Abstraction

Suppose we see two apples. They have many properties in common, but some are different. One of them may have some spots and the other may be more pointed.

We then perform an analysis of what we perceive. We ignore the spots and the pointedness and focus on what is common. These abstracted objects we synthesise into the concept "apple".

The properties that are not discriminating have been abstracted (away) and we have formed an abstraction.

An abstraction is formed from the similarity between several perceptions or concepts (that ultimately are formed from perception) and hence implies a probability argument.

Important

Abstracted concepts occupy a very important position in both memories and reasoning.

Within philosophy they are therefore denoted using many different terms: Categorisation, type, representation, nature (as in human nature), character, fundamental character, general name [Mill], essence, archetype, universal [Aristotle], theoretical, pure (as in pure mathematics), "in itself", "mentally comprehended".

Because abstractions are interesting within epistemology, and in addition require some contemplation to be understood, they have resulted in a large amount of literature which is summarised here:

Perception of abstracted concepts is not possible

When we, based on perception of several apples, have synthesised the concept "apple", and in a similar manner created the concept "pear", we may from these (and other) concepts synthesise the concept "fruit".

The concept "fruit" is not possible to perceive. We may perceive various representations of "fruit", e.g. apples and pears, but the concept itself does not physically exist in reality.

In a similar manner perception of the abstracted concept "apple" is not possible. We merely perceive a certain apple together with its flaws and colour variations.

This was e.g. expressed by Thomas Hobbes that uses "common name" for "concept":

And a common name, being the name of many things severally taken, is therefore called an universal name; and therefore this word universal is never the name of any thing existent in nature.

Hobbes T - On Body (De Corpore) part 1.2.9 (English Works vol.01 (Molesworth, Bohn 1839), p.19-20.

The difficulties in perceiving abstractions functions as a seducing pillow for philosophers claiming that arguments may be formed independent of perception, i.e. a priori, and hence be "absolutely certain".

Wider use

An abstraction /abstracted concept/ has a wider area of use than any of the individual perceptions that are included in the concept.

In case we see a, for us, new type of bear, we may from our concept "bear" analyse what we are seeing, without remembering the exact appearance of bears that we previously have seen.

More credible

An abstraction is created through synthesis of several premises. It therefore becomes more credible than any of the included individual premises.

Example:
In case we are to guess the length of a completely unknown human, the concept "average length" is more useable and credible than the length of some arbitrary person.

"Average length" is formed from measurements of the lengths of many persons, i.e. from many perceptions, while the length of a certain person is formed from just a single perception.

The length of a person, e.g. of a child, may change while the concept "average length" does not vary to the same degree.

Not "absolutely certain"

Because an abstraction is formed from several perceptions, it becomes more useable and more certain when compared to an individual perception. This has inspired some rationalistic philosophers to the opinion that it would represent "absolute certainty".

But because the premises of the argument that leads to the abstraction implies probability arguments, the conclusion of the argument, i.e. the abstraction, also becomes a probability argument.

Abstractions formed from earlier abstractions are quite common and important. The earlier abstracted concepts "apple" and "pear" may, together with additional concepts, form the concept "fruit".

Every further abstraction implies the interesting changes discussed above:

- Fewer associations to perception (but the abstractions are still ultimately formed from perception).

- Wider area of use.

Repeated abstractions of abstractions lead only after a few steps to concepts that appear to be completely devoid of connections to perception (although the connections ultimately exist).

Repeated abstractions lead to a concept taxonomy:

- humans and dogs etc. are abstracted to animals.
- animals and fungi etc. are abstracted to living.
- living and not living are abstracted to objects.
- objects and behaviours etc. are abstracted to phenomena.
- phenomena and free phantasies are abstracted to "everything imaginable".

The final /"highest", furthest away/ abstraction "everything imaginable" may also be cognised as "The Whole" or "The Unity".

The ultimate premises for the final abstraction are still based on perception, and the concepts "The Whole" or "The Unity" hence include every imaginable perception and emotion. They may therefore be analysed into every conceivable concept, which demonstrates that all concepts are directly or indirectly connected.

Historic abstractions

I believe that the pre-Socratic Pythagoreans abstracted their fundamental concept "One" or "The One" in this manner:

Heraclitus about 535-475 BCE was partly a Pythagorean:

- all things are one.

- out of all things there comes a unity and out of a unity all things

McKirahan 2011 - Philosophy before Socrates, p.116, 129.

In a similar manner the concept "a perfect and all-embracing God" was formed through synthesis followed by abstraction from many imaginable arguments (ultimately based on perception) about benevolence and perfection:

Therefore there is ... a subject of all perfections or a most perfect being. ... this being exists, since existence is contained in the number of perfections.

Leibniz 1676 - That a Most Perfect Being Exists, in Loemker - Leibniz, Philosophical Papers and Letters, 2Ed., p.167.

The absence of evident premises in a repeated abstraction implies that it must be exemplified, or deconstructed, using premises based on experience when they are used - it must be analysed.

The concept "apple" may be deconstructed as "tasty", "fresh", or "nutritious". And, as expressed above, Leibniz claimed that "existence" is a premise in the concept "all perfections".

If the sender and receiver in a communication exemplify an abstracted concept using different premises, the communication becomes incomplete, as is discussed under Interpretation.

Correlation

When two compared abstractions vary in a similar manner this is called that they are correlated.

Many human life paths are correlated when they are abstracted to:
"are born, growing, paring, getting children, ages, dies".

Analogy

An analogy /simile/ describes similarity between details in abstractions.

An example is the analogy between fish and human, where fins corresponds to hands and feet, and the tail-fin corresponds to the tailbone.

the word analogy means proportion or proportionality, as we have learned from the Greeks.

(analogy is taken to mean the mutual relationship or proportion of ideas or terms).

Cardinal Cajetan 1498 - The Analogy of Names (Bushinski, Duquesne University Press 1953), p.10, 11 annotation.

Metaphor

A metaphor, like that the world may be compared to a theatre scene, can be seen as a richly expressed analogy:

All the world's a stage,
And all the men and women merely players
They have their exits and their entrances

Shakespeare 1623 - As you like it,
in Shakespeare's Comedies, Histories, Tragedies, & Sonets (Eyre & Spottiswoode 1896 p.216)