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Analysis has always been at the heart of philosophical method, but it has been understood and practised in many different ways. Perhaps, in thematic essay belief systems broadest sense, it might be defined as a process of isolating or working back to what is more fundamental by means of which something, initially taken as given, can be explained or reconstructed. The explanation or reconstruction is often then exhibited in a corresponding process of synthesis, thematic essay belief systems.
This allows great variation in specific method, however. Such criticisms, however, are only directed at particular conceptions of analysis, thematic essay belief systems. If we look at the history of philosophy, and even if we just look at the history of analytic philosophy, we find a rich and extensive repertoire of conceptions of analysis which philosophers have continually drawn upon and reconfigured in different ways.
Analytic philosophy is alive and well precisely because of the range of conceptions of analysis that it involves. It may have fragmented into various interlocking subtraditions, but those subtraditions are held together by both their shared history and their methodological interconnections.
It is the aim of this article to indicate something of the range of conceptions of analysis in the history of philosophy and their interconnections, and to provide a bibliographical resource for those wishing to explore analytic methodologies and the philosophical issues that they raise.
This section provides a preliminary description of analysis—or the range of different conceptions of analysis—and a guide to this article as a whole, thematic essay belief systems. This conception may be called the decompositional conception of analysis see Section 4. This conception may be called the regressive conception of analysis see Section 2.
This suggests that analysis also involves a transformative or interpretive dimension. This too, however, thematic essay belief systems, has its roots in earlier thought see especially the supplementary sections on Ancient Greek Geometry and Medieval Philosophy. These three conceptions should not be seen as competing. In actual practices of analysis, which are invariably richer than the accounts that are offered of them, thematic essay belief systems, all three conceptions are typically reflected, though to differing degrees and in differing forms.
To analyze something, we may first have to interpret it in some way, thematic essay belief systems, translating an initial statement, say, into the privileged language of logic, mathematics or science, before articulating the relevant elements and structures, thematic essay belief systems, and all in the service of identifying fundamental principles by means of which thematic essay belief systems explain it.
The complexities that this schematic description suggests can only be appreciated by considering particular types of analysis. The present document provides an overview, with introductions to the various conceptions of analysis in the history of philosophy.
It also contains links to the supplementary documents, the documents in the bibliography, and other internet resources. The supplementary documents expand on certain topics under each of the six main sections. The annotated bibliography contains a list of key readings on each topic, and is also divided according to the sections of this entry.
The term was readily extended to the solving or dissolving of a problem, and it was in this sense that it was employed in ancient Greek geometry and philosophy. The method of analysis that was developed in ancient Greek geometry had an influence on both Plato and Aristotle. Also important, however, was the influence of Socrates's concern with definition, in which the roots of modern conceptual analysis can be found.
What we have in ancient Greek thought, then, is a complex web of methodologies, of which the most important are Socratic definition, thematic essay belief systems, which Plato elaborated into his method of division, his related method of hypothesis, which drew on geometrical analysis, and the method s that Aristotle developed in his Analytics.
Far from a consensus having established itself over the last two millennia, the relationships between these methodologies are the subject of increasing debate today. At the heart of all of them, too, lie the philosophical problems raised by Meno's paradox, which anticipates what we now know as the paradox of analysis, concerning how an analysis can be both correct and informative see the supplementary section on Mooreand Plato's attempt to solve it through the theory of recollection, which has spawned a vast literature on its own.
Although Euclid's Elements dates from around BC, and hence after both Plato and Aristotle, it is clear that it draws on the work of many previous geometers, most notably, Theaetetus and Eudoxus, who worked closely with Plato and Aristotle.
Plato is even credited by Diogenes Laertius LEPI, with inventing the method of analysis, but whatever the truth of this thematic essay belief systems be, the influence of geometry starts to show in his middle dialogues, and he certainly encouraged work on geometry in his Academy. The classic source for our understanding of ancient Greek geometrical analysis is a passage in Pappus's Mathematical Collectionwhich was composed around AD, and hence drew on a further six centuries of work in geometry from the time of Euclid's Elements :.
In synthesis, on the other hand, we suppose that which was reached last in analysis to be already done, and arranging in their natural order as consequents epomena the former antecedents and linking them one with another, we in the end arrive at the construction of the thing sought.
And this we call synthesis. In investigating the properties of this complex figure we may draw further auxiliary lines between particular points and find that there are a number of congruent triangles, from which we can begin to work out the relationship between the relevant areas.
Pythagoras's theorem thus depends on theorems about congruent triangles, and once these—and other—theorems have been identified and themselves provedPythagoras's theorem can be proved. The theorem is demonstrated in Proposition 47 of Book I of Euclid's Elements. The basic idea here provides the core of the conception of analysis that one can find reflected, in its different ways, in the work of Plato and Aristotle see the supplementary sections on Plato and Aristotle.
Although detailed examination of actual practices of analysis reveals more than just regression to first causes, principles or theorems, but decomposition and transformation as well see especially the supplementary section on Ancient Greek Geometrythe regressive conception dominated views of analysis until well into the early modern period. Ancient Greek geometry was not the only source of later conceptions of analysis, however. Certainly, the roots of conceptual analysis can be traced back to Plato's search for definitions, as we shall see in Section 4 below.
Conceptions of analysis in the medieval and renaissance periods were largely influenced by thematic essay belief systems Greek conceptions. But knowledge of these conceptions was often second-hand, thematic essay belief systems, filtered through a variety of commentaries and texts that were not always reliable. Medieval and renaissance methodologies tended to be uneasy mixtures of Platonic, Aristotelian, Stoic, Galenic and neo-Platonic elements, many of them claiming to have some root in the geometrical conception of analysis and synthesis.
However, thematic essay belief systems, in the late medieval period, clearer and more original forms of analysis started to take shape. In John Buridan's masterpiece of the mid-fourteenth century, the Summulae de Dialecticawe can find all three of the conceptions outlined in Section 1.
He distinguishes explicitly between divisions, definitions and demonstrations, corresponding to decompositional, interpretive and regressive analysis, thematic essay belief systems, respectively. Here, in particular, we have anticipations of modern analytic philosophy as much as reworkings of ancient philosophy. Unfortunately, however, these clearer forms of analysis became overshadowed during the Renaissance, despite—or perhaps because of—the growing interest in the thematic essay belief systems Greek sources.
As far as understanding analytic methodologies was concerned, the humanist repudiation of scholastic logic muddied the waters. The scientific revolution in the seventeenth century brought with it new forms of analysis. The newest of these emerged through the development of more sophisticated mathematical techniques, but even these still had their roots thematic essay belief systems earlier conceptions of analysis.
By the end of the early modern period, decompositional analysis had become dominant as outlined in what followsbut this, too, took different forms, and the relationships between the various conceptions of analysis were often far from clear.
In common with the Renaissance, thematic essay belief systems, the early modern period was marked by a great concern with methodology, thematic essay belief systems.
This might seem unsurprising in such a revolutionary period, when new techniques for understanding the world were being developed and that understanding itself was being transformed.
But what characterizes many of the treatises and remarks on methodology that appeared in the seventeenth century is their appeal, thematic essay belief systems, frequently self-conscious, to ancient methods despite, or perhaps—for diplomatic reasons—because of, the critique of the content of traditional thoughtalthough new wine was thematic essay belief systems poured into the old bottles. The model of geometrical analysis was a particular inspiration here, albeit filtered through the Aristotelian tradition, which had assimilated the regressive process of going from theorems to axioms with that of moving from effects to causes see the supplementary section on Aristotle.
Analysis and synthesis were thus taken as complementary, although there remained disagreement over their respective merits. There is a manuscript by Galileo, dating from aroundan appropriated commentary on Aristotle's Posterior Analyticswhich shows his concern with methodology, and regressive analysis, in particular see Wallace a and b. Thematic essay belief systems wrote a chapter on method in the first part of De Corporepublished inwhich offers his own interpretation of the method of analysis and synthesis, where decompositional forms of analysis are articulated alongside regressive forms [ Quotations ].
But perhaps the most influential account of methodology, from the middle of the seventeenth century until well into the nineteenth century, thematic essay belief systems, was the fourth part of the Port-Royal Logicthe first edition of which appeared in and the final revised edition in Chapter 2 which was the first chapter in the first edition opens as follows:. Hence there are two kinds of method, one for discovering the truth, which is known as analysisor the method of resolutionand which can also be called the method of discovery.
The other is for thematic essay belief systems the truth understood by others once it is found. This is known as synthesisor the method of compositionand can also be called the method of instruction.
While the first two involve regressive analysis and synthesis, the third and fourth involve decompositional analysis and synthesis. As the authors of the Logic make clear, this particular part of their text derives from Descartes's Rules for the Direction of the Mindwritten aroundbut only published posthumously in the editorial comments in PWI, 54, The decompositional conception of analysis is explicit here, thematic essay belief systems if we follow this up into the later Discourse on Methodpublished inthe focus has clearly shifted from the regressive to the decompositional conception of analysis, thematic essay belief systems.
All the rules offered in the earlier work have now been reduced to just four. This is how Descartes reports the rules he says he adopted in his scientific and philosophical work:. The second, to divide each of the difficulties I examined into as many parts as possible and as may be required in order to resolve them better.
The third, to direct my thoughts in an orderly manner, thematic essay belief systems, by beginning with the simplest and most easily known objects in the order to ascend little by little, step by step, to knowledge of the most complex, and by supposing some order even among objects that have no natural order of precedence.
And the last, throughout to make enumerations so complete, and reviews so comprehensive, that I could be sure of leaving nothing out. PWI, The first two are rules of analysis and the second two rules of synthesis. Descartes's geometry did indeed involve the breaking down of complex problems into simpler ones.
Illustrated in analytic geometry in thematic essay belief systems developed form, then, we can see all three of the conceptions of analysis outlined in Section 1. For further discussion of this, see the supplementary section on Descartes and Analytic Geometry. Descartes's emphasis thematic essay belief systems decompositional analysis was not without precedents, however.
Not only was it already involved in ancient Greek geometry, but it was also implicit in Plato's method of collection and division. We might explain the shift from regressive to decompositional conceptual analysis, as well as the connection between the two, in the following way. On this model, in seeking to define anything, we work back up the appropriate classificatory hierarchy to find the higher i. As an elaboration of the Socratic search for definitions, we clearly have in this the origins of conceptual analysis.
But the construals that have been offered of this have been more problematic, thematic essay belief systems. which contains sections on Descartes and Analytic Geometry, British Empiricism, Leibniz, and Kant. As suggested in the supplementary document on Kantthe decompositional conception of analysis thematic essay belief systems its classic statement in the work of Kant at the end of the eighteenth century, thematic essay belief systems.
But Kant was only expressing a conception widespread at the time. The conception can be found in a very blatant form, for example, thematic essay belief systems the writings of Moses Mendelssohn, for whom, unlike Kant, it was applicable even in the case of geometry [ Quotation ].
Typified in Kant's and Mendelssohn's view of concepts, it was also reflected in scientific practice. Indeed, its popularity was fostered by the chemical revolution inaugurated by Lavoisier in the late eighteenth century, the comparison thematic essay belief systems philosophical analysis and chemical analysis being frequently drawn. This decompositional conception of analysis set the methodological agenda for philosophical approaches and debates in the late modern period nineteenth and twentieth centuries.
Responses and developments, very broadly, can be divided into two. On the one hand, an essentially decompositional conception of analysis was accepted, but a critical attitude was adopted towards it. If analysis simply involved breaking something down, then it appeared destructive and life-diminishing, and the critique of analysis that this view engendered was a common theme in idealism and romanticism in all its main varieties—from German, British and French to North American.
On the other hand, thematic essay belief systems, analysis was seen more positively, but the Kantian conception underwent a certain degree of modification and development, thematic essay belief systems.
In the nineteenth century, this was exemplified, in particular, by Bolzano and the neo-Kantians. Bolzano's most important innovation was the method of variation, which involves considering what happens to the truth-value of a sentence when a constituent term is substituted by another.
The neo-Kantians emphasized the role of structure in conceptualized experience and had a greater appreciation of forms of analysis in mathematics and science. In many ways, their work attempts to do justice to philosophical and scientific practice while recognizing the central idealist claim that thematic essay belief systems is a kind of abstraction that inevitably involves falsification or distortion.
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