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New Draft: Classification of the Sciences (Peirce)

intro[edit]

Peirce did considerable work over a period of years on the classification of sciences (including mathematics).[1] In 1902, he divided science into Theoretical and Practical[2]. Theoretical Science was comprised of Science of Discovery and Science of Review, the latter of which he also called "Synthetic Philosophy", a name taken from the title of the vast work, written over many years, by Herbert Spencer. Then, in 1903[3], he made it a three-way division: Science of Discovery, Science of Review, and Practical Science. In 1903 he characterized it as:

...arranging the results of discovery, beginning with digests, and going on to endeavor to form a philosophy of science. Such is the nature of Humboldt's Cosmos, of Comte's Philosophie positive, and of Spencer's Synthetic Philosophy. The classification of the sciences belongs to this department."[4]

Classification of the sciences[edit]

Peirce opens his 1903 classification (the "Syllabus" classification) with a concise statement of method and purpose:

This classification, which aims to base itself on the principal affinities of the objects classified, is concerned not with all possible sciences, nor with so many branches of knowledge, but with sciences in their present condition, as so many businesses of groups of living men. It borrows its idea from Comte's classification; namely, the idea that one science depends upon another for fundamental principles, but does not furnish such principles to that other. It turns out that in most cases the divisions are trichotomic; the First of the three members relating to universal elements or laws, the Second arranging classes of forms and seeking to bring them under universal laws, the Third going into the utmost detail, describing individual phenomena and endeavoring to explain them. But not all the divisions are of this character.."[4]

Online sources:

table[edit]

Name Characterization Examples
Branch' of science Quote Peirce: "There are different classes, so that different students seem to live in different worlds, but yet there is one general animating motive." Examples: Science of Discovery. Science of Review. Practical Science.
Class of science Quote Peirce: "The types of inquiry of the different orders of a department are different, yet these orders are connected together so that students feel that they are studying the same great subject"[5]
Classes of science differ so radically in observation that observations in one class (say physical & psychological sciences) cannot yield the kind of information which another class (say pure mathematics) requires of observation.[6]
Example of different classes: Pure mathematics. The special sciences.
Order of science "...different sorts of conceptions are dealt with in the different families of a department, but the general type of inquiry is the same."[7]

Two orders within one class or subclass may differ hierarchically, one more general, the other more specialized.[6]

Peirce's 1903 example of different orders: General Physics. Biology. Geology.
Family of science Researchers differ in skill sets, but have the same general conceptions and understand each other in a general way. Peirce's 1903 example of different families: Astronomy. Geognosy
Genus of science Researchers differ in acquaintance with particular facts in detail, but share skill sets as well as general conceptions. Peirce's 1903 example of different genera: Optics. Electrics.
Species of science The narrowest division still having societies and journals, each researcher is thoroughly well qualified in all parts. Peirce's 1903 example of different species: Entomology. Ichthyology.
Variety of science Researchers devote lives, but not so numerously as to support distinct societies and journals. Peirce's 1903 example of different varieties: Study of Kant. Study of Spinoza.


Classes Subclasses Orders Other Taxa
Classes of science differ so radically in observation that observations in one class (say physical & psychological sciences) cannot yield the kind of information which another class (say pure mathematics) requires of observation.[6]
"...the types of inquiry of the different orders of a ...[class] are different, yet these orders are connected together so that students feel that they are studying the same great subject"[8]
Subclasses are analogously distinguished by subclasses of observation.
Two orders within one class or subclass may differ hierarchically, one more general, the other more specialized.[6]
"...different sorts of conceptions are dealt with in the different families of a department, but the general type of inquiry is the same."[9]
Suborders, families & subfamilies, genera & subgenera, species & subspecies, varieties & subvarieties.
Family: researchers differ in skill sets, but have the same general conceptions and understand each other in a general way. Peirce's 1903 example of different families: Astronomy. Geognosy.
Genus: researchers differ in acquaintance with particular facts in detail, but share skill sets as well as general conceptions. Peirce's 1903 example of different genera: Optics. Electrics.
Species: the narrowest division still having societies and journals, each researcher is thoroughly well qualified in all parts. Peirce's 1903 example of different species: Entomology. Ichthyology.
Variety: Researchers devote lives, but not so numerously as to support distinct societies and journals. Peirce's 1903 example of different varieties: Study of Kant. Study of Spinoza.
Classes Subclasses Orders Other Taxa
I. Mathematics.

Draws necessary conclusions about hypothetical objects.
A. Mathematics of Logic.
B. Mathematics of Discrete Series.
C. Mathematics of Continua and Pseudocontinua.
(Note: By "continuum" Peirce meant a continuum of points more numerous than any Hilbertian aleph's worth. He held that such a continuum was the true subject matter of that which we now call topology, and that the rationals, the reals, the complex reals, etc., constituted pseudocontinua.)
II. Cenoscopy,
or Philosophy.

(Philosophia Prima, First Philosophy.)

About positive phenomena in general, such as are available to every person at every waking moment, and not about special classes of phenomena. Does not resort to special experiences or experiments in order to settle theoretical questions.
Epistêmy
(1902 classification only)[10].
A. Phenomenology (or Categorics or Phaneroscopy).
(Includes the study of the cenopythagorean categories: Firstness, Secondness, and Thirdness).
B. Normative Science. i. Esthetics. (Study of the good, the admirable. Peirce reserved the spelling "aesthetics" for the study of artistic beauty.)
ii. Ethics. (Study of right and wrong).
iii. Logic
(or Semiotic or Formal Semiotic). (Study of true and false.)
1. Speculative Grammar
(or Philosophical or Universal Grammar)
(or Stechiology)
(Includes the classification of signs).
2. Critic
(or Logical Critic, Critical Logic, or Logic Proper).
(Includes study of the modes of inference: abduction, induction, and deduction).
3. Methodeutic
(or Speculative Rhetoric,
or Universal or Philosophical Rhetoric).
(Is a locus of the Pragmatic Maxim, and includes study of scientific method).
C. Metaphysics. i. Ontology or General.
ii. Psychical or Religious. 1. God.
2. freedom (& destiny).
3. immortality.
iii. Physical.
Theôric (1902 classification only).
"...[theôrics] only resort to special observation to settle some minute details, concerning which the testimony of general experience is possibly insufficient."[10]
Chronotheory &
Topotheory
(1902 only)
III. Idioscopy,
or the Special Sciences.

About special classes of positive phenomena. Resorts to special experience or experiments in order to settle theoretical questions.
[?]. Physical. i. Nomological or General. i. Molar Physics. Dynamics &
Gravitation.
ii. Molecular Physics. Elaterics (pressure) &
Thermodynamics.
iii. Etherial Physics. Optics &
Electrics.
ii. Classificatory.
Peirce in the 1903 Syllabus classification:[11] "Classificatory physics seems, at present, as a matter of fact, to be divided, quite irrationally and most unequally, into i, Crystallography; ii, Chemistry; iii, Biology."
i. Crystallography
ii. Chemistry. 1. Physical.
2. Organic.
Aliphatic & Aromatic.

3. Inorganic
(elements, atomic weights, compounds, periodicity, etc.)

iii. Biology. 1. Physiology.
2. Anatomy.
iii. Descriptive. Geognosy & Astronomy.
[?]. Psychical. i. Nomological Psychics,
or Psychology.
i. Introspectional.
ii. Experimental.
iii. Physiological.
iv. Child.
ii. Classificatory Psychics,
or Ethnology.
1. Special Psychology. 1. Individual Psychology. 2. Psychical Heredity.
3. Abnormal Psychology. 4. Mob Psychology.
5. Race Psychology. 6. Animal Psychology.
2. Linguistics. 1. Word Linguistics.
2. Grammar ("should be a comparative science of forms of composition")
3. Ethnology. 1. Ethnology of Social Developments, customs, laws, religion, and tradition.
2. Ethnology of Technology.
iii. Descriptive Psychics,
or History.
1. History proper.
2. Biography ("which at present is rather a mass of lies than a science")
3. Criticism 1. Literary criticism
2. Art criticism (criticism of military operations, crticism of architecture, etc.)

Notes[edit]

  1. ^ See "Development of Peirce's classification of sciences - three stages: 1889, 1898, 1903" by Tommi Vehkavaara, 2003, "Eprint" (PDF).  (20 kB) and "The outline of Peirce's classification of sciences (1902-1911)" by Tommi Vehkavaara, 2001, "Eprint" (PDF).  (12 kB)
  2. ^ MS L75.355
  3. ^ CP1.181 (1903) Eprint
  4. ^ a b CP1.182 Eprint Cite error: Invalid <ref> tag; name "" defined multiple times with different content (see the help page).
  5. ^ Manuscript L75.353, 1902, Eprint
  6. ^ a b c d CP1.238, 1902, Eprint Cite error: Invalid <ref> tag; name "CP1.238" defined multiple times with different content (see the help page). Cite error: Invalid <ref> tag; name "CP1.238" defined multiple times with different content (see the help page). Cite error: Invalid <ref> tag; name "CP1.238" defined multiple times with different content (see the help page).
  7. ^ Manuscript L75.352-353, 1902, Eprint
  8. ^ Manuscript L75.353, 1902, Eprint
  9. ^ Manuscript L75.352-353, 1902, Eprint
  10. ^ a b CP1.278 Eprint Cite error: Invalid <ref> tag; name "theoric" defined multiple times with different content (see the help page).
  11. ^ CP1.194