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Survey
Weighting
Theme
Thematic and other
symbols
Linkage schemata
Indicators
The value of symbolic notation
This is an informal introduction to 'themes.' For a more formal introduction, in PDF format, click here.
Here, terms I use again and again in this section of the site are explained. The term 'theme' is basic, but the explanation is the most difficult material on this page and so I defer it until later.The section which is the most difficult of all is the section 'thematic and other symbols.' The sections 'Survey' and 'Weighting' are simple to follow and give concrete examples.
A survey is an attempt to gather together all or, more often, as many as possible, of the considerations which are relevant to an issue. Surveys are applied to a very wide range of issues: household products, ethical issues, theories of human nature, issues to do with scientific theory and many, many more. The use of the common term gives a linkage to seemingly unrelated things.
If the issue is concerned with a household product, then appearance, financial cost and functionality are likely to be some of the survey-items: ((appearance, financial cost, functionality)) Very often, these surveys are seriously incomplete, but it's increasingly common for people to include in their survey of household products such considerations as 'costs' in a wide sense: environmental costs (the costs of obtaining the raw materials, the costs of production and transportation), the cost to the producers (such as child labour, dangerous or polluted working conditions), the cost to animals, when, for example, the product has been tested on animals, or when their meat or eggs constitute the product.
A survey involves an attempt to gain adequate information about the issue. If the issue is the death penalty, then complex information about deterrence and reformation will generally be needed, and also information about the comparative costs of imprisonment and proceeding to an execution. Often, views are based on a faulty survey, such as assuming that it's cheaper to execute than imprison for life (in the USA, this isn't the case.) The survey may also include matters which are not 'information,' such as revulsion at the barbarity of the execution process, revulsion at the act of murder, feelings concerning retribution.
Different surveys may be striking in their inclusions and omissions. Whereas the vegan diet gives particular importance - or weighting - to animal welfare, so that the welfare of calves is a very important consideration, this is missing to a very large extent from the survey of many people with an interest in French classical cooking.
Scientism has a restricted survey, one which is concerned with only those aspects of human life which are supposed to be scientifically explainable.
Scientific method has a restricted survey too: necessarily restricted, it can be claimed. It confines itself to those explanations of nature which can be studied by means of repeatable empirical methods, or if not, controlled observations. Missing from the survey are such considerations as our personal preferences, what we would like to be the case, what gives reassurance.
One survey isn't as good as another. Arguments and evidence are employed to find one survey more or less adequate than another. One survey may give far more {distortion} than another.
Although I think that scientific method is the only useful way to study nature - it's obviously far more useful than any other in its practical results, which are based on its laws and theories - I also think that scientism can't be defended.
In general, surveys which omit 'higher' faculties and interests may well be defective. The survey of an environmentalist may be defective if it concentrates exclusive attention on insulation and draught proofing in a house, and neglects, for instance, its aesthetic value. There are many other distortions which can arise from the surveys of environmentalists.
The practicality of mobile phones isn't in doubt. They may be more or less essential to some people in gaining a livelihood, they can save lives (they have transformed mountain rescue), they enable someone with a broken down vehicle to contact breakdown services. This is familiar enough. I think that a survey should include, though, some severe disadvantages of mobile phones, effects upon concentration, the reduction of an essential contrast between the public and the private spheres, a reduction in contrast between places - a loss of richness, uniqueness in places - which is serious in its effects.
A survey of the strengths and advantages of a city may include in its survey the tolerance of its people, its prosperity, but may completely omit intellectual and cultural achievements, like the ones which couldn't be omitted in any adequate survey of Athens in the 5th century B.C.
To move to a less familiar application, themes also have surveys. The theme {resolution} has as part of its survey resolving power in optics - the capacity to distinguish two points - and also the capacity to distinguish, to give just one example, but an important example, useful, useless and harmful applications of a process.
I enclose survey-items in double curved brackets, (( )) and the survey-items
are separated by commas. So, in the case of a household product, then ((appearance,
financial cost, functionality)) In some cases the survey can be complete,
giving all possible survey-items, but in many cases a survey has
to be incomplete. A complete survey is shown by placing the
completion indicator 
before the end double brackets. In the case of a digital rather than an anologue
system, a particular component is either switched on or off. There are no
other possibilities, and so a survey of the states of this component can be
complete: ((on, off )).
Almost always, survey-items are not equally important to us. We make use of {ordering} to give more emphasis to some items than others. For example, in a survey which a person might carry out when deciding that it was time to emigrate, because the person's country seemed now to have too many disadvantages, the survey-items might include climate, cost of living, crime rate, and many more. Particular weighting might be given to climate. The person might be tired of rain and gloom and might decide to move to Spain. Someone who is an animal rights activist might have the same wish for a hotter, sunnier climate but would be likely to give far greater weighting to bullfighting. It would be intolerable to live in a country where bullfighting is still so widely supported.
Evaluations of people involve, implicitly, a survey which is subject to {restriction}. Not all human attributes and characteristics, virtues and faults, can be included. Only a selection is included, and these are subject to {/weighting} which has {ordering}. (This usage is explained below.) The very different weightings throughout the ages constitute a fascinating study. In medieval Christendom, for example, the characteristics of the humanitarian reformer were almost completely absent from surveys of desirable characteristics and the humanitarian reformer was almost completely absent from any survey of the people to be admired. Particular weighting was given to the characteristics of the saint, a type detested and reviled by Nietzsche amongst others: someone who often did not work, or make practical improvements, or even relieve suffering (where suffering was relieved, this was not so much to benefit the sufferer as to demonstrate the holiness of the saint, and it was 'holiness' which was given so much weighting in this age.)
The contrast between admiration on the one hand and self-admiration or mutual admiration on the other seems to me a significant one. In medieval times, sainthood was generally admired by people who didn't consider themselves to be saints. In modern times, virtuoso instrumentalists are admired by classical music lovers who aren't instrumentalists. On the other hand, people who admire liberalism, tolerance and perhaps political correctness often admire these characteristics in other people, and give particular weighting to them. (I generally admire liberalism and tolerance, but see every need for a {reversal} of tolerance in some cases, for example in our response to Moslem extremists, and am in general an enemy of political correctness.)
The weighting of many people doesn't give enough, or any weighting, to the manual work and skills that are necessary for their activities to continue. A common enough complaint is that people are divorced from the land, and don't appreciate the dependence of all human life on soil and the products of the soil. Very often, people are divorced from the technological and practical world on which they depend, the world of roofers, layers of pipes (it's pipes which protect us from cholera, the pipes which bring in clean drinking water and take away sewage and which have done more to lower the death rate than doctors and hospitals), the mechanics and suppliers of vehicle parts, amongst many others (even green activists who take public transport are dependent upon them), the people who deal in ferrous and non-ferrous metal and scrap metal - all essential, vital.) This is George Orwell on miners (from 'On the Road to Wigan Pier):
"Watching coal-miners at work, you realize momentarily what different universes different people inhabit. Down there where coal is dug it is a sort of world apart which one can quite easily go through life without ever hearing about. Probably a majority of people would even prefer not to hear about it. Yet it is the absolutely necessary counterpart of our world above. Practically everything we do, from eating an ice to crossing the Atlantic, and from baking a loaf to writing a novel, involves the use of coal, directly or indirectly.
"For all the arts of peace, coal is needed; if war breaks out it is needed all the more. In time of revolution the mines must go on working or the revolution must stop, for revolution as much as reaction needs coal. Whatever may be happening on the surface, the hacking and shovelling have got to continue without a pause, or at any rate without pausing for more than a few weeks at the most...
"It is only very rarely, when I make a definite mental effort, that I connect this coal with that far-off labour in the mines. It is just 'coal' -- something that I have got to have; black stuff that arrives mysteriously from nowhere in particular, like manna except that you have to pay for it. You could quite easily drive a car across the north of England and never once remember that hundreds of feet below the road you are on the miners are hacking at the coal."
This has a particular meaning in Linkage Theory. My explanation here, which includes explanation of the notation I use, has to be supplemented by the pages which deal with some of the themes, which are listed on the right side of the 'Map for themes...' A theme can be regarded as an organizing principle but is far more than that. This thematic approach is ambitious - an attempt to remap knowledge, as well as the arguments and opinions which don't amount to knowledge. Themes very often include the most diverse items. The items are linked in the theme and I claim that the linkage isn't 'loose,' but 'real.' To be more exact, there is homoiolinkage not heterolinkage. Compare Kant's use of homogeneous.
The elements which are linked in a theme are contrasting, and the contrasts are sometimes very marked. Often, then, knowledge, and the arguments and opinions which don't amount to knowledge, are included in the same theme. I often include in a theme scientific and evaluative elements, or scientific and mathematical elements, a priori and a posteriori elements, which have very different origins. I argue, for example, that addition of number belongs to the same theme as increase in biomass. This is a radical claim.
The name of a theme is given in curly brackets, for example {distortion}, a theme which includes as sub-themes {distortion in optics} and the evaluative distortion produced, I claim, when a person's estimate of someone else is affected by focussing attention, not on the core personality, but on, for example, smoking. {resolution} or {resolving power} again has an optical sub-theme, measuring the ability of an optical instrument to form separable images of close objects, and an evaluative sub-theme, for example, the ability to distinguish real and apparent goodness.
Whereas {resolving power} is an example here of a root theme, {/optical resolving power} is an example of a sub-theme. I use the term {theme} has {/subtheme} but the order is immaterial: {/subtheme} has {theme} has the same meaning. The stroke identifies the sub-theme.
A sub-theme may in turn have sub-themes, which are written as {//sub-theme}
When the sub-theme is the focus of attention, and not at all the root theme, then the sub-theme can be regarded as a root theme and the stroke is omitted.
Examples of a theme or sub-theme are instances and can be given in a list. Whereas an attempt can be made to make a survey exhaustive, as complete as possible, this is rarely the case with a list. A list is almost always incomplete, a selection.
Themes have a sphere of application, shown by a the sphere of application indicator, a colon - {theme}: sphere of application. Alternatively, a slightly less concise notation, {theme} has: sphere of application. Colons which are used in the text with their usual sense, as punctuation marks, don't follow {theme}: or {theme}has: If a sphere of application is not applicable, then this is shown as ~ : as in {theme}~ : sphere of application. For example, {modification}: empirical reality in a possible world and {modification}~ : transformation of a tautology into a non-tautology. If a theme is actually applied, then I use the notation :- and if a theme is not applied the notation ~ :-
Examples of the use of this notation:
{restriction} is regarded as unchanging. It does not include, in itself, progressive restriction, for example. However, {modification} has: {/restriction}. {modification} has {/increase} and {/decrease}, both of which have: {/restriction}. Further, {diversification} has {/{{decrease}:-{restriction}}} This illustrates the more complex use of bracketing.
It's important to be able to show scope, that is, the extent
of an application. This is important in areas other than linkage
theory, for example in symbolic logic. There are various methods of indicating
scope, for example underlining. The scope of the universal quantifier in (
x)
Fx 
Gx is 'Fx,' which is the nearest complete expression to the right. I don't
give here any explanation of the fact that 'the scope of a quantifier is the
complete expression which immediately follows it.' (Samuel Guttenplan, 'The
Languages of Logic.') The scope in longer logical statements can be shown
by horizontal underlining. In the case of logical derivations, to the numbered
formulas there can be added a vertical line to show scope - the scope line.
There may be a primary scope line and other scope lines.
I see the need for a more general treatment of scope and sphere of application. Obviously, these logical examples are only instances of scope. And scope should be recognized as an instance of {restriction} of inclusion and exclusion. As for indicating scope, horizontal and vertical underlining have their uses, but short sections of underlining may be confused with the indication of links in Web sites and underlining is impractical for long sections. I use the scope indicator, two asterisks * * to indicate scope. This is useful to indicate 'short scope' and 'long scope.' An example of 'long scope:' if a paragraph has * at top left and * at bottom right, then everything between the asterisks is shown as a sphere of application.
There are two thematic modes: free and bound. (These have no connection with the use of 'free' and 'bound' to refer to variables within the scope of a universal or existential quantifier in logic.) I refer to the free mode as one in which an agent is apparently free to implement a theme, for example lifting up a hand, (which is {modification} of position) or arranging the independent variable in a scientific experiment. I very much believe myself that free will exists, but use of the term is compatible with a deterministic viewpoint - the agent is not actually free. In the bound mode, the theme isn't implemented by the agent, for example, a change in dependent variables in a scientific experiment. For a mathematical example, consider the simple equation a + b = c If the agent decides to move b to the other side of the equation, to give the equation a = c - b, then {/movement}, which has {modification} is in free mode and the change of sign is in bound mode.
I use the terms 'free' and 'bound' more widely than in connection with themes. For example, 'directed reading' is bound. Paul Duro, in 'Containment and Transgression,' an essay in the volume edited by him, 'The Rhetoric of the Frame,' writes, of instances where "...the idea of the frame (if not its literal presence) is necessary to maintain a directed reading of the image."
Very many themes have an evaluative interpretation, as well as non-evaluative interpretations. Often, evaluations are difficult or disputed. There are evaluative claims. Wherever necessary, {resolution} is used to make a clear-cut evaluation possible. ev+ is appended to a theme for positive evaluation and ev- is appended to a theme for a negative evaluation. I think that again and again, this form of interpretation leads to useful results - or useful claims.
As an example of evaluative interpretation, consider a sub-theme of {modification}, which of course is a very comprehensive theme indeed, {instituting reforms} This may be {instituting reforms}ev+ or {instituting reforms}ev- The Australian philosopher David Stove claimed that more often than not, reforms were inadvisable, not to be recommended. There were many more ways to ruin an institution, a political system, or whatever, than to improve it. Conservative thinkers and others often advocate {reversal} in these cases. I believe that David Stove was mechanical in his general opposition to reform, not stressing nearly enough the need for judgment.
Some themes can be shown symbolically. In each case, the symbol indicates an activity, for example, 'to modify' but the name is a noun. I use
for {modification}read
as 'to modify.' (The use of capital delta is suggested by its use in science
for 'change of,' as in 'change of enthalpy.)
Ô for {ordering}
// for {separation}This symbol will not be confused with the symbol to indicate
a sub-theme of a sub-theme, as in the example {modification} has {/expansion}
and {/expansion} has {//diversification} since in this case // appears immediately
after {
== for {restriction} In symbolic notation, 'to restrict.'
==(f) is 'free {restriction}', the activity of a free agent.
==(b) is 'bound {restriction}.
The {reversal} of {restriction} is {expansion}, shown as =/=, the crossing-out of {restriction}.
‚ is {completion} and ~‚ is {continuation}.
Separate pages in this section of the site give information about these and other themes.
These, and other themes, may be used together with established connectives of symbolic logic, including the symbols of modal logic:
for 'possibility.'
Conjunction: 'and.'
Disjunction: 'or.'
~ Negation. ~~
Cancellation of negation.
The conditional: 'if...then.'
However, these symbols are used in the most general sense, not with their
restricted logical sense. So {resolution} has:
and
denotes contingent possibility as well as logical possibility. If the restricted
logical sense is used, then the symbols are enclosed in declaration
brackets <> as in <>..
The contents of the brackets are 'declared' as being of a restricted mathematical,
logical or other sense, as in this mathematical example: == :- < * >
(+, -, x ...) where < * > is the binary operator.
is used in a non-restricted
sense meaning 'to give' when it follows:- and the 'if...then' sense of the
symbol is preserved: for example, if operation P is applied to entity X or
theme Y then Z is the result. So, {restriction} when applied to the linkage
symbol gives the logical symbol
< > the brackets indicating
that the symbol is not used in a generalized sense but its restricted logical
sense. Symbolically, == :- (
) <
> .Here, the brackets ( ) are used to indicate that
is the object of application. They can be omitted when the meaning is clear.
Other symbols may be used in a restricted, established way or in a generalized way. For example, ‚ is my generalized completion indicator and also the mathematical halmos symbol, showing the completion of a mathematical proof.
If a whole section (mathematical, logical or other) uses symbols in only a mathematical, logical or other restricted sense, then this can be made clear by using the declaration indicator, Dn, together with an indication of the scope of the declaration, instead of using <> to enclose individual symbols. A declaration indicator is often used, in effect, in legal argument, as in the case of entitiies which are clearly not x but are declared to be x within the meaning of an act.
Another example, showing the transformation of the unordered elements of
a mathematical set into a mathematical ordered set: Ô :- <(a,b)>
<<a,b>> The ordered
set is shown by the mathematical notation of angle brackets (the inner brackets),
whilst the outer angle brackets indicate declaration.
Examples of the use of thematic symbols and connectives
P 'to modify P,' {modification}
of P. The thematic symbol is written before the variable, except in the case
of //, written between the variables to be separated.
/ == is 'modification by
restriction.'
/ =/= is 'modification
by expansion.'
P // Q 'to separate P and Q.'
P // Q // R 'to separate P, Q and R'
P // Q 'possible to separate
P and Q ' or 'P and Q are separable.'
~
P 'not possible to modify P,' or 'P is not modifiable.'
ÔP ÔQ 'to order
P is to order Q.' If P is ordered then Q is ordered.
~
(
P
Q) 'it's not possible to
modify P and also to modify Q.'
P // Q
R // S 'if it's possible
to separate P and Q then it's possible to separate R and S.'
Using the completion indicator to show completion of a thematic activity:
‚P is 'modification
of P is complete.'
== ‚Q is 'restriction of Q is complete.'
Objects, entities // themes
° is used for objects and entities which fall within the sphere of application
of a theme, or to which a theme has actually been applied. For example: °
:- objects which have been
modified. The general term ° is qualified and the qualification is placed
after the general term in 'post-notation.'
° ~// ° objects which have not been separated.
Objects and entities are inclusive and generalized in their scope. No claim is made that they have real existence. Platonic forms as regarded by a nominalist are also objects. {restriction}:-° will give objects acceptable to the nominalist.
It's convenient to separate objects and the themes which are the operations on objects by means of axis organization. Compare axis poetry. (This page mentions the organization of mathematical equations.) Axis organization shows the thematic or other operations carried out on the objects/entities on the left and objects/entities on the right of the axis line. {separation} has {spatial separation}. Typographically, it's often easier not to show the axis line as a vertical line but to indicate it by means of the special axis separator /A/ As an example, {}/A/ ° obviously shows {axial separation} between thematic operator and object/entity.
Modification of themes by tense etc
It's often convenient to apply grammatical terms to themes to indicate tense
and, in some contexts, mood and modality. The name of the theme is a noun,
such as {modification} The theme can be read 'modification of' or 'to modify,'
as in P, which can be read
'modification of P' or 'to modify P.' From this base, other forms can be derived:
tenses, for example are applied to the theme. Past is indicated by the subscript
p and future by the subscript f
The notation for these is explained more fully in the General Glossary but an extension is described here, in connection with the theme {restriction}.
In the linkage schema [A] <> [B] A is shown as linked with 'B.' [ ] are the contents brackets and <> are the linkage brackets. If these are reversed, >< then A is not linked with B.
The contents of the linkage brackets are ontologically general but can be restricted, the restrictions being determined by ontological views and arguments. For example, they may be restricted to the common-sense physical objects of the world, such as tables and chairs. The contents of the content-brackets then restrict the contents of the linkage brackets:
== [P] == [Q]
== <R>
For example, the schema [table 1] <gravitational attraction> [table 2] is possible, but not [table 1] <nuclear reaction> [table 2].
As the contents of [] are generalized they may include activities, processes, themes - and linkages - as well as objects and entities.
The contents of the contents brackets may be restricted to the common-sense physical objects of the world and to common-sense mental particulars. There are other metaphysical views which would give widely differing contents: the forms of Plato, the possible non-existents of Meinong, the monads of Leibniz, for example. There are simple and composite contents, atomic and molecular contents.
Relations
Declaration is obviously necessary in many cases for the contents of content
and linkage brackets, by using <> or Dn. If angle brackets are used
for declaration, then they are the inner brackets and the linkage angle brackets
are the outer brackets, as in [x] <<R>> [y] where R is declared
to be a mathematical relation. If R is a mathematical relation on the set
S and x, y are elements of S, then instead of using the conventional notation
of kR'y for the negation of 'xRy' then I use the notation [x] ><R><
[y]. A particular relation, such as equality or identity is a {restriction}
on a mathematical relation. And {resolution}:- <R>
(( < = , < , > , > )) Dn: all the survey-items are mathematical
symbols, so that the survey-items < and > stand for 'less than' and
'greater than.'
If, again, Dn: R: mathematical relation, then == :- R
((reflexive R, so that a,
aRa,,symmetrical R, so that a,
b,
aRb <>
bRa,,transitive R)) Here, single commas are used within each survey-item so
double commas ,, are now used to separate survey-items.
A philosophical treatment of relations is much wider and more contentious. The Platonic view of relations is very different from the nominalistic view, reflecting different views of properties. Bertrand Russell's contention (in 'The Problems of Philosophy) that 'All a priori knowledge deals exclusively with the relations of universals' would not be accepted by all philosophers.
The value of symbolic notation
The value, the necessity, of symbolic notation are obviously recognized in the spheres of mathematics and symbolic logic. Ordinary language would be hopelessly cumbersome as a replacement. Information is very commonly presented in tabular form, in rows and columns, allowing comparisons to be made, linkages and contrasts to be shown, with the maximum clarity. To present the same information in sentences in ordinary language would generally be possible but again would be unworkable in practice.
It's my contention that in many contexts, the use of ordinary language obscures the structure of an argument and hides linkages and contrasts which it's essential to recognize. There are many ways of expressing an argument by means of ordinary language and differences in expression may well hide a common structure or development. Ordinary language has redundancy, ambiguity and other drawbacks which can be reduced or sometimes eliminated by using a symbolic notation, as well as a concise notation which doesn't involve symbols, such as the use of {themes} and linkage schemata. Obviously, I have no intention of substituting symbolic notation and concise notation for ordinary language in cases where something essential would be lost, as, to give only one example, in any use of language to convey emotion. Symbolic and concise notation will not usually be a complete replacement for ordinary language but a clarification or enhancement, showing, for example, very clearly the essential structure of an extended philosophical argument, the stages in an extended piece of mathematical reasoning, the introduction of evaluative terms (permissibly or not) into an account otherwise based on factual information. Symbolism and sentences will be given together. The presentation of ordinary language and symbolic language together has a counterpart in coding for the Web, in the code view which gives HTML code together with ordinary language, as in this example from the code view of a paragraph of this page:
<p>It's convenient to separate objects and the themes which are the
operations
on objects by means of <strong>axis organization. </strong>Compare
<strong><a href="../glossarylit.htm#axis"><u>axis
poetry</u></a><u>. </u></strong>(This page mentions
the organization of mathematical
equations.) Axis organization shows the thematic or other operations carried
out on the objects/entities on the left and objects/entities on the right
of the axis line. {separation} has {spatial separation}. Typographically,
it's often easier not to show the axis line as a vertical line but to indicate
it by means of the special <strong>axis separator </strong>/A/
As an example,
{}/A/ ° obviously shows {axial separation} between thematic operator
and
object/entity. </p>
By using thematic names, thematic symbols, thematic connectives and linkage schemata, for ethical, legal, mathematical, logical, aesthetic arguments, and many others, we can show very vividly the common thought processes, tactics of reasoning, the repertoire of different activities of the mind - and the mind as it finds expression in practical activities of all kinds, including war (just or unjust), sport, economic systems, the activities of organizations.
Use of symbolic or other concise notation to accompany ordinary language is restatement. If nothing of significance for the argument is omitted then restatement is complete, otherwise restatement is incomplete.
Indicators
The indicators discussed and used above are collected here.
Completion indicator. This is shown as
Mathematicians refer to the symbol as the 'Halmos symbol,' after the mathematician
Paul R. Halmos and use it to indicate that a proof is complete. Completion
is generalized here, so that indicating the end of a proof is only one of
its uses. The symbol can be used to indicate that a thematic activity such
as {modification} is complete, or to show that an event is complete or that
a survey is complete, ((.....
))
Declaration indicator. Both Dn and the
declaration brackets < > are used to indicate
declaration. For example, if the symbol
is used in a restricted logical sense in an argument which uses the symbol
in a generalized sense, then the symbol has to be 'declared.'
Qn instead of a question mark is used to indicate a question.
Scope indicator. This is shown by using two asterisks to indicate scope *....* If, for example, it's necessary to show the exact scope of the existential quantifier.
Note
*Kant's 'homogeneous' in this extract from the Critique of Pure Reason is included in my 'homoiolinked: 'In all subsumptions of an object under a concept the representations of the former must be homogeneous with the latter, i.e. the concept must contain that which is represented in the object that is to be subsumed under it, for that is just what is meant by the expression "an object is subsumed under a concept." Thus the empirical concept of a plate has homogeneity with the pure geometrical concept of a circle, for the roundness that is thought in the former can be intuited in the latter.' (The Transcendental Doctrine of the Power of Judgment (or Analytic of Principles), First Chapter, On the schematism of the pure concepts of the understanding. Translation of Paul Guyer and Allen W. Wood.)
