The following diagram (used with permission) illustrates the intertwinement of the aspects. Each aspect has echoes of all the others and each builds on or anticipates all the others.
Understanding the nature of anticipation can help us identify the important aspects of things.
Anticipation is of two types: dependency and analogy. Dependency in the anticipatory direction is when something in an aspect is there 'for the purposes of' the later aspect, and, unless the meaning of that later aspect is taken into account, feels arbitrary and is little more than a curiosity in its own aspect. Analogy (which can be either anticipatory or retrocipatory) is a non-dependency similarity, an 'echo', of one aspect in another; for example, logical entailment echoes causality. Dependency entails necessity or meaningfulness; analogy does not. In this page we deal mainly with dependency.
But the meaning of organic chemistry - its importance, its interestingness - becomes apparent when we think from the point of view of the biotic aspect of life. It is organic materials of which living things are composed, and which possess the special properties that allow life to occur.
Those physical-chemical-material properties are not life themselves - because the notion of 'life' has no meaning from the physical aspect - but rather they are the very properties that support and implement what, from the point of view of the biotic aspect, we would call life.
That is, the physical aspect anticipates the biotic. They anticipate the biotic life functions. The life-supporting physical phenomena are there all the time, but they have no special meaning from the point of view of the physical aspect. Rather, their meaning, their special significance, lies in the biotic aspect.
You might wonder whether one could ever obtain a situation in which the numbers merged with each other continuously, but, if you stayed with countability, you would never discover continuous number, nor would you even find a need for them. You might speculate about them, argue whether they 'exist' or not, but (as long as you did not make reference to meaning from other aspects) they would remain at best meaningless curiosities.
But if you start to think about space rather than amount and countability - that is start to think from the point of view of the spatial aspect whose kernel meaning is continuous extension - then you would start to find a need for continuous number and encounter what mathematicians call irrational numbers - numbers that cannot be expressed perfectly as a ratio of two integers. Pi is a well known example. Then, as you use number to express spatial phenomena - via graphs, trigonometry, etc. - you start to see number as continuous rather than discrete. In fact, after a time - at least so I found - the continuity of number became such an ingrained assumption that it seems artificial to think of number as fundamentally discrete.
Neither continuous number nor the need for it can never be discovered if our thinking stays within the realms of the quantitative aspect. But it seems such numbers lurk there nevertheless, waiting to be discovered when we move our thinking to the spatial aspect.
This is one way in which the quantitative aspect anticipates the spatial: the continuity of number has no meaning from within the former, but only within the latter aspect.
|Quantitative||Discrete amount||Integers, ratios||
'Irrational' numbers |
|Spatial||Continuous extension||Length, position, shape, orientation||Direction, Changing position|
Atoms, Molecules, Chemicals, Materials
Organic chemicals |
Life functions; |
Maintenance of Organism
Respiration, Digestion, Repair, Reproduction; |
Cells, Systems, Skin
Nerve cells and ability to respond
|Sensitive||Sensing and Feeling||
Hearing, Seeing, Remembering; |
Figure-Ground separation, Pattern recognition, Cartesian Subject-Object separation; |
Recognising similarities; |
Linking of concepts
Achieving, Shaping, Planning; |
Goals, Structure, Skills
|Structuring of concepts for some end|
|Lingual||Meaning carried by Symbols||
Semantic meaning, Writing, Speaking; |
Topic or content of text, utterances
Cultural connotations; |
Greeting, Deferring; |
Social relationships, Institutions,
Management, Production, Consumption; |
Limits, Resources, Goods, Customers
|Aesthetic||Harmony and Fun||
Resting, Playing, Harmonizing; |
|Juridical||Giving Each Their Due||
Appropriateness, Proportionality; |
Responsibility, Rights, Legal systems
|Goodness (or Badness) of Law; "The notion of juridical guilt anticipates that of ethical guilt, and could not be understood without it." [Henderson:165].|
Agape-Loving, Giving of Oneself; |
Acts of Sacrifice, Repentance?, Forgiveness?; |
A genuinely self-critical attitude.
Believing, Trusting; |
Faith, Loyalty, Certainty
|(Ultimate commitment to what we take to be Divine)|
To construct it we have tried to avoid simply 'slot-filling'. Rather, we have asked ourselves the very specific questions centred on meaningfulness:
"In what way is 'amount' or 'more, less' meaningful in this aspect? Is there any special, meaningful way in which amounts, more or less stand in relation to each other in this aspect? Is there any special, meaningful way in which amounts, more or less are manipulated that is required by this aspect?"
|Aspect||Kernel||Types of quantity||How quantity is used|
|Quantitative||Discrete amount||Integers, Ratios, Unity (as oneness), Averages||Arithmetic operations, Statistics|
Irrationals [NC, II:185]. |
(But not size nor number of dimensions; see note below.)
|Approximation [NC, II:185], Raising to a powers (e.g. square, cube)|
|Kinematic||Flowing movement||Complex numbers [NC, II:170,172]. Negative numbers (movement in number). Infinitesimals.||Differentiation [NC, II:185],|
|Physical||Energy, mass||Basic physical constants?|
Life functions; |
Maintenance of Organism
|Unity (the organism as itself and not another)||Fibonacci series? (much in evidence in living things) (but might this have meaning in the quantitative aspect without the biotic?)|
|Sensitive||Sensing and Feeling||Logarithms, e.g. decibels for sound level, levels of brightness perceived||Circular quantity, in which when we get to a certain amount we start again at zero, e.g. piano octaves, the colour circle Green - Cyan - Blue - Purple - Red - Orange - Yellow - Green ... (But we also find circularity in compass directions in the spatial aspect.)|
Perhaps discreteness itself anticipates analytic distinction? |
(The usage of 0, 1 to represent TRUE and FALSE is mere symbolic convention, and not a true quantitative anticipation of the analytic aspect.)
|Enumeration (integers used to identify distinct items, such as chapters in a book). Logical quantification?|
|Formative||Formative power||Dates. Numerical order: the direction of numeric sequence (See note below..|
Can anyone think of one? |
(Digits? I don't think so; that is symbols used to signify specifically quantitative meaning, not amounts that are of a special type that would remain a speculative curiosity until linguality is taken into account.)
|Economic||Frugality||Limits||Double-entry book keeping (in which as you increase one number you must always decrease another number by the same amount)|
|Aesthetic||Harmony, Fun, Interestingness||
Problematic: there might be no genuine quantitative anticipation of the aesthetic because of the nature of the aesthetic aspect. We must avoid slot-filling. See note below. |
Maybe Factors? ("The same in the other") (but this is more like the aesthetic retrocipating the quantitative aspect, because factors have meaning within the quantitative aspect without reference to the aesthetic).
Maybe numbers that are 'interesting' (e.g. primes) are those that anticipate the aesthetic? (But primes have meaning in the quantitative aspect without reference to the aesthetic.)
|Likewise, there seems to be no special way in which we manipulate or relate amounts for aesthetic purposes.|
|Juridical||Giving Each Their Due||('Proportionality' would seem to have quantitative connotations, but when we look at its true juridical meaning, these connotations fade.)|
If you can think of better or more examples, please contact me.
2. Formative aspect. I believe, against Dooyeweerd, that numerical order anticipates the formative aspect, because without the latter there is no reason to place them in order; see fuller reasons.
3. Aesthetic aspect. Maybe there is no genuine quantitative anticipation of the aesthetic aspect. It is difficult to see how the aesthetic can be quantitative. While we might say "This music is more harmonious than that", it is very difficult to say what greater or lesser harmony is. Similarly "more funny". There seems to be no special type of amount, moreness or lessness that is specifically aesthetic, and for which we employ amount, moreness, lessness in a special way in relation to this aspect. I can think of no way of answering our core questions for the aesthetic aspect.
Copyright (c) 2002 Andrew Basden. But you may use this material subject to conditions.
Number of visitors to these pages: . Written on the Amiga with Protext.
Created: ? 16 Jan 2003. Last updated: 3 March 2003 .nav. 8 August 2003 Table of 'Next' anticipations, and list of later anticipations of quantitative aspect. 14 August 2003 self-critical attitude. 4 September 2003 feelings of justice. 11 October 2003 jur-eth, qv-kin anticipations from Henderson. 18 January 2005 corrected links. 25 May 2005 revamped; table of quantitative anticipations; Guidelines added. 19 March 2008 asp.neighbours. 14 June 2010 ant. as animating. 14 October 2013 Janet Danielson's lovely diagram.