what is the most difficult: one starts with possibility, with existence in general, with necessity and contingency, and so on – all of them concepts which demand great abstraction and close attention. And the reason for this is to be sought chiefly in the fact that the signs for these concepts undergo numerous and imperceptible modifications in use; and the differences between them must not be overlooked. One is told that one ought to proceed synthetically throughout. Definitions are thus set up right at the beginning, and conclusions are confidently drawn from them. Those who practise philosophy in this vein congratulate each other for having learnt the secret of thorough thought from the geometers. What they do not notice at all is the fact that geometers acquire their concepts by means of synthesis, whereas philosophers can only acquire their concepts by means of analysis – and that completely changes the method of thought. ...

    Metaphysics has a long way to go yet before it can proceed synthetically. It will only be when analysis has helped us towards concepts which are understood distinctly and in detail that it will be possible for synthesis to subsume compound cognitions under the simplest cognition, as happens in mathematics. (IDP, 2:289-90/TP, 262-3) {§4.5}

  • Such a system of pure (speculative) reason I hope myself to deliver under the title Metaphysics of Nature, which will be not half so extensive but will be incomparably richer in content than this critique, which had first to display the sources and conditions of its possibility, and needed to clear and level a ground that was completely overgrown. Here I expect from my reader the patience and impartiality of a judge, but there I will expect the cooperative spirit and assistance of a fellow worker; for however completely the principles of the system may be expounded in the critique, the comprehensiveness of the system itself requires also that no derivative concepts should be lacking, which, however, cannot be estimated a priori in one leap, but must be gradually sought out; likewise, just as in the former the whole synthesis of concepts has been exhausted, so in the latter it would be additionally demanded that the same thing should take place in respect of their analysis, which would be easy and more entertainment than labor. (CPR, Axxi) {§4.5}

  • I understand by an analytic of concepts not their analysis, or the usual procedure of philosophical investigations, that of analyzing [zergliedern] the content of concepts that present themselves and bringing them to distinctness, but rather the much less frequently attempted analysis [Zergliederung] of the faculty of understanding itself, in order to research the possibility of a priori concepts by seeking them only in the understanding as their birthplace and analyzing its pure use in general; for this is the proper business of a transcendental philosophy; the rest is the logical treatment of concepts in philosophy in general. We will therefore pursue the pure concepts into their first seeds and predispositions in the human understanding, where they lie ready, until with the opportunity of experience they are finally developed and exhibited in their clarity by the very same understanding, liberated from the empirical conditions attaching to them. (CPR, A65-6/B90-1) {§4.5}

  • [in offering a refutation of Mendelssohn’s proof of the persistence of the soul] If we take the above propositions in a synthetic connection, as valid for all thinking beings, as they must be taken in rational psychology as a system, and if from the category of relation, starting with the proposition “All thinking beings are, as such, substances” we go backward through the series of propositions until the circle closes, then we finally come up against the existence of thinking beings, which in this system are conscious of themselves not only as independent of external things but also as being able to determine themselves from themselves (in regard to the persistence belonging necessarily to the character of a substance). But from this it follows that idealism, at least problematic idealism, is unavoidable in that same rationalistic system, and if the existence of external things is not at all required for the determination of one’s own existence in time, then such things are only assumed, entirely gratuitously, without a proof of them being able to be given.

    If, on the contrary, we follow the analytic procedure, grounded on the “I think” given as a proposition that already includes existence in itself, and hence grounded on modality, and then we take it apart so as to cognize its content, whether and how this I determines its existence in space or time merely through it, then the propositions of the rational doctrine of the soul begin not from the concept of a thinking being in general but from an actuality; and from the way this is thought, after everything empirical has been detached from it, it is concluded what pertains to a thinking being in general ... (CPR, B416-19) {§4.5}

  • Give a philosopher the concept of a triangle, and let him try to find out in his way how the sum of its angles might be related to a right angle. He has nothing but the concept of a figure enclosed by three straight lines, and in it the concept of equally many angles. Now he may reflect on this concept as long as he wants, yet he will never produce anything new. He can analyze [zergliedern] and make distinct the concept of a straight line, or of an angle, or of the number three, but he will not come upon any other properties that do not already lie in these concepts. But now let the geometer take up this question. He begins at once to construct a triangle. Since he knows that two right angles together are exactly equal to all of the adjacent angles that can be drawn at one point on a straight line, he extends one side of his triangle, and obtains two adjacent angles that together are equal to two right ones. Now he divides the external one of these angles by drawing a line parallel to the opposite side of the triangle, and sees that here there arises an external adjacent angle which is equal to an internal one, etc. In such a way, through a chain of inferences that is always guided by intuition, he arrives at a fully illuminating and at the same time general solution of the question. (CPR, A716-7/B744-5) {§4.5}

  • although a mere plan that might precede the Critique of Pure Reason would be unintelligible, undependable, and useless, it is by contrast all the more useful if it comes after. For one will thereby be put in the position to survey the whole, to test one by one the main points at issue in this science, and to arrange many things in the exposition better than could be done in the first execution of the work.

    Here then is such a plan subsequent to the completed work, which now can be laid out according to the analytic method, whereas the work itself absolutely had to be composed according to the synthetic method, so that the science might present all of its articulations, as the structural organization of a quite peculiar faculty of cognition, in their natural connection. (PFM, 4:263/ 13) {§4.5}

  • In the Critique of Pure Reason I worked on this question [Is metaphysics possible at all?] synthetically, namely by inquiring within pure reason itself, and seeking to determine within this source both the elements and the laws of its pure use, according to principles. This work is difficult and requires a resolute reader to think himself little by little into a system that takes no foundation as given except reason itself, and that therefore tries to develop cognition out of its original seeds without relying on any fact whatever. Prolegomena should by contrast be preparatory exercises; they ought more to indicate what needs to be done in order to bring a science into existence if possible, than to present the science itself. They must therefore rely on something already known to be dependable, from which we can go forward with confidence and ascend to the sources, which are not yet known, and whose discovery not only will explain what is known already, but will also exhibit an area with many cognitions that all arise from these same sources. The methodological procedure of prolegomena, and especially of those that are to prepare for a future metaphysics, will therefore be analytic. (PFM, 4:274-5/ 25-6) {§4.5}

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