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# Bibliography

Minute Logic: Chapter III. The Simplest Mathematics

## Htabs

Type:

Manuscript

Title:

Minute Logic: Chapter III. The Simplest Mathematics

Id:

MS [R] 429

Year:

1902

Description:

**From the Robin Catalogue:**

TS., for most part, G-c.1902-2, pp. 1-127.

Published as 4.227-323, with historical notes on signs and several theorems in algebra and logic omitted.

Language:

English

Peirce, C. S. (1902).

*Minute Logic: Chapter III. The Simplest Mathematics*. MS [R] 429.The entry in BibTeX format.

author = "Charles S. Peirce",

title = "{Minute Logic: Chapter III. The Simplest Mathematics. MS [R] 429}",

year = 1902,

abstract = "{From the Robin Catalogue: TS., for most part, G-c.1902-2, pp. 1-127. Published as 4.227-323, with historical notes on signs and several theorems in algebra and logic omitted. }",

language = "English",

note = "From the Commens Bibliography | \url{http://www.commens.org/bibliography/manuscript/peirce-charles-s-1902-minute-logic-chapter-iii-simplest-mathematics-ms-r-429}"

}

title = "{Minute Logic: Chapter III. The Simplest Mathematics. MS [R] 429}",

year = 1902,

abstract = "{From the Robin Catalogue: TS., for most part, G-c.1902-2, pp. 1-127. Published as 4.227-323, with historical notes on signs and several theorems in algebra and logic omitted. }",

language = "English",

note = "From the Commens Bibliography | \url{http://www.commens.org/bibliography/manuscript/peirce-charles-s-1902-minute-logic-chapter-iii-simplest-mathematics-ms-r-429}"

}

Commens Dictionary entries from ‘Minute Logic: Chapter III. The Simplest Mathematics’

1902 | CP 4.233
How it can be that, although the reasoning is based upon the study of an individual schema, it is nevertheless necessary, that is, applicable, to all possible cases, is one of the questions we shall have to consider. Just now, I wish to point out that after the schema has been constructed according to the precept virtually contained in the thesis, the assertion of the theorem is not evidently true, even for the individual schema; nor will any amount of hard thinking of the philosophers’ corollarial kind ever render it evident. Thinking in general terms is not enough. It is necessary that something should be DONE. In geometry, subsidiary lines are drawn. In algebra permissible transformations are made. Thereupon, the faculty of observation is called into play. Some relation between the parts of the schema is remarked. But would this relation subsist in every possible case? Mere corollarial reasoning will sometimes assure us of this. But, generally speaking, it may be necessary to draw distinct schemata to represent alternative possibilities. Theorematic reasoning invariably depends upon experimentation with individual schemata. We shall find that, in the last analysis, the same thing is true of the corollarial reasoning, too; even the Aristotelian “demonstration why.” Only in this case, the very words serve as schemata. Accordingly, we may say that corollarial, or “philosophical” reasoning is reasoning with words; while theorematic, or mathematical reasoning proper, is reasoning with specially constructed schemata. |

1902 | CP 4.318
What is experience? It is the resultant ideas that have been forced upon us. We find we cannot summon up what images we like. Try to banish an idea and it only comes home with greater violence later. |

1902 | CP 4.240
Mathematical logic is formal logic. Formal logic, however developed, is mathematics. Formal logic, however, is by no means the whole of logic, or even its principal part. It is hardly to be reckoned as a part of logic proper. |

1902 | CP 4.235
The most ordinary fact of perception, such as “it is light,” involves |

1902 | CP 4.229
It was Benjamin Peirce, whose son I boast myself, that in 1870 first defined mathematics as “the science which draws necessary conclusions.” This was a hard saying at the time; but today, students of the philosophy of mathematics generally acknowledge its substantial correctness. |

1902 | CP 4.233
How it can be that, although the reasoning is based upon the study of an individual schema, it is nevertheless necessary, that is, applicable, to all possible cases, is one of the questions we shall have to consider. Just now, I wish to point out that after the schema has been constructed according to the precept virtually contained in the thesis, the assertion of the theorem is not evidently true, even for the individual schema; nor will any amount of hard thinking of the philosophers’ corollarial kind ever render it evident. Thinking in general terms is not enough. It is necessary that something should be DONE. In geometry, subsidiary lines are drawn. In algebra permissible transformations are made. Thereupon, the faculty of observation is called into play. Some relation between the parts of the schema is remarked. But would this relation subsist in every possible case? Mere corollarial reasoning will sometimes assure us of this. But, generally speaking, it may be necessary to draw distinct schemata to represent alternative possibilities. Theorematic reasoning invariably depends upon experimentation with individual schemata. We shall find that, in the last analysis, the same thing is true of the corollarial reasoning, too; even the Aristotelian “demonstration why.” Only in this case, the very words serve as schemata. Accordingly, we may say that corollarial, or “philosophical” reasoning is reasoning with words; while theorematic, or mathematical reasoning proper, is reasoning with specially constructed schemata. |