Two fundamental questions concerned philosophers ever since the inception of epistemology. (a) How do we arrive at knowledge? And (b) How do we know that the arrived knowledge is true? These questions can also be put in a different manner: (a’) What factors make the genesis of knowledge possible? (b’) What factors make knowledge true? Retrospectively we may say, following Reichenbach’s famous distinction, that the two questions relate to the context of discovery and the context of justification respectively.1 Any discussion regarding the context of genesis of scientific knowledge in the contemporary discourse is questioned on the ground that epistemology has nothing to do with the questions of genesis or origin of ideas. Or even if the questions are rated legitimate for epistemology, no formal pattern of genesis is believed to be possible.
However, as we have just stated, such has not been the case since the inception of epistemology. Philosophers have attempted to answer the question of origin of knowledge, ever since knowledge making or seeking has been realized as a component of human nature, as if it is natural for them to do so. Why did this become a natural question to start with? And why is this not so with us in this century, when it is no longer considered that a theory of discovery/invention would naturally form a part of epistemology? Today some philosophers, who find it interesting to address this question, have been addressing this question only by way of defense, with hesitation and with little confidence. So they have to attend in the first place to a meta-philosophical problem of legitimizing the problem, and then attend to the relatively first-order philosophical problem of searching for an order in the context of discovery.
For traditional epistemology the question of finding the method/s of arriving at knowledge has been a necessary problem, because justification of knowledge was thought to be partly, or completely dependent on the basis of generation, i.e., the problem of genesis and justification were not thought to be independent. On the other hand, for the majority of the contemporary epistemologists the epistemological problem consists in finding methods, if any, of justifying knowledge by deducing specific truthful consequences from general abstract laws or theories. We will call, following the terminology of Larry Laudan (1980), the former position generativism, and the latter consequentialism.
How did this philosophical transformation from generativism to consequentialism take place? To give a detailed and critical explanation to this interesting transformation in epistemology would in itself require a separate work. We are not attempting to provide such an account in this work. However, some explanatory observations pertaining to the transformation will be presented which would form a background to this work.
This part is written with the view that the problem of this work can be best stated if we understand the situation or the historical circumstance of its origin, i.e. the context of the genesis of epistemology and scientific method, for it is our diagnosis that mainstream epistemology ever since its inception lacked certain necessary elements of analysis for characterizing scientific knowledge. We assume that the problems of epistemology can be better understood by knowing some of the necessary conditions that made a theory of knowledge possible. Especially, from the point of view of the present work, it is necessary to seek answers to these questions: Why, in the first place, did the early philosophers felt that there should be a method of arriving at knowledge? Why did epistemology, as a theory of knowledge, come into being? With these questions in mind if we look back at the history of Greek thought, we may possibly come to know the genealogy of the problem at hand, the pitfalls of the various answers given, and the direction in which to seek the answer today.
We will be presenting this as an account of the genesis and dynamics of thematic-pairs. The following material, let us make it clear, may not contain any new historical ‘facts’ of philosophy that most of us are unaware of. What we have done is to realign the ‘substance’ in a new form, which being a ‘rational reconstruction’, is intended to form an argument in itself. Though the thesis is an argument in favor of the analytico-synthetic epistemology, it is not however written in an argumentative style. Rather, we have adopted a different kind of style which may be described as that of a quasi-historico-philosophical narrative.
It is quasi-historical because the character of our research is not similar to that of a historian. And at the same time we cannot say that the work has nothing to do with the history of ideas. It is quasi-philosophical because it is not presented in the form of a rigorous argument, rather it is presented in the form of an extended argument with internal coherence, which emanates from the alternative framework that we have in mind. This framework will be identified by comparative characterization, and in this sense we frequently attend to various epistemologies by comparing them with ours. We have called it a narrative because the objective is to tell of or explicate, a possible alternate framework, and reformulate some of the problems of epistemology and philosophy of science from this new point of view. It is also a narrative because there is reconstruction involved in our attempt to retell the otherwise familiar material.
The method of organizing that we have adopted consists basically in the manner in which the presuppositions of a given thought are analyzed into antinomies or thematic-pairs. Some examples of such thematic-pairs are: reality and appearance, variable and invariable, Being and Becoming, simple and complex, universals and particulars, genus and species, analysis and synthesis etc. We will see that these thematic-pairs by their intrinsic anchorage in a tradition--being presuppository in nature--function as regulatory constraints, controlling the thinking process of the tradition. Thus they not only make some line of thinking possible, but at the same time they put a limit on that thinking, on that very basis. It is due to the possibility of knowing both the necessary conditions as well as limitations of epistemology, that we intend to narrate the story of early stages of epistemology in a form based on thematic-pairs and their dynamics. The semantics of theoretical order, we think, can best be understood by this method of thematic analysis based on opposites of various kinds.
If there was ever a period in the history of ideas that was fruitful in terms of variety and creativity, it certainly was the period from the 7th century BC to the 4th century BC. It was during this period that a variety of early conceptions of nature were proposed starting with Thales and ending with Plato. The conceptions of nature will be presented separately in Chapter-7, because the neglected thematic-pairs based on inversion have been playing a central role in their development. Since our objective is also to show the inherent limitation of mainstream epistemology, by way of looking at the context of its genesis, for the present we shall limit our presentation to the developments pertaining to early conceptions about knowledge.
Earlier to the Sophists, who went on to develop conceptions about human nature as well, there are certain conceptions ‘about’ knowledge, which are based on the thematic-pair, appearance and reality, an early precursor of another modern thematic-pair, primary and secondary qualities. We may recall that the early theoreticians of nature, often described as the physiologues, presumed that the apparent world is confusing, complex, everchanging (in constant flux), and so on, and that the real world is ordered, simple, and has a permanent form. The thematic-pairs Becoming and Being are thus connected to the apparent and the real. This is possibly the first attempt to understand the underlying reality in a manner which is different from the mythological and theological modes of knowing.
This distinction between the ‘physiological’ mode on the one hand and the mythological and theological modes on the other is not intended to show that the former is superior to the latter modes of knowing. With the assumption that mainstream epistemology has not much to offer on mythological and theological modes of knowing, and because mainstream epistemology at least claims to be about ‘scientific knowledge’, we concentrate only on the physiological mode to begin with. We intend to demonstrate that mainstream epistemology could not give a satisfactory and complete account of scientific knowledge because it has not been able to delineate one of the essential and basic components of scientific thinking. Another of our assumptions is that we consider the physiological mode as a precursor to the scientific mode of knowing.
That there is something beyond what is given to us in experience has been generally explained on the basis that a large number of events that we experience have no visible causes, given the assumption that we have a natural tendency to search for causes. In order to bring in security, closure and symmetry, the human mind has created many invisible ‘theoretical’ (it may be appropriate to say mythological or theological) entities, including ghosts, demons, gods, etc. The invisible has somehow taken the ‘primary’ level of reality, while the visible has become the ‘secondary’ level of appearance. These presuppository themes such as hidden and visible, apparent and real, primary and secondary, appear to have animated one of the basic modes of knowing, namely the explanatory mode, which is at some level of generality common to all the modes of knowing. Thus some of the first thematic-pairs that started moulding our thinking can be stated to be the visible and the invisible, and the apparent and the real.
In the first phase of the genesis of scientific knowledge, characterized by a manner of theorizing at a global level, various proposals have been made regarding what is that underlying invisible reality. We can easily see that the expression ‘underlying invisible reality’ is a composition of the thematic-pairs mentioned above. As mentioned already except towards the end of this phase, proper epistemological questions were not a central concern. Thematic analysis of ‘theories’ about nature are presented in Chapter 7, where the role of inversion in the genesis of scientific knowledge is elaborated. In what follows we shall begin narrating the crucial moments in the genesis of epistemology.
It is generally noted by historians that Greek philosophy begins with an inquiry into the objective world and then gradually turns its attention to man himself, leading to the study of the human mind, human conduct, logic, knowledge, ethics, psychology, politics, and poetics. Such a turn took place due to the Sophists, who shifted the attention of thinkers from the problems of nature to the problems of human knowledge and conduct. Before them, there had not been any attempt to question the possibility of knowledge. It is assumed that men can know and rightfully ‘theorize’ about the world.
An antithesis to this trend was provided by the Sophists, who thought that cosmological and metaphysical speculations are futile. Having seen the diversity of opinions found among the Greek naturalists, they concluded that this was due to the limitations of human thought and abilities. According to the Sophists our opinions about nature would necessarily be diverse, paradoxical, and without any interpersonal agreement. The picture given by them appears to be true because, different thinkers chose different ‘things’ as the underlying invisible reality. As is well known, while some considered water as the underlying principle, some considered air, and some others fire. A few others ‘created’ highly abstract things like apeiron, undifferentiated substance, and proposed a mechanism of creating the rest of the substances from them. Which among these ‘theories’ is the best? It is almost impossible to answer this question because each of them is internally coherent, and ultimately it is just a matter of one’s choice. The theories are proposed at such a highly global level that it is difficult to judge or verify them. Karl Popper would describe these theories as unfalsifiable, therefore nonscientific, though meaningful.2 The Sophist’s criticism, however, was not based on this modern notion of falsifiability, but rather on the impossibility of solving the riddle of the universe. It is impossible because knowledge depends upon the knower. What appears to be true for one need not be true for the other. There is no objective truth, only subjective truth. They preached that “man, collectively, is the new corporate entity which replaces the cosmos; it provides its own measures.”3 Thus, man is the measure of all things--Homo mensura. They repudiated the earlier thinkers in favor of common sense judgments of the individual. This, to our understanding, is the initial problem of knowledge, challenging the efforts of knowledge seekers in an uncritical manner.
We think that this challenge remains only partially resolved, from the philosophical point of view, by Socrates, Plato and Aristotle. However partial their solution may be, from the point of view of the positive contributions they have made towards the birth of scientific knowledge, their success consists in creating the initial categories into which a precursor of scientific knowledge in the form of systematic knowledge started pouring in. We will critically elaborate the attempts made by these great thinkers starting with Socrates.
The genesis of mainstream epistemology can be narrated by first looking at the pattern of the Socratic method used to generate knowledge of the universals. The Socratic method, which consists in asking questions in feigned ignorance and refuting all answers is in fact identical with the Sophistic method of argument intended to disclose contradictions in the opponent’s statements or views. But in contrast with the Sophists who seek to prove that knowledge is impossible in principle, Socrates only comes out against false knowledge. His goal is to expose false claims to wisdom and lay bare human ignorance.
It is well known that Socrates’ attention was not directed towards knowing the physical world, because he thought that our abilities to know it are limited. The subject of his inquiry is human nature. A host of questions raised by Socrates in the early Dialogues of Plato, which are about virtue, courage, temperance, etc., give us this indication. However these inquiries have an inherent pattern that was explicitly identified and defined by Plato in his later Dialogues, i.e., from Theaetetus onwards.
From a study of the early Dialogues of Plato, we now present an account of how the discovery of the thematic-pair universals and particulars took place.4
The discussion will be conducted, as mentioned above, as a part of the account of his method, usually called the Socratic method, for the distinction between universals and particulars become operative in the method. The central concerns of a philosopher can best be understood by examining the questions raised by them. Here we make use of a study by Santas on the type of questions raised in Plato’s Dialogues, which in turn is based on the study by Belnap on the logic of questions. It has been demonstrated by Santas that in Plato’s Dialogues mainly two kinds of questions are asked, namely, which-questions and whether-questions.5
How is the classification of questions relevant for our purpose? The answer is that it enables us to understand the underlying expectations, and motivations of Socrates while asking questions. These expectations clearly reveal that he distinguished between universals and particulars. The following account on which-questions indicates how one can ‘define’ or fix a universal, and the subsequent account on whether-questions explicates what is peculiar to the Socratic method, which aims at an ultimately clearer understanding of universals through the imperfect knowledge of particulars.
Which-questions are non-dialectical and whether-questions are dialectical. This division is made on the basis of whether the alternatives provided by the question are infinite or finite and also on the basis of the manner of presenting the alternatives. It must immediately be made clear that this division is not merely made on the basis of which questioning expression occurs in the question, but, as we shall see, solely on the basis of the alternatives suggested by the question--whether the alternatives are infinite or finite. This will become clearer from the examples given below. Examples of whether-questions will be given later in an extended discussion on the Socratic method (§1.2 page 29), while examples of which-questions shall be discussed here.
Which-questions allow great latitude to the respondent, therefore these are also called ‘infinite’ questions.6 According to Belnap which-questions and whether-questions are differentiated on the basis of the manner of presenting the alternatives. In a whether-question the alternatives are explicitly mentioned, while in a which-question the alternatives are described by reference to some condition and an appropriate set of names or terms. To arrive at any answer the conditions are to be provided, otherwise it would not be clear to the respondent from what kind or range of alternatives to choose.
In the Dialogues of Plato which-questions, in relation to whether-questions are not numerous. But it is with a which-question that each of his Dialogue is initiated. The most famous kind of questions raised by Socrates are which-questions. For example, What is knowledge? (Theaetetus) What is virtue? (Meno) What is courage? (Laches) What is temperance? (Charmides) What is justice? (The Republic) What is beauty? (Hippias Major).
These questions are of the form ‘What is X?’. We could see that no further conditions are given in the question, unlike in a typical example of a which-question ‘What is the smallest prime number greater than 45?’, where ‘greater than 45’ provides a condition. They have only a main term. But as the Dialogue proceeds some conditions are introduced subsequently by Socrates, in order to delimit the scope of the question and also to clear the misunderstandings of the respondents.
An analysis of the which-question and its complete form will throw great light on the objective of the Dialogues, which is to arrive at a definition of an idea. A preliminary characterization of universals can be obtained from a longer version of a which-question, which looks like a typical which-question with generalized conditions. According to Santas the longer version of the question can be stated as follows:
What is the kind (characteristic, property) which (a) is the same (common) in all F things, and (b) is that by reason of which all F things are F, and (c) is that by which F things do not differ, and (d) is that which in all F things one calls ‘the F’?7
Here (a) and (c) characterize F on the basis of similarity and difference, while (b) and (d) give reasons for calling some thing/s F. The main part of each Dialogue starts with a which-question, which defines the scope of the question, and since each Dialogue generally addresses itself entirely to that very question it defines also the scope of the entire Dialogue. It is not the terms, like ‘knowledge’, ‘beauty’, or ‘virtue’, that appear in the questions which do this, but the conditions (a), (b), (c), and (d) of the longer version of the question form quoted above. These conditions from (a) to (d) clearly tell us what Socrates is looking for. These conditions are just those criteria which define the universals. In the language of Plato they define the Forms, whereas particulars are represented in those conditions as ‘F things’. If the form of the question is any indication to the thematic-pair guiding the Socratic method in the Dialogues, it is clearly the thematic-pair universal and particular.
This pair further presupposes certain familiar ideas of similarity and difference, one and many. Things around us have certain similar qualities, and one quality can characterize many things. The one is an instance of a universal and the many are called particulars. This pair thus presupposes the ideas of similarity and difference. However, certain other significant aspects are involved, but are not clear from the question form explicated above. One of them is the involvement of a logical operation called negation. The question form explicated above however does not capture this important logical relation. Through the mention of difference, as it occurs in one of the conditions above, one might say, the relation is captured. However picking out examples of a type is most often not a trivial job. Therefore we think it appropriate to further explicate the conditions (a) to (d) as follows: What is the kind (characteristic, property) which (a) is the same (common) in all F things and not the same in non-F things, and (b) is that by reason of which all F things are F, and all non-F things are non-F, and (c) is that by which F things do not differ, and is that by which F-things and non-F things differ, and (d) is that which in all F things, but not in any non-F thing, one calls ‘the F’?
This brings out the essential logical relation that is involved in relating a set of tokens to a type, for similarity cannot be captured independently of difference. It is rather well known that Socrates displays a tendency to know the examples of some kind, and the class of objects is delimited by means of separating out those objects that do not belong to that kind. We conclude therefore that negation is the logical basis of the thematic-pair universal and particular.
This is how, we can best reconstruct the reasons why Socrates attempts to capture the essence of a property by means of both positive and negative examples. Of the various kinds of thematic-pairs this pair of universals and particulars is unique in many ways. While negation is certainly one of the unique ‘properties’ of the pair there are few other ways of capturing the uniqueness.
Another significant manner in which the uniqueness of the thematic-pair can be highlighted is by distinguishing the two levels to which the elements of the pair belong. Traditionally speaking universals belong to the level of Being, and particulars to the level of Becoming. Considering the type-token relation of the elements, we can say, in rather non-traditional terms, that universals belong to the conceptual realm, and particulars to the object-realm. It can also be said that the former belongs to the intensional level and the latter to the extensional level. The significance of this characterization gets enhanced specially in relation to another fundamental thematic-pair of epistemology, genus and species. After introducing the context in which the notions genus and species enter into epistemology we will be highlighting this characterization once again.
Let us now consider the significance of these developments in the context of the Sophists’ challenge. Knowledge of particulars is impossible, since there can not be knowledge of things that change. Socrates and Plato agree with the Sophists on this point. But, then they would say the knowledge of universals, i.e. our understanding of the nature and essence of qualities of things, is unchanging, therefore we can know universals.
This development is interesting, because new objects of knowledge, namely universals or Forms are defined. To the best of our knowledge the contribution of Socrates and Plato to epistemology mainly consists precisely in the discovery of universals. To understand the nature of this move let us look at its character.
The Sophists demonstrated that there is change in the object as well as the subject of knowledge. How is then knowledge of the world possible? One possible way of finding a solution to the problem is to show that knowledge is possible despite the variation involved on the part of the subject as well as the object. One way out is to show that the variation in knowledge is due to variation in the objects (Becoming), while invariance in knowledge, if possible can be due to the invariant object (Being). This demands a further distinction within knowledge into its variable component and invariable component, and also a corresponding division into the resulting kinds of knowledge. Socrates’ solution consists in making precisely this kind of move. The variable component of knowledge is named opinion or doxacorresponding to the knowledge of the variable particulars, and the invariable component, episteme, corresponds to the knowledge of the invariable universals. Thus two forms of knowledge have been distinguished corresponding to its two objects. Socrates and Plato concede the point made by the Sophists only with respect to the opinion of particulars, and not with respect to the episteme of universals. This is how we think Socrates tried to meet the challenge of the Sophists’.
The reconciliation could have been impossible had Socrates not ‘discovered’ the need for the creation of an idealized world of Forms, and we will see how this step of idealization is necessary even for scientific knowledge. We will also see below that without this move the transformation of Pythagorean mathematics into Euclidean mathematics would be impossible. Details of the precise role of idealization will be discussed later.
Not only that this distinction between objects of knowledge on the one hand and the distinction between common-sense (opinion) and episteme (systematized knowledge) on the other hand, was found essential to the development of science, but most of mainstream epistemology depends heavily upon this distinction.
Is this the only possible way of solving the riddle posed by the Sophists? Aren’t there other alternatives? We think that there exists at least one more clear alternative.
The other alternative is to suppose that variance or change at the level of objects is real, not apparent. But this real variance has an order or a pattern in it, such that that order of variance can be called invariant. Even if the objects of knowledge are of the changing kind, knowledge is possible, because there is a possibility of finding invariance in the changing objects of knowledge. This latter possibility, it can be seen, is significantly different from the previous one, where the invariance is ascribed to an unchanging object of knowledge, universals. The objects of knowledge are not assumed to be invariant. Instead it is assumed that the variance has an invariant structure. There may be other alternatives. But for our purposes distinguishing these two possible answers is sufficient. The epistemological framework that we are going to elaborate below tries to address the epistemological question of the possibility of knowledge based on this second possibility. We claim that mainstream epistemology, since it is based on the distinction of universals and particulars, can not capture the essence of changing objects.
Though this alternative also depends on abstracting or idealizing a Form out of the given, this Form is different in nature from Forms based on the thematic-pair universals and particulars. We would be basing this Form upon another basic logical relation, that of inversion, and not negation. The attempt of the thesis is to work out a basis for this alternative.
Once universals are taken to be the objects of knowledge new problems crop up. We have just seen that the thematic-pair universals and particulars was conceptualized in order to distinguish variable and invariable elements of knowledge. The notion of universals is not immediately given, for an understanding of this requires a meta-level abstraction. Since it is held by Socrates and Plato that true knowledge is the knowledge of universals, which is not easily (‘naturally’) accessible, the acquisition of the knowledge of universals requires deliberate and conscious effort. Since universals are not like the familiar objects which have spatial and temporal properties, they cannot be ‘looked’ at directly.
This problem is very acutely recognized by both Socrates and Plato. Their answer briefly is that the knowledge of universals can be gained only by conscious effort, and the effort consists of an ordered search towards reaching universals. Knowledge of universals like scientific knowledge cannot be obtained without some form of training. Indeed unless some sort of difficulty is involved in the acquisition of such knowledge the question of method does not arise. For it makes little sense to conceive of a method when the objects of knowledge are immediately and naturally grasped. With these comments about the need for a method, let us look at the essential aspects of the Socratic method.
Two stages can be identified in the Socratic method. In the first stage, the questioner elicits from the respondent what he thinks he knows by asking a question. His answers are then taken as suggestions or hypotheses, which are criticized by deducing consequences conflicting with other opinions the respondent holds by a series of questions and answers. The second stage proceeds by the same method by considering fresh suggestions, criticized and amended until it reaches an end, which is the correct definition of the form.8
In this method, the role of a which-question is mainly to elicit from the respondent what he thinks he knows. The conditions that form part of the question, as elaborated above, play the actual role of regulating the thinking of the respondent toward understanding the meaning of an idea. To have an understanding of an idea is to be able to explicitly define it. A notable feature of these conditions is that they are ‘known’ to the respondent, in the sense that he understands the meaning of the conditions. This is the most significant and essential feature common to most of the methods proposed for arriving at knowledge, i.e., moving from the known (familiar) to the unknown (unfamiliar). Not surprisingly, it is also an essential element of any pedagogy.
Coming now to the other type of questions, i.e. the whether-questions or the dialectical questions, they are those for which generally either ‘yes’ or ‘no’ are the appropriate answers. Usually the alternatives presented in these questions are a proposition and its negation, or they state explicitly a finite number of alternatives and make some request to the respondent concerning these alternatives. In Plato’s Dialogues these constitute the majority of Socrates’ questions. Some examples of dialectical or whether-questions raised by Socrates are: “Don’t you see that I am looking for that which is the same in all such things?”9 “Do you suppose that anyone can know that something is an element (part) of virtue when he does not know virtue?”10 “Do you consider that there is one health for a man, and another for a woman? Or, wherever we find health, is it the same nature (or kind) in all cases, whether in a man or anyone else? ... Is it not so with size and strength also?”11
The role of whether-questions is to help the respondent to see for himself (a) how some of his answers contradict his more secure beliefs and (b) to see the worth of certain alternatives by demonstrating how the response fits with common beliefs. It is in the course of raising whether-questions and answers, which constitute the major part of the Dialogue, that definitive answers are arrived at.
It is well known that the Socratic method is dialectical. It can also be characterized as inductivo-deductive for it has both the elements of induction and deduction.12 The method is inductive in the sense that it lays emphasis on grasping the commonness of a given set of particular opinions. It is deductive in the sense that the proposed commonness of a Form is tested by drawing out its consequences, to see whether they ‘cohere’ with commonly accepted beliefs. However from this, one should not jump to the erroneous conclusion that Socrates characterized his method to be either inductive or deductive, for he never gave a meta-level analysis of the method he practiced and preached. It was Aristotle who explicitly identifies the two logical methods. We will come to this a little later.
The initial developments of epistemology thus consist in the discovery of universals, and a method of arriving at them. The most important contribution of Socrates in this context is the coordinate set of abstract thinking, universals and particulars, which continues to regulate and structure philosophical reflection since then. The kind of amplification in philosophical reflection that took place after Socrates is undoubtedly due to this coordinate set. It is an instance of a fertile philosophical idea that is responsible for the proliferation of other philosophical ideas. The most significant developments that result from this coordinate took place in the hands of Plato and Aristotle.
Plato develops his edifice upon the foundation prepared by his teacher Socrates, and one of the most important ‘brick’ in that foundation, as already stated, is the idea of universal (and particular). Plato’s views about the questions ‘What can be or cannot be known?’ and ‘What are the criteria of knowability?’ are to a large extent similar to the views of Socrates. Let us recall from the above discussion that to know, according to Socrates, is to be able to give an explicit definition of the universal (Form). An ‘advancement’ over Socrates is that Plato introduces a distinction between two kinds of Forms, simple and complex. There are enough indications to believe that Plato, in the course of time, clearly made up his mind about the need to further distinguish universals, for he thought that if the objective of episteme is not only to arrive at universals but also to characterize them by definition, it is necessary to show how one Form relates to another Form. And the notion of definition requires that the definiendum be analyzed into simpler elements. His dialectic differs from his teacher’s in this significant respect. Thus after Theaetetus, Plato’s attention turned from a group of individuals (particulars) with its common Form (universals) to the relations between Forms themselves, and specifically the relations between Forms that occur in the definition of a Form.13 The method of arriving at the complex Form or genus and dividing it into its ultimate simple Forms or species has been formulated in the new dialectic as the methods of synthesis and analysis respectively. Thus to our understanding Plato’s dialectic is one of the first comprehensive methods which has incorporated both the contexts of ‘discovery’ and ‘justification’, and it is here that we see the rudiments of the method of analysis, which has become part and parcel of scientific method ever since.
One may raise the question: ‘Why was the need felt for introducing the genus-species distinction?’. The supposition, as mentioned above, is that knowledge is about Forms, and true knowledge consists of a description or a characterization of Forms. The nature of this characterization is such that to describe one Form we need other Forms, for only Forms can combine to form Forms. Particulars can combine to give rise to another particular, but can never become a Form. This is because, according to Plato universals and particulars cannot belong to the same world. While particulars are accessible to the senses, universals are accessible only to reason.
One may raise also the question ‘Why is Plato after definitions of Forms or universals alone, why not define particulars or individuals?’. We cannot raise the question of defining particulars, Plato would answer, because they are, by nature, not definite or determinable. A definition would use the term ‘is’ or ‘being’, which can only be applied to ‘Beings’ and not ‘Becomings’. Since ‘Becoming’ is associated with ‘being produced’, ‘perishing’, and ‘changing’, Plato refuses to use the term ‘is’ or ‘being’ to individuals which are ‘Becoming’.14 Thus we see that the epistemological thematic-pair universal and particular is related to the corresponding ontological thematic-pair Being and Becoming. Since ‘Being’ is immutable, definite etc., only universals which are Beings can be defined. For Plato, definability is a criterion of knowability. Hence sensible particulars are not the object of episteme.
Here we shall briefly see how the changes mentioned above have come about leading to the dialectic, a method of conceptual analysis.
Plato’s earlier conception about Forms is that they are indivisible ( atomon) and simple. But he realises at the end of Theaetetus that the objects of knowledge (Forms) are complex, for a definition is an analysis of a complex Form into simple Forms. Socrates, it seems, is not aware of the contradiction between the views that universals be simple and and that they be defined. But, Plato realising this, abandons the earlier view that Forms are absolutely simple and indivisible. It is clear that this is a natural consequence of any view which requires that the object of knowledge be defined. Since definition should not be by enumeration of particulars, the Form to be defined and also the Forms with which it should be defined are all to be found within the world of Forms, he has to make some of the Forms simple and others complex.15 It follows from this that simple Forms cannot be defined, and hence cannot be known by the method. With this added distinction all the sufficient conditions (sufficient concepts) are available for him to formulate the method of synthesis and analysis. What constitutes the method of analysis? The method of analysis as described by Socrates, (Plato’s mouthpiece) in Philebus is as follows:
[W]e ... ought in every enquiry to begin by laying down one idea of that which is the subject of enquiry; ... Having found it, we may next proceed to look for two, if there be two, or, if not, then for three or some other number, subdividing each of these units, until at last the unity with which we began is seen not only to be one and many and infinite, but also a definite number; the infinite must not be suffered to approach the many until the entire number of the species intermediate between unity and infinity has been discovered,then, and not till then, we may rest from division, and without further troubling ourselves about the endless individuals may allow them to drop into infinity.16
Thus, the proposed method of analysis starts with a single genus, which will be divided systematically spreading downwards on the basis of differences (differentia) until an indivisible species is obtained. Below the species are individual things (particulars) which partake of the indivisible specific Forms. These individuals however are indefinable and are not the objects of scientific knowledge (systematic ordering of Forms).17
But this does not mean that comprehension of particulars is not possible. Plato does allow the possibility of having opinions about particulars, and what he does not allow is the possibility of systematic knowledge of particulars. It may be pointed out that some authors have rendered ‘episteme’ as scientific knowledge. But since there is a clear difference between ‘scientific knowledge’ as used in the modern sense of the term and the Platonic sense, we shall use the expression ‘systematic knowledge’ for Plato’s episteme.
The method of analysis, however, should be preceded by the method of synthesis or collection. In the method of collection we take a synoptic view and bring widely scattered things under one idea, so that one may make clear by definition whatever it is that one wants to expound at the time, while the method of division allows us to be able to cut it up at its natural joints, not hack at any part like an incompetent butcher.18 The method of collection is a process of generalization and abstraction culminating in the recognition of a single common Form.19 Thus it fixes the genus to be analyzed.
But no methodological or systematic procedure is possible in collection. The idea must be divined by an act of intuition for which no rules can be given.20 Then, why call it method? We can still call it so, because this stage is said to be closely related to the method of hypothesis and the Socratic method on the one hand and to the theory of recollection on the other.21
Plato’s latter account in Republic clearly shows an element of the hypothetical nature in the method of collection.
[U]sing the hypotheses not as first principles, but only as hypotheses--that is to say, as steps and points of departure into a world which is above hypotheses, in order that she [reason] may soar beyond them to the first principle of the whole; and clinging to this and then to that which depends on this, by successive steps she descends again without the aid of any sensible object, from ideas through ideas, and in ideas she ends.22
Here we see not only the hypothetical nature of the method, we also see how it is linked with the complementary method of analysis, which operates above all kinds of indefiniteness.
This in a way looks like a hypothetico-deductive schema of Popper. However, at least two striking differences should be looked at. First of all Plato has a method of collection, which contains inductive elements of the Socratic method, while Popper goes to the extreme by rejecting any possibility of the synthetic method. Popper’s arguments against induction, along the lines of Hume, are rather well known. Second, Plato’s analysis is with respect to Forms, and as the above quotation reveals, it starts and ends in ideas, while in Popper’s hypothetico-deductive schema we have general and particular statements, where particular statements are reports of sensory experience. Plato’s dialectic, as we have already mentioned, has no such objective to describe the objects of perception given by sensory experience. Further Plato’s episteme is not Popper’s scientific knowledge. We think that Popper’s epistemology is unique in the sense that it is an epistemology minus synthesis, though this development has a history, while Plato’s is evidently analytico-synthetic despite lacunae.
It is worth noting that the method of analysis is clearly an original feature of Plato’s dialectic and has no clear place in the Socratic method, for it was never discussed in the earlier Dialogues. The only possible rudiment of the method of analysis in the Socratic method is when, intermittently, while leaping towards the universals from particulars, there is an attempt to see if the ‘leaps’ are proper by enumerative examination, to see whether the consequences are contradictory to common belief. It is possible, therefore, to argue that the Socratic method is a method of arriving at ideas (synthesis or discovery), which fixes universals, and the method of analysis, which is ‘deductive’, is a method of confirmation or justification. It ensures that the result of the former method is coherent (or true). Analysis takes place purely within universals. This is possibly the beginning of conceptual analysis and systematic knowledge, and also a step essential for the development of logic. In the Republic Plato makes the point very clear that the method of analysis proceeds ‘without the aid of any sensible object’ that it starts from ideas, through ideas and in ideas it ends. On this point the two complementary methods on the one hand, and Plato’s dialectic and the Socratic method on the other hand, differ.
What is the application of the method apart from the claim of gaining a clear understanding of the world? The knowledge of the new dialectic will guide the progress of actual discourse; it is the philosopher’s science of dividing correctly. An expert in dialectic will not confuse one Form with another. In the Sophist the Stranger speaks about the utility of the method as follows.
[H]e who can divide rightly is able to see clearly one form pervading a scattered multitude, and many different forms contained under one higher form; and again, one form knit together into a single whole and pervading many such wholes, and many forms, existing only in separation and isolation. This is the knowledge of classes which determines where they can have communion with one another and where not.23
Here we see a glimpse of what Plato has in mind regarding the objective and the outcome of episteme.
We shall see below that for understanding the nature and structure of scientific knowledge, the notion of complex universal (“single form knit together into a single whole and pervading many such wholes, and many forms”), is inevitable. We shall interpret a scientific definition to be a complex predicate, ‘truly’ attributable only to an idea or ideal system. According to the semantic view of theories, a version of which is being defended in the thesis, modern scientific definitions are taken to be complex predicates or models attributable to an idealized system. (Details are worked out in Chapter 5 and 6.)
From this point of view Plato’s contribution with regard to the detailed structure of Forms, interrelating one with the other, can readily be seen as highly significant. However we will base our analysis of non-Platonic (modern) scientific definitions not on the relation between genus and species, but the inverse relation between universals. This is not to say that modern science has no definitions relating genus and species. The whole of taxonomic systematization of various elements of natural science is in the form of Plato’s world of Forms. In the present thesis, however, we will specifically concentrate on inversion based relations between special kinds of Forms which we call dimensions. It is also important to make another distinction for our purposes which is that the analysis that we find in this world of Forms, will be taken as conceptual analysis, as contrasted with the analysis of arguments where the elements are not Forms but statements or judgements. We will shortly see how Aristotle ‘invented’ an analysis of judgements, as contrasted with Platonic analysis of concepts. Before we turn our attention to another master’s contributions, we first recapitulate, and then end with a statement of what is going to come.
If one looks at the general picture of philosophical speculation after Socrates and Plato, we find that a new abstract level is created ‘above’ the concrete. This is not to say that thinkers before them did nothing abstract. But the difference, according to our understanding, is that the abstract entities and relations ‘invented’ were given the same place along with other ‘corporeal’ things. When Pythagoreans, for instance, abstracted out the notion of number, they held that what they see in reality are numbers, for they did not postulate an independent world of numbers. Both apparent and real aspects are seen in a ‘undivided’ region. Plato’s picture, on the other hand, consists of an independent world order of Forms, distinct from the unreal world of particulars to which we have access through sensations. Metaphorically we can describe the development as follows: Before Plato, thinkers thought that both Being and Becoming ‘occupied’ the same plane, while after Plato, we can say that there are two planes, one of Being and another of Becoming, one above the other with a gap in between, as shown in the figure 1.1.
Philosophers disagreed about the ontological status of the planes. Which plane is virtual and which real? Plato, as is well known, argued for the reality of the upper plane. Aristotle made the upper plane a nous dependent world, and the lower plane real and independent of the nous.24 This gave rise to the problem of realism. Philosophers also disagreed on the problems related to the content of universals. Plato argued that the objects of the upper plane are the objects of scientific knowledge, while Aristotle argued that the upper plane is an essential ‘instrument’ for having scientific knowledge of the objects belonging to the lower plane.
Plato denied any logical relation between particulars and universals, consequently propositions for Plato are only relations between universals. Aristotle invented a heterogeneous relation between them in the form of thematic-pair subject and predicate, necessary for forming a judgement or statement. (The Stoics also have a possible hand in this invention.) The formal logic of categorical statements is based on this heterogeneous relation.
Before we consider the other important thinker, Aristotle, a few observations are in order regarding the place and role of particulars in the methods of Plato and Socrates, the role and place of universals being secure in their method. This is found necessary because Plato’s preoccupation with universals and his seemingly idealist or rationalist position has overshadowed the usual discussions to such an extent that his epistemology has been portrayed as one that does not in principle give any significance either to experience or to particulars. There are certain apparent pointers to show that he does not appreciate the role played by particulars. However we will see that these hints are misleading and have led to incoherent portrayals of Plato’s thought. By carefully following the role played by particulars in the process of the method of recollection (the method of synthesis) leading to the discovery of knowledge of universals, we shall try to show that Plato did not deny the role of experience and of ‘opinion’ of particulars in the process. Without this, the method, which is characterized as dialectical remains bereft of one of its complements. M.F. Burnyeat has argued that Plato did not depreciate the role of particulars in his method.
The mistaken view of particulars must have emerged due to Socrates’ disapproval of definition of forms by way of examples. Whenever examples are given as an answer to Socrates’ which-questions by the respondents, he ridicules them on the ground that they are not answers to his question. For example Theaetetus responds to Socrates’ question ‘What is knowledge?’ by giving examples such as geometry, the art of the cobbler and other craftsmen.25 To that Socrates replies that that is not the kind of answer he wants. He illustrates to Theaetetus the nature of the answer that he is looking for. To the question ‘What is clay?’, to reply that clay is potter’s clay, oven-maker’s clay, brick maker’s clay etc., would be ridiculous. He says a desirable answer would be that clay is moistened earth.26 This illustration is usually cited as that which demonstrates a depreciatory role for particulars in the method.
Socrates disregards examples even as a preliminary answer to the question ‘What is knowledge?’. Why? Because he considers that to know or to understand is to be able to give a explicit definition of the Form or universal. A definition of a Form cannot be obtained by enumeration. He says so because we may have learned to use a name for a collection of things, without ever giving a thought to the question of what is common in that collection of things. The philosophical turn that takes place with Socrates and Plato, to our understanding, consists precisely in this. They have seen a possibility of talking about something other than the common name that stands for all the examples--a non-trivial characterization that describes the common quality applicable to a collection of things.
To arrive at this sort of understanding giving attention to examples (particulars) is necessary in Plato’s dialectic. This is clear from the way Socrates examines various definitions suggested during the Dialogues. The definitions suggested are examined with reference to examples. He only insists that the commonness of all examples be explicitly stated. Sometimes he himself would add examples to help the respondent. He rejects examples only because examples alone do not constitute knowledge or an adequate definition. He regards them as data from which a definition is to be reached by a process of ‘leaping’ generalization. There are enough indications to believe that this is an inductive leap. (Aristotle characterizes the Socratic method as inductive.) Socrates explains that if the definition of an idea is known then we will be able to tell what is and what is not an example of the idea.27
Plato held that the knowledge of Forms is present in us in dormant state, and it can be brought back to our consciousness by the help of the method of dialectic.28 There are certain ‘facts’ which upon initial consideration appear unfamiliar, even incredible, but after, attending to them by pure reason, they appear self-evident. This is usually experienced with regard to mathematical ‘facts’. This is the nature of the truth that is achieved after recollection. In Plato’s dialectic, as well as in the Socratic method, one property of method that is mentioned above is necessarily present, which is to help learning, either in oneself or to others. This process is never complete without the knowledge of particulars (examples), for how could one judge whether there is real understanding or consistent rule following behavior?29 So it is one thing to say that Socrates and Plato argued going beyond opinions about particulars (examples) and consequently have lowered the rating of opinionated knowledge, but another thing to say that particulars have no role to play in the dialectic. The former statement applies to Plato’s view but the latter does not. Without the method of recollection, where sensory experience of particulars has a definite role to play in the process of generating knowledge of Forms, Plato’s dialectic is incomplete. It is, we think, correct to say that for Plato sensory experience and eventually the knowledge of particulars plays an instrumental role in gaining the real knowledge of Forms. We shall see below that Aristotle differs with his master on this issue in a subtle way.
Before we go on to a statement of Aristotle’s method of scientific demonstration, it is worthwhile to compare him with his master, for he disagreed on crucial matters and it is from these disagreements that his method, which is generally considered the real scientific method, emerged.
The most crucial difference is with regard to the status of the dialectical method. Aristotle differentiates two kinds of methods, viz. the empirical and dialectical methods. Empirical inquiry begins from perception, followed by induction and generalization, and tests theories by appeal to experience. Dialectical inquiry is initiated from common beliefs, followed by raising and solving puzzles, and tests theories amongst common beliefs.30 Philosophers, according to him, argue according to the truth which is known by nature, and we can reach this by the empirical method. Dialecticians on the other hand argue according to common belief.31
Why did Aristotle demand two distinct methods? An answer to this question can be furnished if we understand the intent of some of the new divisions he introduced, his major differences with Plato, and some of his original, and positive contributions to philosophy and logic.
Aristotle’s differences are based on the fundamental distinction between substance and quality. Aristotle thinks that, dialectic fails to yield scientific knowledge because it deals only with attributes, let loose from the beings to which they are attributed. In Metaphysics, for instance, he says, “dialectic and sophistic deal with the attributes of things that are, not of things qua being, and not with being itself in so far as it is being; ... ”32 Here Aristotle is pleading for a distinction between attributes on one hand and substance on the other reintroducing the thematic-pair, substance and quality, prevailing in the thinking of Thales, Anaximander and Anaximenes.33
More significantly Plato and Aristotle differed on the notion of definitions. Definitions, according to Aristotle, are statements of essence of a substance which inheres in it, while for Plato they represent the way in which a particular Form is related to other Forms. For Aristotle’s predecessors no definition of substance is possible, since there was no ‘being-what-it-is’, and therefore they were not knowable. M. Grene justifiably maintains that Aristotle’s predecessors including Plato were unable to unequivocally state the prerequisite for the establishment of scientific knowledge. The prerequisite is real definition in contrast to conventional definition. Plato’s definition ultimately depends on conventions held by the community because, as mentioned above, Plato’s dialectic is initiated by common beliefs. A real definition is a statement of the essence of things, belonging to the lower plane, and it speaks of “the peculiar substance of each thing, and what it is to be that thing”. Aristotle contends that substances fall naturally into classes in such a way that we can specify, in carefully chosen formulae, their essential natures.34
With this added distinction Aristotle classifies universals into accidental and essential. This new distinction should not be viewed as an alternative to Plato’s distinction of Forms into genus and species. Aristotle also holds this Platonic division of universals. The object of scientific knowledge is to know the essence of things by discovering real definitions, and the knowledge of the essence is obtained through universals. Besides the essence inheres in particular substances. Certain universals which describe a thing without referring to its essence, are accidental; these do not constitute the objects of scientific knowledge. This is a point of difference with his master who believes that all universals have a world of their own and are the objects of scientific knowledge.
The character of this transformation in view, rather an inverted view of Aristotle, is that scientific knowledge is about the essence/s present in the lower plane, while Plato’s is about the Forms present in the upper plane. (See figure above.)
There is another point of difference between Plato and Aristotle with regard to the dialectical method and the scientific method, which is very crucial for understanding the nature of scientific knowledge, in the modern sense of the term. This is in relation to fixing the subject-matter. The demonstrative arguments of the scientific knower, on the other hand, predicates essential attributes of a carefully restricted subject-genus. The dialectician does not restrict his subject. He maneuvers the argument to his advantage whatever the context of his argument. Therefore, dialectical arguments, though formally valid, are baseless and unscientific.35 Aristotle says, in Posterior Analytics, that we should not try to know the whole of existence, the summum genus, through scientific method.
We can never know anything about anything, as distinct from having opinions about it, unless we cut out one limited subject-matter out of a wider range and restrict ourselves to it.36
Plato on the other hand seeks definition, against a background of indefinite flux. Grene presents the difference between the two methods cogently as follows:
The unambiguous predications of science are possible only because things sort themselves out naturally into kinds; knowledge results from the mind’s response to such natural groupings. Transcend them and you transcend the limits of univocal speech, which are the bounds of science. You have strayed beyond the well-fenced limits of the being-what-it-is and are lost in the quicksands of dialectic once more.37
We will see below that one of the important differences that can be found between the pre-Platonic inquiries and post-Aristotelian inquiries consists precisely in this point of confining oneself to a subject matter. Problems of inquiry are defined within the limits of this local, vis á vis., global, domain of inquiry. Without localization, essentially paradigmatic science cannot be said to have begun. In this sense, the earlier conceptions about nature before Plato, and of Plato, can not be called proper scientific knowledge.
It is therefore claimed in the thesis, that despite Aristotle’s failure in arriving at correct scientific conceptions, his successful contribution in directing the attention of scholars towards problem oriented research can be rated as a revolutionary suggestion. We will see in detail his specific suggestions in the Case Studies. Aristotle had very strong ground to differ from Plato on certain basic assumptions. There is another dramatic development by Aristotle, which is regarding the kind of relation that is admissible between universals and particulars.
It is one of the unique features of Aristotle’s philosophy that while Plato associated universals and particulars with the thematic-pair Being and Becoming, Aristotle associates them with the thematic-pair subject and predicate. This is an indication of his attention towards statements and language. Unlike Plato, Aristotle concentrates on statements as elements of his study. Plato’s interest was either on a single idea or on relationships between ideas. This is not to say that the Platonic association is not accepted by Aristotle, for he never rejects the distinction between Being and Becoming. Rather he continues to think with the same metaphysical orientation, though he prefers for a very important reason, which becomes clear as we proceed, to use the terms ‘Form’ and ‘Substance’.
Nothing is available in Plato’s works in favor of subject-predicate distinction. Besides he would not have agreed with this distinction to be associated with universals and particulars, because, according to him, a statement is an instance of a blending or ‘weaving-together’ of Forms.38 That is, it is a combination or synthesis of two or more universals. This point is significant because we can distinguish only two significant ways of relating Forms in Plato’s philosophy, granting his view on statements, viz., part-whole relation and identity relation. All non-definitional statements are statements relating genus and species. For example, ‘Man is an animal’ means the species Form ‘Man’ is a part of the genus Form ‘Animal’. And according to Plato if the Forms are ‘properly’, i.e., coherently combined, they are true, otherwise false--a coherence theory of truth. All definitional statements on the other hand are statements where a Form is defined by identifying it with the combination of Forms that define it. For example, in the statement “Man is a rational, biped, animal” the Form ‘Man’ is identical with the synthesis of the Forms, ‘Animal’ + ‘Biped’ + ‘Rational’. This can appropriately be termed a chemistry of Forms.
It is necessary to digress and make an observation here about a deficiency of Plato’s conceptual analysis, which is dubbed as a chemistry of Forms. This is with regard to the lack of any scope for stating invariance of changes in the Platonic framework. Modern natural science captures the Form of Becoming (variable and changing phenomena) by discovering the invariant proportionality relations between variables. It it however clear that Plato has a reason for not searching for this. As mentioned above Plato is working out one of the possible options, and certainly not the only possible option, of responding to the Sophists’ challenge. For Plato Forms represent invariance, therefore the question of entertaining a possible science of variations is inconceivable in his theory of knowledge.
Even in Plato’s metaphysics, as presented in Timaeus, where a mathematical Atomistic theory of reality is proposed, what we see is that Beings are allowed to combine and separate giving rise to a variety of species. Despite his mathematical maturity he could not foresee the other possibility of a Form ‘within’ variations. To our understanding he was obsessed with his discovery of Forms, with the ‘one over many relation’, and can not see the possibility of ‘one to one relation’, necessary for capturing the Form of functions based on proportionality.
Aristotle makes a genuine attempt, though ultimately he too fails, to study a science of motion in De Caelo, and Physics. An attempt to explain his failure is made in the Case Studies. Let us return to the Aristotle’s views on the subject-predicate relation.
Aristotle’s views on predication are more elaborate and different from Plato’s. The difference is not merely that he allows a subject-predicate relation between universals and particulars, he furthermore insists that the subject of a statement can refer to either a Substance or a Form, but the predicate of a statement should necessarily be a Form. He says in Metaphysics (1017 b 10-14) that Substances are not said of a subject. One of his criteria for recognizing a Substance from Form is that it be a basic subject.39
Since anything that can be said of something else as its subject must have some kind of generality, i.e. it can be said of other objects also, and since only universals can have this character, only universals can act as adjectives. “An adjective which could be used only on one unique occasion would not function as an adjective; and the something unique it designated would not be something sayable of a subject.”40 Therefore all things that are predicable of subjects are non-individual.
On the basis of the condition ‘present in a subject’ (inherence) we can distinguish between two kinds of individuals, dependent and independent individuals, things that do not exist by themselves and things that do. Those things which are individuals and independent, e.g. this man, this horse etc., are first substances. These are the ultimate subjects in which dependent individuals (individual accidents) are present, and of which other predicates are said. Scientific Knowledge depends wholly on the right application of predicates, which are general, to kinds of substances, which are also general. Thus science can approach as far as independent individuals, while dependent individuals, being accidental, cannot be approached by science. Thus Grene writes:
The propositions which constitute a science are univocal statements attributing certain characteristics to certain kinds of substances. ... In order to establish a science of some subject matter, we must take a natural class of first substances, and elicit from some other category or categories, also at appropriately generalized levels, the right predicates for the characterization of its essence.41
A correct relation between a class of first substances and an appropriately chosen predicate produces a real definition. Let us recall that, according to Aristotle, a real definition is the prerequisite for the establishment of scientific knowledge, and that it is a statement of the essence of the thing defined.
Another most remarkable achievement of Aristotle is that almost single handedly he developed the foundations of formal logic. Though Aristotle’s logic is limited to Categorical propositions, it is nevertheless a landmark achievement in the history of ideas. Our concern here, however, is to highlight the too obvious point that unlike the conceptual (philosophical) logic of Plato, Aristotle’s syllogistic logic is a logic of statements of the subject-predicate form. It is important to make this observation that this logic, like most of modern logic of statements, is based on the principle of non-contradiction.
The same attribute cannot at the same time belong and not belong to the same subject and in the same respect.42
The crux of the proposal of the present work lies in presenting a visualization of a possible logic of construction based on the logical relation of inversion, which has at least three contrasting characters with the deductive logic. First, it is not based on the principle of non-contradiction, second, it is not a logic of statements, and third, the outcome of the inference is not a statement but a constructed structure. Detailed characterization, and argument will be presented in Part-II, and Part-III.
Having noted the main thematic features of Aristotle we shall highlight certain important features of his scientific or empirical method, which can be regarded as one of the first scientific methods.
Aristotle talks of ‘the right method of investigation’ in the Posterior Analytics (Bk. II, ch 13), which “starts by observing a set of individuals, and considers what they have in common”,43 and then examines another set of individuals, generically identical, and so on till we arrive at a ‘principle’.44
This is the description that he offers for the starting point of the method of investigation, which is clearly induction - from particulars to universals. This is Aristotle’s second level of induction which makes use of the ‘products’ of the first level of induction. The first level fixes the universals and the latter the first principles or real definitions. According to the traditional method of investigation we arrive at the knowledge of the unknown (first principles) from known (the knowledge of the universals). The knowledge of the universals comes from intuitive faculties of human being or nous, which includes the operation of perception, experience and memory. Knowledge of the first principles depends on nous. The first step does not require the expertise of the investigator, in the sense that he need not consciously use his faculty of thinking. In the sense explicated above about the nature of method, this first step cannot be properly regarded as a methodological step. Aristotle says the following regarding this first level of induction.
[All human beings] have an innate faculty of discrimination, which we call sense-perception ... after the act of perception is over the percipients can still retain the perception in the soul.45
If this happens repeatedly a coherent impression is produced, thus giving rise to memory. And repeated memories of the same thing constitutes experience, i.e., memories of a thing may be many but they constitute a single experience.
And experience, that is, the universal when established as a whole in the soul - the One that corresponds to the Many, the unity that is identically present in them all - provides the starting-point of art and science.46
These faculties arise from sense-perception, just as, when a retreat has occurred in battle, if one man halts so does another, and then another, until the original position is restored. The soul is so constituted that it is capable of the same sort of process. Up to this point Aristotle is talking of the first level of induction, which is a prerequisite for the second level of induction, which alone is a part of the joint method of scientific investigation. Regarding this Aristotle (100 a 15-b 5) says:
As soon as one individual percept ‘has come to a halt’ in the soul, this is the first beginning of the presence there of a universal ... Then other ‘halts’ occur among these (proximate) universals, until the indivisible genera or (ultimate) universals are established. E.g. a particular species of animal leads to genus ‘animal’, and so on. Clearly then it must be by induction that we acquire knowledge of the primary premises, because this is also the way in which sense perception provides us with universals.
Thus the path to the first principles is inductive. Clearly the processes that the term ‘induction’ designates in modern and Aristotle’s sense are so different. This is more akin to the method of synthesis in Plato’s dialectic, except that it is rooted in sensory experience, while in Plato this is aided by hypothetical ‘leaps’.
After fixing the genus by induction, he describes how a definition can be established through the method of division in Ch.13. The investigator begins with the subject-genus and divides it carefully to get the order of differentia correct, checking that the divisions are exhaustive and that members of the species being divided all lie under one branch of the genus.47
This latter method of division, as we clearly see, is akin to that of the method of analysis in Plato’s dialectic. But, one thing we must bear in mind, which is that Aristotle provided only hints and no explicit statements in this regard, and is therefore subject to the whims of the interpreter. Nevertheless a few points are clear: The induction should precede the method of division. The inductive method arrives at the definition, while division establishes it. Induction moves from the particular to the general, and division from the general to the specific.
Interpretations offered by the Italian Aristotelians of the school of Padua suggest that Aristotle is the champion of the joint method of analysis and synthesis. However it should be kept in mind that their writings are commentaries mainly of Physics and Posterior Analytics, where the search is to discover causes of specific physical events. In this sense, the terms, “analysis” and “synthesis” in the following discussion describe different methodological procedures. This difference is the difference between the methods used in conceptual understanding (relations between genus and species) on the one hand, and indirect understanding of natural phenomena by demonstrative syllogism on the other.
Aristotle never explicitly used the terms “analysis” and “synthesis”, but these terms are used by the later Aristotelians appropriately following the description he gives of the two kinds of demonstrations, which are two complementary modes of knowing the fact. All syllogisms, Aristotle says, will not yield scientific knowledge which is by demonstration, i.e. by demonstrative syllogism. The premises of the demonstrative syllogism must be true, primary, immediate and better known than the conclusion.48 The relationship between the premises and conclusion is like that of cause and effect.
Of the two modes of knowing the fact, the first one is called demonstration qua which follows the natural way of discovering the cause or the fact, which is possibly by inductive method, and the second one is called demonstration propter quid, which follows the causal order starting with the discovered cause and deducing the effect.49 The Greek terms for the two modes are oti and dioti.
In the beginning of Physics (Bk.I 184a) Aristotle says that the starting point of science is a confused mass, usually interpreted as that of effects, which require analysis.50 That is science (not the episteme of Plato, but Physics of Aristotle begins with the known or proximate (effect), by the help of which the unknown or the ultimate (cause) can be reached by the method. The former movement from effect to cause is called the resolution, while the latter movement from cause to the effect is called the composition. After the discovery of the cause, the effect would be explained in terms of the cause, i.e., the effect is approached again in the method indirectly, via the knowledge of the cause. There is thus a regress or return to the effect with which the inquiry started. However there is no circularity in the process. Paul of Venice (one of the Italian Aristotelians) defends Aristotle’s joint method from the charge of circularity as follows:
For in scientific method (in processu naturali) there are three knowledges: the first is of the effect without any reasoning, called quia, that it is. The second is of the cause through knowledge of that effect; it is likewise called quia. The third is of the effect through the cause; it is called propter quid. But the knowledge of why (propter quid) the effect is, is not the knowledge that (quia) it is an effect.51
In other words, first, the knowledge of the effect thus obtained is arrived at indirectly via the cause, and second, the modality of the knowledge involved is explanatory. Using contemporary expressions, the knowledge of the effect via the cause is theory impregnated. Since the causes are the sorts that are usually not given to our direct sensory experience, they need to be ‘discovered’ by theoretical imagination. While the place where reason should play its role is properly identified, the nature of the reason, except that it has a name of resolution, is not clearly specified.
We think that this deficiency remained uncorrected not only in the entire Aristotelian thinking, but also in other methodologies proposed later. We shall see in detail in the case study below, how Archimedes, and later Galileo, who belong to a mixed tradition, could devise a model method based on inverse reasoning, for the discovery of ‘causes’, followed by the explanatory regress.52 The exact role and nature of reason, complementing the role of experience, is specified, giving rise to the proper scientific knowledge in the modern sense of the term.
The worthiness of the Aristotelian model, however, lies in properly identifying the place where the role of reason is involved in the context of discovery.53 Niphus (another Italian scholar) interprets that the resolution of effect is captured in a conjectural syllogism, while the composition of effect with the help of cause is captured in a demonstrative syllogism.54 A long period of critical reconstruction of Aristotelian teachings culminated in the works of Zabarella, who, it is claimed by Randall, influenced Galileo.
Typical to the tradition Zabarella characterizes method as an intellectual instrument producing knowledge of the unknown from the known. Method is a kind of syllogism, according to him, because it connects one with the other through inference. There are only two possible methods, composition or demonstrative method and resolution.
Demonstrative method is a syllogism generating science from propositions that are necessary, immediate, better known, and the causes of the conclusion ... Resolutive method is a syllogism consisting of necessary propositions, which leads from posterior things and effects better known to the discovery of prior things and causes.55
Zabarella and the whole new generation of scientists that followed him, of which Galileo is also a crucial figure, entertained the belief that scientific experience springs from mere ordinary observation. They insisted that experience must be first carefully analyzed to discover the principle or cause of the observed effects. Thus, science proceeds from rigorous resolution of a few selected instances to a general principle, and then from that principle to the systematized science, and then composition as a proof.56
He finds four stages in the process of this regress: observation of the effect; resolving the complex fact into its components and conditions; mental examination of the hypothetical cause to find its essential elements; and demonstration of the effect from that cause. The third stage is called “mental examination”, which Niphus called negotiatio of the intellect. He elaborates, then, the two things that are considered in the middle stage of mental examination, which helps us toward knowing the cause distinctly.
It is interesting to see that the first three stages are part of the method of resolution, while the fourth demonstrative stage, which is deductive syllogism, is all that there is to the method of composition. This is an indication that the problem of discovery is the more dominating concern than the problem of justification. Today’s situation is just the reverse, as we will see below. Another point to note here is that the Aristotelians have seen that without the involvement of “mental examination”, i.e., involving a source other than sense experience, the discovery of causes is impossible. It is therefore well recognized by Aristotelians that scientific investigation depends on both creative and sensory faculties.
One of the shortcomings of Zabarella’s method, as well as of any other Aristotelian, is that in the discovery of scientific principles no role is assigned to mathematics. However he makes interesting observations worthy of consideration. Like his predecessors, such as the Averroists, he makes the distinction between the method of resolution suitable for natural science and the method of “analysis” of mathematics. In the latter we can start from either the principles or the consequences. In the former, however, we must start with effects observed by the senses, i.e. with the method of resolution. In the mathematical method whether we start from resolution or composition is merely a technical matter, and each of the methods here are independent.
This is a general sketch of the joint analytico-synthetic methods in Aristotelian thinking. We distinctly see that the method, over a period of time, has been enriched without a corresponding development of scientific knowledge. Either something is wrong with the methodology, or it is preached but never practiced, or it could also be that methodology has nothing to do with the actual development of scientific knowledge. All these doubts and speculations are natural, for this whole stream of philosophical reflection from Plato’s Academy to the University of Padua could not produce scientific knowledge, in the modern sense of the term. But this is just one stream that emanated from the Academy. There are other rather fertile streams, from the point of view of the development of scientific knowledge.
One such stream is based on Euclid’s mathematical edifice, while another stream is based on Archimedes’ experimental edifice. Needless to say, both these have eventually become very hard bricks in the bedrock of scientific knowledge. Interestingly both the streams developed in the School of Alexandria. What is peculiar to this School? We will have to wait till it gets answered eventually in the course of the essay. Presently our concern is not to narrate the success story, but the unsuccessful story of philosophical reflections on scientific knowledge and method.
Before we end this section on Aristotle we shall make, what we regard, an observation of some interest. It is to note that the method of resolution can be said to be a part of, what we today call, the context of discovery, while the method of composition can be regarded as a part of the context of justification. We are aware that in the current usage the context of justification is deductive, and hence called analytical, while the context of discovery is ampliative or inductive, and hence synthetic.57 It therefore appears that, in the same context, one has seen resolution, while the other has seen synthesis. This terminological inversion should not cause much confusion, when we realize that the Aristotelians are talking in terms of what is happening to the objects of inquiry, causes and effects, while methodologists of the current century use a linguocentric vocabulary, which cares more about what is happening to the ‘instruments’ of inquiry in the process of inquiry, such as statements. This inversion in the philosophical orientation, as it appears to us, is due to the shift in points of view from the extensional view to the intensional view. Despite this transformation in orientation, the central concern, which is to attempt answering the two fundamental questions of epistemology, which continued till the middle of this century. It would be a very interesting problem for a historian of ideas to study what factors led to this change. To understand this change demands a separate work. Since we are not presently engaged in understanding the intricacies of this historical problem, it suffices to make the following observation.
In the conceptual methods of synthesis and analysis, which are discussed above, i.e., those of Plato and of Aristotle, there exists a process called synthesis, which refers to the process of cognitive movement from the level of particulars to the level of universals. And there exists another process called analysis which refers to the division of genus to species, both of which belonging to the level of universals. Thus in different contexts the terms meant different things. However it is interesting to note that in this case too, the two processes correspond to the contexts of discovery and justification. Thus the joint methods should be properly contextualized to know the proper reference and thus to avoid confusion. The general methodological theme of analysis and synthesis remains only a theoretical model functioning as a meta-level guide to organize epistemological thinking, which can be seen in several contexts in the history of methodology.
One significant theme of the joint method is that science does not start from scratch, for it starts from something which is already known. This theme remains a part of the other successful stream mentioned above, which (so we claim) generated science proper. To this we now turn.
Among the ancient mathematicians too the method of discovering solutions to mathematical problems followed the pattern of reaching the unknown from the known, and then returning to the known from the newly discovered knowledge, in order to validate newly arrived knowledge. The method employed by ancient geometers to calculate the area of any regular shaped surface can be a best example to illustrate the method of reducing the unknown to the known. It was taken for granted that the area of a rectangle is the product of its base and height, (Area= b × h), which is the known constituent of knowledge. From this they found out methods of calculating the areas of all polyhedrons. The method can be generally characterized thematically according to the joint method as follows. As shown in the figure 1.2, any other
The same method was applied to calculate the area of irregular shapes, though the value obtained would be true only approximately. It is well known that Archimedes extended the same method to know the measurements of other complicated shapes like the circle, the oval etc. His method has later come to be known as the method of approximation.
This instance of the joint method in mathematics is clear and simple, because the operations involved are ‘extensional’. However Euclid’s version is pretty involved due to its highly theoretical character. The characterization of the method can be found in Euclid’s Elements, Book XIII. The account of the method as understood by Euclid and other Greek mathematicians is given by Pappus (c.300 AD). The method, Pappus says, is for those who “are desirous of acquiring the power of solving problems ... and it is useful for this alone.” The method, according to Pappus, was worked out by Euclid, Apollonius and Aristaeus, which proceeds by way of analysis and synthesis.
Analysis ... takes that which is sought as if it were admitted and passes from it through its successive consequences to something which is admitted as a result of synthesis: for in analysis we assume that which is sought as if it were (already) done, and we inquire what it is from which this results, and again what is the antecedent cause of the latter, and so on, until by so retracing our steps we come upon something already known or belonging to the class of first principles, and such a method we call analysis as being solution backwards.
But in synthesis, reversing the process we take as already done that which was last arrived at in the analysis and, by arranging in their natural order as consequences what were before antecedents, and successively connecting them one with another, we arrive finally at the construction of what was sought; and this we call synthesis.58
This method is fundamental to Plato’s program in mathematics, which is to find trivially true axioms and to deduce all of arithmetic and geometry from them. Euclid was considered by Proclus as one who completed Plato’s program.59 However, from the point of view of our search for a logic of discovery, this method does not have much to offer, because so much is assumed in the process of the method, such as first principles which are already considered to be a part of accepted knowledge. What would be interesting is to know how we arrive at the first principles. The above method does not appear to have any scope for that. But from the remarks of Pappus it is clear that it is intended to be a problem solving method. Lakatos and Szabo have suggested that the method can be viewed as a discovery method provided the starting point of the principles is regarded as hypothetical. If the hypotheses are rigidly fixed, their use becomes less interesting.
Assuming that problem solving belongs to the context of application of already arrived principles, we find it reasonable to think that Euclid’s method does not properly belong to the context of discovery. Further it should be noted that in this version of the joint method, the order of analysis and synthesis appear to be irrelevant. If it is a method of discovery, however, the starting point and the nature of the starting point would matter significantly, because the initial step should be that which leads to the principles or hypotheses. But the method is clearly a perfect “circulatory system”, as Lakatos would put it, without beginning and end. Therefore we think that whatever be the significance of the method for problem solving heuristics, it does not throw enough light on the problem of discovery, with which we are presently concerned.