Philosophy 207a: Mind - The Levels of Abstraction - revised

Contents

Introduction
Section 1: The levels of abstraction
Section 2: Constraints on abstraction
Section 3: Concepts of God and the levels of abstraction
Section 4: Analysis, synthesis, synopsis, and abstraction
Section 5: Knowledge in the levels of abstraction
Section 6: The aesthetic, intellectual, and hedonic levels of abstraction

Appendix: The Three Groups in this topic

Introduction

Abstraction is the body/brain/mind's ability to separate out from the world the formal aspects of things. The formal aspects of things are their 'bare bones', their more or less basic structures. Abstraction is 'more or less', and the more abstract our concept of something becomes the less content it has.

The importance of abstraction goes almost entirely unrecognised in everyday life. It is not until we think, and think philosophically, that we recognise that thinking itself can only proceed at an abstract level.

The psychologist / philosopher William James, in trying to describe how he imagined the mental life of infants, used the phrase "a blooming, buzzing confusion". Without the levels of abstraction (which develop beyond those available to infants) our experience of the world would indeed be a blooming, buzzing confusion. It would be all sensation and no perception, or all perception and no proposition, or all description and no explanation.

Section 1: The Levels of Abstraction

With the abstracted entities at each level of abstraction come also regulative entities that constrain them. This section lists only the regulated entities at each level. The regulatory entities are discussed in Section 2.

First level: sensations abstracted from environment

The nerve impulses that are transmitted to the brain and felt there as sensations carry only a sampling of all the information present in the environment. We know, for example, that dogs can hear sounds and smell odours that are present in the environment but unavailable to humans because of limitations in our sensitivity.

Second level: perceptions abstracted from sensation

The faculty of perception abstracts information from sensations and in doing so allows us to 'know-as' - which is to know, for example, certain sonic sensations as birdcalls. We do not, of course know a birdcall as such on the first occasion we hear one. Initial perception is merely the first step in the construction of concepts.

Third level: simple concepts abstracted from perceptions

Repeated experience of birds and calls builds the simple concepts (as distinct from the complex scientific concepts) of 'bird' and 'call'. The concepts are not the words, of course. The words become linked to the concepts by further experience of birds and calls and of the words 'bird' and 'call'.

Fourth level: complex concepts abstracted from simple concepts.

From simple concepts and language and further experience of both are abstracted all the ingredients of cognition (thinking), which occurs in the form of complex sequences of concepts and, sometimes, the words that express them. Not all thinking is necessarily done in words. Many kinds of thinking (and not only the simplest kinds) can occur without being accompanied with words.

Fifth level: simple propositions abstracted from complex concepts

Propositions express concept sequences that are candidates for belief. A belief is a fixed or static proposition. A belief is a static entity in that it is a proposition held (by the will) as being true (or as being false). It is important to realize that it is propositions, not beliefs, that are the main ingredients of thinking. Thinking is conjectural. Belief comes before and after thinking, not during it. Beliefs enter into thinking in their unfixed form, as propositions, and the will removes propositions from the thought processes by making them beliefs. Consider that the currency of reasoning is propositions, not beliefs. Reasoning does not say 'x is true, therefore y is true', it says 'IF x is true, y follows (and is true IF x is true)'. It is willing, not reasoning, that fixes x and y as being true (or false).

The level of simple proposition is the first of the levels at which we 'know-that'. Thus it is also the first of the levels at which we doubt-that.

Sixth level compound propositions abstracted from simple propositions

From simple propositions and further experience are abstracted compound propositions. These are the stuff of theory of all sorts, whether folk-theory, philosophical conjecture, or scientific hypothesis.

Seventh level Logic abstracted from compound propositions

See Section 2.

Nothing can be said about the seventh, eighth and ninth levels (beyond what is said in naming them) without anticipating the content of Sections 2, 3 and 4.

Eighth level Mathematics abstracted from reasoning

See section 2.

Ninth level God abstracted from mathematics?

See Section 3.

Section 2: Constraints on abstraction

At each level of abstraction, the abstracted entities and their content, which together are the ingredients of experience at that level, also exhibit form and context. At each level, context is simply 'all of the below', all of what occurs in the levels beneath. However, the form of entities at each level is specific to the entities at that level. It is these formal entities that constrain or regulate experience at that level.

Also, the content of the primary entities at each level is the primary entities at the level immediately beneath. For example, the content of perceptions is sensations.

For more on content, form and context, see Philosophy 200: Language Meaning.

Level 1: Sensations constrained by natural kinds

Sensations are abstracted from the body/brain/mind's external environment, so that environment (a sampling of it) is the content of sensations.

The forms of sensations are the 'natural kinds'. The natural kinds are universals (as distinct from particulars), and they are the constraints on experience at the level of sensation. (Of course, limitations on human sensitivity (compared with, say, dog sensitivity) also constrain our sensations.)

Cause-effect is a natural kind, and so our somatic skills, our basic skills at making our bodies move (walking, eating, etc.) are gained via sensation (including, of course, sensation from our own bodies). Somatic kills are one of the three sorts of 'know-how' (see Section 5).

For more on universals see Philosophy 203: The Real and the Unreal.

Level 2: Perceptions constrained by artificial kinds

Perceptions are abstracted from the sensations, and so sensations are the content of perceptions.

The forms of perceptions are the 'artificial kinds'. The artificial kinds, like the natural kinds, are universals (as distinct from particulars), but they are artificial in that they are forms of perceptions and as such are determined by a faculty of the mind. Contrastingly, the natural kinds are natural in that (i) they are the forms of sensations and (ii) the contents of sensations are samplings of the external 'natural' environment.

It is the artificial kinds that are the constraints on experience at the perceptual level.

Level 3: Simple concepts constrained by properties

Simple (that is, individual) concepts are abstracted from perceptions, so perceptions are the contents of simple concepts. The forms of simple concepts are the properties: qualities, relations, and quantities. Like natural kinds and artificial kinds, properties are universals (as distinct from particulars). It is qualities, relations and quantities that constrain experience at this level.

Level 4: Complex concepts constrained by non-propositional syntax

Complex (that is, grouped) concepts are abstracted from the simple concepts, so simple concepts are the contents of complex concepts. The forms of complex concepts are generated by the non-propositional syntax. This syntax is the 'grammar', the formulae, for constructing all complex concepts other than propositions. So it is this syntax that generates the constraints on experience at this level.

Complex concepts are the raw materials upon which the faculty of passive imagination (that is, dreaming) works. The passive (that is, unwilled) imagination disassembles and reassembles complex concepts producing variety and novelty of complex concepts.

Level 5:Simple propositions constrained by propositional syntax

Simple (that is, individual) propositions are abstracted from complex concepts, so complex concepts are the contents of propositions. The forms of simple propositions are generated by the propositional syntax. This syntax is the 'grammar', the formulae, for constructing propositions. So it is this syntax that generates the constraints on experience at this level.

Propositions are the main ingredients of cognition (thought). But, at this level, thought is limited to the construction of simple propositions.

Level 6:Complex propositions constrained by the modal dichotomies

Complex (that is, grouped) propositions are abstracted from the simple propositions, so simple propositions are the content of complex propositions. The forms of complex propositions are limited by the three modal dichotomies:

G1: possibility and impossibility
G2: actuality and potentiality
G3: necessity and sufficiency.

So it is these three dichotomies that constrain experience at this level.

This level is the level of active (that is, willed) imagination. The faculty of imagination disassembles and reorders and reassembles complex concepts and in doing so produces variety and novelty of complex propositions.

This level is the level of synthesizing processes such as imagination, fantasy, fiction, scientific hypothesis, philosophical hypothesis and criticism, etc.

The faculty of will fixes (puts in stasis) some propositions, both simple and complex. A belief is a proposition that has been fixed (held to be true or held to be false) by the will.

Level 7:Reasoning constrained by the laws and principles of logic

Reasoning is abstracted from complex (that is, grouped) propositions, so complex propositions are the content of reasoning. The forms of reasoning are generated by the principles and laws of reasoning (see Philosophy 201, Section 5).

Level 8: Mathematics constrained by the three sorts of algorithm

Math is abstracted from reasoning (that is, from the contents and forms and context of reasoning), so the contents, forms, AND CONTEXT of reasoning are the content of math. The forms of math are the algorithms (the formulae for generating math expressions). It is the algorithms that constrain math expressions, and the algorithms are themselves constrained by the three number scales: valency, ordinal and cardinal. This is made evident by the consideration that such diverse things as numbers, music, and moral values are structured according to those scales.

The context of math is everything other than God. (That is how, for example, God can be both singular and triple.)

Level 9: God the unconstrained?

If God is abstracted from mathematics, then math (that is, the content, forms, AND CONTEXT of math) are the content of God.

If there is no more abstract concept than God, God cannot be constrained by any more abstract concept. So, if God is constrained, He must be constrained by something at a lower level of abstraction.

Section 3: God in the levels of abstraction

Religion, philosophy and science have it in common that they are concerned with the concept 'God'.

Consider the God of the Judaic-Christian Bible. In the Old Testament, God is hardly more abstract than man. He's a person (has a personality), He has desires, He is even subject to emotions, notably anger. God in the New Testament He's not only a person He's a human being - is born, suffers, dies - then returns to His Heaven, showing, Christians claim, that He's more a loving than an angry God. The God of religion is a God whose believers believe in Him unreasoningly and wilfully.

The God of philosophy is a God whose believers must defend his existence using human reason. He is such relatively abstract things as God the designer, God the necessarily existent, God the uncaused first cause, God who has the problems of evil, foreknowledge of free choice, and competing religions.

The God of science is a God whose mind is mathematics, which is not far from saying a God that *is* mathematics (see The Mind of God by Paul Davies).

The concept of the God of philosophy/science is much more abstract (and thus has less content) than the concept of the God of religion. Therefore these two concepts of God come in at two different levels of abstraction. I suggest that the God of religion originally came in at the third level (the level of simple concept) and was elaborated at the fourth level. The God that comes in at the seventh level is, of course, the God of philosophy/science.

Is God constrained by what constrains math? The constraints on math allow the infinite (several infinites), so God's infinity is not constrained by math.

Is God constrained by what constrains logic? Well, the God of science and philosophy is (their God cannot do the logically impossible), but the God of religion is not.

Is the God of religion constrained by the three modal dichotomies?

The possible-impossible dichotomy is applicable to God, but it does not constrain God because it seems to be inconceivable that God is impossible.

The actuality-potentiality dichotomy does not apply to God, because God's actuality is very decidedly in question.

The necessity-sufficiency dichotomy does apply to God. Is God sufficient to the explanation of the world? Is God necessary to the explanation of the world? These questions are perhaps the most important questions that can be asked about God.

Section 4: Analysis, synthesis, synopsis and abstraction

Philosophy proceeds at a highly abstract level, and its three methods are analysis, synthesis (including the construction of questions, hypotheses, criticisms, and revisions of these), and synopsis.

G1: Analysis and abstraction

Analysis is the reduction (without elimination) of complex concepts to their component simple concepts. So analysis proceeds from a higher to a lower level of abstraction. Thus also, analysis proceeds from a lower to a higher level of content.

G2: Synthesis and abstraction

Synthesis is the construction of (i) complex concepts from simple concepts, (ii) simple propositions from complex concepts, (iii) complex propositions from simple propositions, (iv) linguistic arguments from complex propositions, (v) mathematical arguments from the principles of reasoning and from the contents (numbers) and forms (algorithms) of math.

Thus synthesis proceeds from a lower to a higher level of abstraction, and thus from a higher to a lower lever of content.

Note also that synthesis ranges much more widely among the levels of abstraction than does analysis.

Because synthesis proceeds in the direction of abstraction, it is much more prolific than analysis.

G3: Synopsis and abstraction

Synopsis is the reduction of complex concepts and complex propositions to their component simple concepts and simple propositions. Thus, like analysis, synopsis is reductive. But, unlike analysis, synopsis seeks to make complex concepts precise by (i) making them complete (that is, by ensuring that they contain every simple concept that is necessary to them), and (ii) ensuring that they are not over-complete (by eliminating from them any simple concepts that are not necessary to them). And synopsis seeks also to make complex propositions precise.

So synopsis, while proceeding away from abstraction and towards content, also might add some content (to achieve completion) but is more likely to remove some content (to achieve parsimony).

Arguably, synopsis is also applicable to the levels of reasoning and mathematics. If it is applicable to those levels, its range among the levels of abstraction is as wide as the ranges of analysis and synthesis combined.

Section 5: Knowledge in the levels of abstraction

There are three main sorts of knowledge:

G1: Perceptual (knowing-as)
G2: Propositional (knowing-that)
G3: Practical (knowing-how)

Perceptual knowing occurs at the second level of abstraction, so its content is sensations.

Propositional knowing occurs at the fifth level and each higher level. It's content is complex (that is, grouped) concepts of all sorts.

There are four sorts of practical knowledge:

G1: Somatic skills
G2: Group skills
G3a: Mechanical skills
G3b: Propositional technological knowledge

Somatic skills (knowing how to walk, eat, grasp, etc.) are gained at Level 1, the level of sensation.

Group skills (such as cooperative hunting, team sports, etc.) can be gained at Level 4, the level of complex concept, and thus can be gained without (or with) propositional help.

Mechanical skills, knowing how to use tools, are also gained at level 4.

Propositional technological knowledge is gained at Levels 5 and above, the levels of complex proposition.

Section 6: The aesthetic, intellectual, and hedonic levels of abstraction

The second and third levels of abstraction can also be termed the aesthetic levels. (Levels four through nine are the intellectual levels, and level one is the hedonic level.) If I am correct in my account of the aesthetic levels and in placing the original religious concept of God in the third level, this goes some of the way toward explaining the connection between religion and art, a connection that seems (not just to me) more than coincidental or due to historical
circumstances.

Appendix: The Three Groups in this topic

Group 1: Second and third levels (the perceptual / aesthetic levels)

Group 2: Fourth to ninth levels, inclusive (the propositional / intellectual levels)

Group 3. First level (the sensational / hedonic level).

The modal dichotomies:
G1: possible-impossible
G2: actual-potential
G3: necessity-sufficiency

The sorts of practical knowledge:
G1: Somatic skill
G2: Group skill
G3a: Mechanical skill
G3b: Propositional technological knowledge