## 1. General Introduction




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.


### 1.1 Characterizations of Analysis




If asked what 'analysis' means, most people today 
immediately think of breaking something down into its components; and
this is how analysis tends to be officially characterized. In the 
*Concise Oxford Dictionary*, for example, 
'analysis' is defined as the "resolution into 
simpler elements by analysing (opp. *synthesis*)", the 
only other uses mentioned being the mathematical and the 
psychological 
 [Quotation].
 And in the *Oxford Dictionary of Philosophy*, 
'analysis' is defined as "the process of breaking a
concept down into more simple parts, so that its logical structure is
displayed" 
 [Quotation].
 The restriction to concepts and the reference to displaying 
'logical structure' are important qualifications, but the
core conception remains that of breaking something down.




This conception may be called the *decompositional* conception
of analysis (see 
 Section 4).
 But it is not the only conception, and indeed is arguably neither the
dominant conception in the pre-modern period nor the conception that 
is characteristic of at least one major strand in 
'analytic' philosophy. In ancient Greek thought, 
'analysis' referred primarily to the process of working 
back to first principles by means of which something could then be 
demonstrated. This conception may be called the *regressive* 
conception of analysis (see 
 Section 2).
 In the work of Frege and Russell, on the other hand, before the 
process of decomposition could take place, the statements to be 
analyzed had first to be translated into their 'correct' 
logical form (see 
 Section 6).
 This suggests that analysis also involves a *transformative* 
or *interpretive* dimension. This too, however, 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, 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, 
translating an initial statement, say, into the privileged language 
of logic, mathematics or science, before articulating the relevant 
elements and structures, and all in the service of identifying 
fundamental principles by means of which to explain it. The 
complexities that this schematic description suggests can only be 
appreciated by considering particular types of analysis.




Understanding conceptions of analysis is not simply a matter of 
attending to the use of the word 'analysis' and its 
cognates--or obvious equivalents in languages other than 
English, such as '*analusis*' in Greek or 
'*Analyse*' in German. Socratic definition is 
arguably a form of conceptual analysis, yet the term 
'*analusis*' does not occur anywhere in 
Plato's dialogues (see 
 Section 2
 below). Nor, indeed, do we find it in Euclid's 
*Elements*, which is the classic text for understanding 
ancient Greek geometry: Euclid presupposed what came to be known as 
the method of analysis in presenting his proofs 
'synthetically'. In Latin, 
'*resolutio*' was used to render the Greek word 
'*analusis*', and although 
'resolution' has a different range of meanings, it is 
often used synonymously with 'analysis' (see the 
supplementary section on 
 Renaissance Philosophy).
 In Aristotelian syllogistic theory, and especially from the time of 
Descartes, forms of analysis have also involved 
'reduction'; and in early analytic philosophy it was 
'reduction' that was seen as the goal of philosophical 
analysis (see especially the supplementary section on 
 The Cambridge School of Analysis).
 




Further details of characterizations of analysis that have been 
offered in the history of philosophy, including all the classic 
passages and remarks (to which occurrences of 
 '[Quotation]'
 throughout this entry refer), can be found in the supplementary 
document on



> Definitions and Descriptions of Analysis.




A list of key reference works, monographs and collections can be 
found in the



> Annotated Bibliography, SS1.


### 1.2 Guide to this Entry




This entry comprises three sets of documents:


1. The present document
2. Six supplementary documents (one of which is not yet
available)
3. An annotated bibliography on analysis, divided into six
documents




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.


## 2. Ancient Conceptions of Analysis and the Emergence of the Regressive Conception




The word 'analysis' derives from the ancient Greek term 
'*analusis*'. The prefix 
'*ana*' means 'up', and 
'*lusis*' means 'loosing', 
'release' or 'separation', so that 
'*analusis*' means 'loosening up' or 
'dissolution'. 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, 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 
 Moore),
 and Plato's attempt to solve it through the theory of 
recollection, which has spawned a vast literature on its own.




'Analysis' was first used in a methodological sense in 
ancient Greek geometry, and the model that Euclidean geometry 
provided has been an inspiration ever since. Although Euclid's 
*Elements* dates from around 300 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 (*LEP*, I, 299) with inventing the method of 
analysis, but whatever the truth of this may 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 
Collection*, which was composed around 300 AD, and hence drew on 
a further six centuries of work in geometry from the time of 
Euclid's *Elements*:



> Now analysis is the way from what is sought--as if it
> were admitted--through its concomitants (*akolouthon*)
> in order[,] to something admitted in synthesis. For in analysis we suppose
> that which is sought to be already done, and we inquire from what it
> results, and again what is the antecedent of the latter, until we on
> our backward way light upon something already known and being first in
> order. And we call such a method analysis, as being a solution
> backwards (*anapalin lysin*). 
> 
> 
> 
> 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. 
>  [Full Quotation]
>  
> 
> 
> 




Analysis is clearly being understood here in the regressive 
sense--as involving the working back from 'what is 
sought', taken as assumed, to something more fundamental by 
means of which it can then be established, through its converse, 
synthesis. For example, to demonstrate Pythagoras's 
theorem--that the square on the hypotenuse of a right-angled 
triangle is equal to the sum of the squares on the other two 
sides--we may assume as 'given' a right-angled triangle with the
three squares drawn on its sides. 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 proved), 
Pythagoras'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 Geometry),
 the 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. Plato may not have used the term 
'analysis' himself, but concern with definition was 
central to his dialogues, and definitions have often been seen as 
what 'conceptual analysis' should yield. The definition 
of 'knowledge' as 'justified true belief' (or
'true belief with an account', in more Platonic terms) is
perhaps the classic example. Plato's concern may have been with
real rather than nominal definitions, with 'essences' 
rather than mental or linguistic contents (see the supplementary 
section on 
 Plato),
 but conceptual analysis, too, has frequently been given a 
'realist' construal. Certainly, the roots of conceptual 
analysis can be traced back to Plato's search for definitions, 
as we shall see in 
 Section 4
 below.




Further discussion can be found in the supplementary document on



> Ancient Conceptions of Analysis.




Further reading can be found in the



> Annotated Bibliography, SS2.


## 3. Medieval and Renaissance Conceptions of Analysis




Conceptions of analysis in the medieval and renaissance periods were 
largely influenced by ancient Greek conceptions. But knowledge of 
these conceptions was often second-hand, 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, in the late medieval period, clearer and more
original forms of analysis started to take shape. In the literature 
on so-called 'syncategoremata' and 
'exponibilia', for example, we can trace the development 
of a conception of interpretive analysis. Sentences involving more 
than one quantifier such as 'Some donkey every man sees',
for example, were recognized as ambiguous, requiring 
'exposition' to clarify.




In John Buridan's masterpiece of the mid-fourteenth century, 
the *Summulae de Dialectica*, we can find all three of the 
conceptions outlined in 
 Section 1.1
 above. He distinguishes explicitly between divisions, definitions and
demonstrations, corresponding to decompositional, interpretive and 
regressive analysis, 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 original Greek 
sources. As far as understanding analytic methodologies was 
concerned, the humanist repudiation of scholastic logic muddied the 
waters.




Further discussion can be found in the supplementary document on



> Medieval and Renaissance Conceptions of Analysis.




Further reading can be found in the



> Annotated Bibliography, SS3.


## 4. Early Modern Conceptions of Analysis and the Development of the Decompositional Conception




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 in earlier conceptions of analysis. By 
the end of the early modern period, decompositional analysis had 
become dominant (as outlined in what follows), but this, too, took 
different forms, and the relationships between the various 
conceptions of analysis were often far from clear.




In common with the Renaissance, the early modern period was marked by
a great concern with methodology. 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, frequently self-conscious, to ancient methods (despite,
or perhaps--for diplomatic reasons--because of, the 
critique of the *content* of traditional thought), although 
new wine was generally 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 came to be seen as a method of discovery, working back from 
what is ordinarily known to the underlying reasons (demonstrating 
'the fact'), and synthesis as a method of proof, working 
forwards again from what is discovered to what needed explanation 
(demonstrating 'the reason why'). Analysis and synthesis 
were thus taken as complementary, although there remained 
disagreement over their respective merits.




There is a manuscript by Galileo, dating from around 1589, an 
appropriated commentary on Aristotle's *Posterior 
Analytics*, which shows his concern with methodology, and 
regressive analysis, in particular (see Wallace 1992a and 1992b). 
Hobbes wrote a chapter on method in the first part of *De 
Corpore*, published in 1655, which 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, was the fourth part of the Port-Royal *Logic*, the 
first edition of which appeared in 1662 and the final revised edition
in 1683. Chapter 2 (which was the first chapter in the first edition)
opens as follows:



> The art of arranging a series of thoughts properly, either
> for discovering the truth when we do not know it, or for proving to
> others what we already know, can generally be called method. 
> 
> 
> 
> Hence there are two kinds of method, one for discovering the truth, 
> which is known as *analysis*, or the *method of 
> resolution*, and which can also be called the *method of 
> discovery*. The other is for making the truth understood by 
> others once it is found. This is known as *synthesis*, or the 
> *method of composition*, and can also be called the *method
> of instruction*. 
>  [Fuller Quotations]
>  
> 
> 
> 




That a number of different methods might be assimilated here is not 
noted, although the text does go on to distinguish four main types of
'issues concerning things': seeking causes by their 
effects, seeking effects by their causes, finding the whole from the 
parts, and looking for another part from the whole and a given part 
(*ibid*., 234). 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 Mind*, written around 1627, but only published 
posthumously in 1684. The specification of the four types was most 
likely offered in elaborating Descartes's Rule Thirteen, which 
states: "If we perfectly understand a problem we must abstract 
it from every superfluous conception, reduce it to its simplest terms
and, by means of an enumeration, divide it up into the smallest 
possible parts." (*PW*, I, 51. Cf. the editorial 
comments in *PW*, I, 54, 77.) The decompositional conception 
of analysis is explicit here, and if we follow this up into the later
*Discourse on Method*, published in 1637, the focus has 
clearly shifted from the regressive to the decompositional conception
of analysis. 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 first was never to accept anything as true if I did not
> have evident knowledge of its truth: that is, carefully to avoid
> precipitate conclusions and preconceptions, and to include nothing more
> in my judgements than what presented itself to my mind so clearly and
> so distinctly that I had no occasion to doubt it. 
> 
> 
> 
> 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, 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. (*PW*, I, 120.)
> 
> 
> 




The first two are rules of analysis and the second two rules of 
synthesis. But although the analysis/synthesis structure remains, 
what is involved here is decomposition/composition rather than 
regression/progression. Nevertheless, Descartes insisted that it was 
geometry that influenced him here: "Those long chains composed 
of very simple and easy reasonings, which geometers customarily use 
to arrive at their most difficult demonstrations, had given me 
occasion to suppose that all the things which can fall under human 
knowledge are interconnected in the same way." (*Ibid*. 
 [Further Quotations])
 




Descartes's geometry did indeed involve the breaking down of 
complex problems into simpler ones. More significant, however, was 
his use of algebra in developing 'analytic' geometry as 
it came to be called, which allowed geometrical problems to be 
transformed into arithmetical ones and more easily solved. In 
representing the 'unknown' to be found by 
'*x*', we can see the central role played in 
analysis by the idea of taking something as 'given' and 
working back from that, which made it seem appropriate to regard 
algebra as an 'art of analysis', alluding to the 
regressive conception of the ancients. Illustrated in analytic 
geometry in its developed form, then, we can see all three of the 
conceptions of analysis outlined in 
 Section 1.1
 above, despite Descartes's own emphasis on the decompositional 
conception. For further discussion of this, see the supplementary 
section on 
 Descartes and Analytic Geometry.
 




Descartes's emphasis on 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. Consider a simple 
example, as represented in the diagram below, 
'collecting' all animals and 'dividing' them 
into *rational* and *non-rational*, in order to define 
human beings as rational animals.



> ![division](Diagplat.jpg)




On this model, in seeking to define anything, we work back up the 
appropriate classificatory hierarchy to find the higher (i.e., more 
basic or more general) 'Forms', by means of which we can 
lay down the definition. Although Plato did not himself use the term 
'analysis'--the word for 'division' was 
'*dihairesis*'--the finding of the 
appropriate 'Forms' is essentially analysis. As an 
elaboration of the Socratic search for definitions, we clearly have 
in this the origins of conceptual analysis. There is little 
disagreement that 'Human beings are rational animals' is 
the kind of definition we are seeking, defining one concept, the 
concept *human being*, in terms of other concepts, the 
concepts *rational* and *animal*. But the construals 
that have been offered of this have been more problematic. 
Understanding a classificatory hierarchy *extensionally*, that
is, in terms of the classes of things denoted, the classes higher up 
are clearly the larger, 'containing' the classes lower 
down as subclasses (e.g., the class of animals includes the class of 
human beings as one of its subclasses). *Intensionally*, 
however, the relationship of 'containment' has been seen 
as holding in the opposite direction. If someone understands the 
concept *human being*, at least in the strong sense of knowing
its definition, then they must understand the concepts 
*animal* and *rational*; and it has often then seemed 
natural to talk of the concept *human being* as 
'containing' the concepts *rational* and 
*animal*. Working back up the hierarchy in 
'analysis' (in the regressive sense) could then come to 
be identified with 'unpacking' or 
'decomposing' a concept into its 
'constituent' concepts ('analysis' in the 
decompositional sense). Of course, talking of 
'decomposing' a concept into its 
'constituents' is, strictly speaking, only a metaphor (as
Quine was famously to remark in SS1 of 'Two Dogmas of 
Empiricism'), but in the early modern period, this began to be 
taken more literally.




For further discussion, see the supplementary document on



> Early Modern Conceptions of Analysis,




which contains sections on Descartes and Analytic Geometry, British 
Empiricism, Leibniz, and Kant.




For further reading, see the



> Annotated Bibliography, SS4.


## 5. Modern Conceptions of Analysis, outside Analytic Philosophy




As suggested in the supplementary document on 
 Kant,
 the decompositional conception of analysis found its classic 
statement in the work of Kant at the end of the eighteenth century. 
But Kant was only expressing a conception widespread at the time. The
conception can be found in a very blatant form, for example, in 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 between philosophical 
analysis and chemical analysis being frequently drawn. As Lichtenberg
put it, "Whichever way you look at it, philosophy is always 
analytical chemistry" 
 [Quotation].
 




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. One finds it reflected, for example, in remarks about the 
negating and soul-destroying power of analytical thinking by Schiller

 [Quotation],
 Hegel 
 [Quotation]
 and de Chardin 
 [Quotation],
 in Bradley's doctrine that analysis is falsification 
 [Quotation],
 and in the emphasis placed by Bergson on 'intuition' 
 [Quotation].
 




On the other hand, analysis was seen more positively, but the Kantian
conception underwent a certain degree of modification and 
development. 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. This formed the basis for
his reconstruction of the analytic/synthetic distinction, 
Kant's account of which he found defective. 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 analysis is a kind of abstraction that inevitably
involves falsification or distortion. On the neo-Kantian view, the 
complexity of experience is a complexity of form and content rather 
than of separable constituents, requiring analysis into 
'moments' or 'aspects' rather than 
'elements' or 'parts'. In the 1910s, the idea
was articulated with great subtlety by Ernst Cassirer 
 [Quotation],
 and became familiar in Gestalt psychology.




In the twentieth century, both analytic philosophy and phenomenology 
can be seen as developing far more sophisticated conceptions of 
analysis, which draw on but go beyond mere decompositional analysis. 
The following 
 Section
 offers an account of analysis in analytic philosophy, illustrating 
the range and richness of the conceptions and practices that arose. 
But it is important to see these in the wider context of 
twentieth-century methodological practices and debates, for it is not
just in 'analytic' philosophy--despite its 
name--that analytic methods are accorded a central role. 
Phenomenology, in particular, contains its own distinctive set of 
analytic methods, with similarities and differences to those of 
analytic philosophy. Phenomenological analysis has frequently been 
compared to conceptual clarification in the ordinary language 
tradition, for example, and the method of 'phenomenological 
reduction' that Husserl invented in 1905 offers a striking 
parallel to the reductive project opened up by Russell's theory
of descriptions, which also made its appearance in 1905.




Just like Frege and Russell, Husserl's initial concern was with
the foundations of mathematics, and in this shared concern we can see
the continued influence of the regressive conception of analysis. 
According to Husserl, the aim of 'eidetic reduction', as 
he called it, was to isolate the 'essences' that underlie
our various forms of thinking, and to apprehend them by 
'essential intuition' 
('*Wesenserschauung*'). The terminology may be 
different, but this resembles Russell's early project to 
identify the 'indefinables' of philosophical logic, as he
described it, and to apprehend them by 'acquaintance' 
(cf. *POM*, xx). Furthermore, in Husserl's later 
discussion of 'explication' (cf. *EJ*, 
SSSS 22-4 
 [Quotations]),
 we find appreciation of the 'transformative' dimension of
analysis, which can be fruitfully compared with Carnap's 
account of explication (see the supplementary section on 
 Carnap and Logical Positivism).
 Carnap himself describes Husserl's idea here as one of 
"the synthesis of identification between a confused, 
nonarticulated sense and a subsequently intended distinct, 
articulated sense" (1950, 3 
 [Quotation]).
 




Phenomenology is not the only source of analytic methodologies 
outside those of the analytic tradition. Mention might be made here, 
too, of R. G. Collingwood, working within the tradition of British 
idealism, which was still a powerful force prior to the Second World 
War. In his *Essay on Philosophical Method* (1933), for 
example, he criticizes Moorean philosophy, and develops his own 
response to what is essentially the paradox of analysis (concerning 
how an analysis can be both correct and informative), which he 
recognizes as having its root in Meno's paradox. In his 
*Essay on Metaphysics* (1940), he puts forward his own 
conception of metaphysical analysis, in direct response to what he 
perceived as the mistaken repudiation of metaphysics by the logical 
positivists. Metaphysical analysis is characterized here as the 
detection of 'absolute presuppositions', which are taken 
as underlying and shaping the various conceptual practices that can 
be identified in the history of philosophy and science. Even among 
those explicitly critical of central strands in analytic philosophy, 
then, analysis in one form or another can still be seen as alive and 
well.



For further reading, see the



> Annotated Bibliography, SS5.


## 6. Conceptions of Analysis in Analytic Philosophy and the Introduction of the Logical (Transformative) Conception




If anything characterizes 'analytic' philosophy, then it 
is presumably the emphasis placed on analysis. But as the foregoing 
sections have shown, there is a wide range of conceptions of 
analysis, so such a characterization says nothing that would 
distinguish analytic philosophy from much of what has either preceded
or developed alongside it. Given that the decompositional conception 
is usually offered as the main conception today, it might be thought 
that it is this that characterizes analytic philosophy. But this 
conception was prevalent in the early modern period, shared by both 
the British Empiricists and Leibniz, for example. Given that Kant 
denied the importance of decompositional analysis, however, it might 
be suggested that what characterizes analytic philosophy is the 
*value* it places on such analysis. This might be true of 
Moore's early work, and of one strand within analytic 
philosophy; but it is not generally true. What characterizes analytic
philosophy as it was founded by Frege and Russell is the role played 
by *logical analysis*, which depended on the development of 
modern logic. Although other and subsequent forms of analysis, such 
as linguistic analysis, were less wedded to systems of formal logic, 
the central insight motivating logical analysis remained.




Pappus's account of method in ancient Greek geometry suggests 
that the regressive conception of analysis was dominant at the 
time--however much other conceptions may also have been 
implicitly involved (see the supplementary section on 
 Ancient Greek Geometry).
 In the early modern period, the decompositional conception became 
widespread (see 
 Section 4).
 What characterizes analytic philosophy--or at least that central
strand that originates in the work of Frege and Russell--is the 
recognition of what was called earlier the *transformative* or
*interpretive* dimension of analysis (see 
 Section 1.1).
 Any analysis presupposes a particular framework of interpretation, 
and work is done in *interpreting* what we are seeking to 
analyze as part of the process of regression and decomposition. This 
may involve *transforming* it in some way, in order for the 
resources of a given theory or conceptual framework to be brought to 
bear. Euclidean geometry provides a good illustration of this. But it
is even more obvious in the case of analytic geometry, where the 
geometrical problem is first 'translated' into the 
language of algebra and arithmetic in order to solve it more easily 
(see the supplementary section on 
 Descartes and Analytic Geometry).
 What Descartes and Fermat did for analytic geometry, Frege and 
Russell did for analytic philosophy. Analytic philosophy is 
'analytic' much more in the sense that analytic geometry 
is 'analytic' than in the crude decompositional sense 
that Kant understood it.




The interpretive dimension of modern philosophical analysis can also 
be seen as anticipated in medieval scholasticism (see the 
supplementary section on 
 Medieval Philosophy),
 and it is remarkable just how much of modern concerns with 
propositions, meaning, reference, and so on, can be found in the 
medieval literature. Interpretive analysis is also illustrated in the
nineteenth century by Bentham's conception of 
*paraphrasis*, which he characterized as "that sort of 
exposition which may be afforded by transmuting into a proposition, 
having for its subject some real entity, a proposition which has not 
for its subject any other than a fictitious entity" 
 [Full Quotation].
 He applied the idea in 'analyzing away' talk of 
'obligations', and the anticipation that we can see here 
of Russell's theory of descriptions has been noted by, among 
others, Wisdom (1931) and Quine in 'Five Milestones of 
Empiricism' 
 [Quotation].
 




What was crucial in the emergence of twentieth-century analytic 
philosophy, however, was the development of quantificational theory, 
which provided a far more powerful interpretive system than anything 
that had hitherto been available. In the case of Frege and Russell, 
the system into which statements were 'translated' was 
predicate logic, and the divergence that was thereby opened up 
between grammatical and logical form meant that the process of 
translation itself became an issue of philosophical concern. This 
induced greater self-consciousness about our use of language and its 
potential to mislead us, and inevitably raised semantic, 
epistemological and metaphysical questions about the relationships 
between language, logic, thought and reality which have been at the 
core of analytic philosophy ever since.




Both Frege and Russell (after the latter's initial flirtation 
with idealism) were concerned to show, against Kant, that arithmetic 
is a system of analytic and not synthetic truths. In the 
*Grundlagen*, Frege had offered a revised conception of 
analyticity, which arguably endorses and generalizes Kant's 
logical as opposed to phenomenological criterion, i.e., (ANL) rather than (ANO) (see the
supplementary section on 
 Kant):
 



> (AN) A truth is *analytic* if its proof depends only
> on general logical laws and definitions.




The question of whether arithmetical truths are analytic then comes 
down to the question of whether they can be derived purely logically.
(Here we already have 'transformation', at the 
theoretical level--involving a reinterpretation of the concept 
of analyticity.) To demonstrate this, Frege realized that he needed 
to develop logical theory in order to formalize mathematical 
statements, which typically involve multiple generality (e.g., 
'Every natural number has a successor', i.e. 'For 
every natural number *x* there is another natural number 
*y* that is the successor of *x*'). This 
development, by extending the use of function-argument analysis in 
mathematics to logic and providing a notation for quantification, was
essentially the achievement of his first book, the 
*Begriffsschrift* (1879), where he not only created the first 
system of predicate logic but also, using it, succeeded in giving a 
logical analysis of mathematical induction (see Frege *FR*, 
47-78).




In his second book, *Die Grundlagen der Arithmetik* (1884), 
Frege went on to provide a logical analysis of number statements. His
central idea was that a number statement contains an assertion about 
a concept. A statement such as 'Jupiter has four moons' 
is to be understood not as predicating of Jupiter the property of 
having four moons, but as predicating of the concept *moon of 
Jupiter* the second-level property *has four instances*, 
which can be logically defined. The significance of this construal 
can be brought out by considering negative existential statements 
(which are equivalent to number statements involving the number 0). 
Take the following negative existential statement:



> (0a) Unicorns do not exist.




If we attempt to analyze this *decompositionally*, taking its 
grammatical form to mirror its logical form, then we find ourselves 
asking what these unicorns are that have the property of 
non-existence. We may then be forced to posit the 
*subsistence*--as opposed to *existence*--of 
unicorns, just as Meinong and the early Russell did, in order for 
there to be something that is the subject of our statement. On the 
Fregean account, however, to deny that something exists is to say 
that the relevant *concept* has no instances: there is no need
to posit any mysterious *object*. The Fregean analysis of (0a)
consists in *rephrasing* it into (0b), which can then be 
readily formalized in the new logic as (0c):



> (0b) The concept *unicorn* is not instantiated. 
> 
> 
> 
> (0c) ~([?]*x*) *Fx*.
> 
> 
> 




Similarly, to say that God exists is to say that the concept 
*God* is (uniquely) instantiated, i.e., to deny that the 
concept has 0 instances (or 2 or more instances). On this view, 
existence is no longer seen as a (first-level) predicate, but 
instead, existential statements are analyzed in terms of the 
(second-level) predicate *is instantiated*, represented by 
means of the existential quantifier. As Frege notes, this offers a 
neat diagnosis of what is wrong with the ontological argument, at 
least in its traditional form (*GL*, SS53). All the 
problems that arise if we try to apply decompositional analysis (at 
least straight off) simply drop away, although an account is still 
needed, of course, of concepts and quantifiers.




The possibilities that this strategy of 'translating' 
into a logical language opens up are enormous: we are no longer 
forced to treat the surface grammatical form of a statement as a 
guide to its 'real' form, and are provided with a means 
of representing that form. This is the value of logical analysis: it 
allows us to 'analyze away' problematic linguistic 
expressions and explain what it is 'really' going on. 
This strategy was employed, most famously, in Russell's theory 
of descriptions, which was a major motivation behind the ideas of 
Wittgenstein's *Tractatus* (see the supplementary 
sections on 
 Russell
 and 
 Wittgenstein).
 Although subsequent philosophers were to question the assumption that
there could ever be a definitive logical analysis of a given 
statement, the idea that ordinary language may be systematically 
misleading has remained.




To illustrate this, consider the following examples from Ryle's
classic 1932 paper, 'Systematically Misleading 
Expressions':



> (Ua) Unpunctuality is reprehensible. 
> 
> 
> 
> (Ta) Jones hates the thought of going to hospital.
> 
> 
> 




In each case, we might be tempted to make unnecessary reifications, 
taking 'unpunctuality' and 'the thought of going to
hospital' as referring to objects. It is because of this that 
Ryle describes such expressions as 'systematically 
misleading'. (Ua) and (Ta) must therefore be rephrased:



> (Ub) Whoever is unpunctual deserves that other people
> should reprove him for being unpunctual. 
> 
> 
> 
> (Tb) Jones feels distressed when he thinks of what he will undergo if
> he goes to hospital.
> 
> 
> 




In these formulations, there is no overt talk at all of 
'unpunctuality' or 'thoughts', and hence 
nothing to tempt us to posit the existence of any corresponding 
entities. The problems that otherwise arise have thus been 
'analyzed away'.




At the time that Ryle wrote 'Systematically Misleading 
Expressions', he, too, assumed that every statement had an 
underlying logical form that was to be exhibited in its 
'correct' formulation 
 [Quotations].
 But when he gave up this assumption (for reasons indicated in the 
supplementary section on 
 The Cambridge School of Analysis),
 he did not give up the motivating idea of logical analysis--to 
show what is wrong with misleading expressions. In *The Concept of
Mind* (1949), for example, he sought to explain what he called 
the 'category-mistake' involved in talk of the mind as a 
kind of 'Ghost in the Machine'. His aim, he wrote, was to
"rectify the logical geography of the knowledge which we 
already possess" (1949, 9), an idea that was to lead to the 
articulation of *connective* rather than *reductive* 
conceptions of analysis, the emphasis being placed on elucidating the
relationships between concepts without assuming that there is a 
privileged set of intrinsically basic concepts (see the supplementary
section on 
 Oxford Linguistic Philosophy).
 




What these various forms of logical analysis suggest, then, is that 
what characterizes analysis in analytic philosophy is something far 
richer than the mere 'decomposition' of a concept into 
its 'constituents'. But this is not to say that the 
decompositional conception of analysis plays no role at all. It can 
be found in the early work of Moore, for example (see the 
supplementary section on 
 Moore).
 It might also be seen as reflected in the approach to the analysis of
concepts that seeks to specify the necessary and sufficient 
conditions for their correct employment. Conceptual analysis in this 
sense goes back to the Socrates of Plato's early dialogues (see
the supplementary section on 
 Plato).
 But it arguably reached its heyday in the 1950s and 1960s. As 
mentioned in 
 Section 2
 above, the definition of 'knowledge' as 'justified 
true belief' is perhaps the most famous example; and this 
definition was criticised in Gettier's classic paper of 1963. 
(For details of this, see the entry in this Encyclopedia on 
 The Analysis of Knowledge.)
 The specification of necessary and sufficient conditions may no 
longer be seen as the primary aim of conceptual analysis, especially 
in the case of philosophical concepts such as 
'knowledge', which are fiercely contested; but 
consideration of such conditions remains a useful tool in the 
analytic philosopher's toolbag.




For a more detailed account of the these and related conceptions of 
analysis, see the supplementary document on



> Conceptions of Analysis in Analytic Philosophy.




For further reading, see the



> Annotated Bibliography, SS6.


## 7. Conclusion




The history of philosophy reveals a rich source of conceptions of 
analysis. Their origin may lie in ancient Greek geometry, and to this
extent the history of analytic methodologies might be seen as a 
series of footnotes to Euclid. But analysis developed in different 
though related ways in the two traditions stemming from Plato and 
Aristotle, the former based on the search for definitions and the 
latter on the idea of regression to first causes. The two poles 
represented in these traditions defined methodological space until 
well into the early modern period, and in some sense is still 
reflected today. The creation of analytic geometry in the seventeenth
century introduced a more reductive form of analysis, and an 
analogous and even more powerful form was introduced around the turn 
of the twentieth century in the logical work of Frege and Russell. 
Although conceptual analysis, construed decompositionally from the 
time of Leibniz and Kant, and mediated by the work of Moore, is often
viewed as characteristic of analytic philosophy, logical analysis, 
taken as involving translation into a logical system, is what 
inaugurated the analytic tradition. Analysis has also frequently been
seen as reductive, but connective forms of analysis are no less 
important. Connective analysis, historically inflected, would seem to
be particularly appropriate, for example, in understanding analysis 
itself.