## Samenvatting

In his 2002 paper, "The speculative generalization of the function: A key to Whitehead," James Bradley writes:

"It is no accident that Whitehead describes philosophy as 'imaginative generalization' (PR 5), and sees his thought as a 'generalized mathematics' (ESP 109). [...] What he means by this is evident throughout Process and Reality (1929), which is the revision and the culmination of his earlier mathematical and philosophical work, in particular his collaboration with Russell in Principia Mathematica (1910-1912). For in Process and Reality and subsequent writings, Whitehead builds on the brilliant success of the Frege-Russell generalization of the mathematical function and develops his philosophy on that basis." (Tijdschrift voor filosofie, 64/2002, p.254.)

A year later, in a similar paper, "Whitehead and the analysis of the propositional function," Bradley repeats:

"It is no accident that Whitehead calls his speculative philosophy a "generalized mathematics" (ESP 109). For in Process and Reality (1929), as the revision and culmination of his work in Principia Mathematica (1910-1912), he builds on the brilliant success of the Frege-Russell generalization of the mathematical function as the propositional function." (In: George W. Shields (ed.), Process and Analysis, SUNY, 2003, p.145.)

However, if we consult Whitehead's Essays in Science and Philosophy (ESP 109), we discover that he utilizes the expression "generalized mathematics" to stress that mathematics evolved from the specific study of numbers and quantities to the general study of patterns: "The essence of this generalized mathematics is the study of the most observable examples of the relevant patterns; and applied mathematics is the transference of this study to other examples of the realization of these patterns." (ESP 109-110) Whitehead does not explicitly link generalized mathematics to speculative philosophy (on page 109 of ESP). Moreover, if we consult the first chapter on "Speculative Philosophy" in Process and Reality, we do read that "the study of philosophy is a voyage towards the larger generalities" (PR 10), but also:

"Philosophy has been haunted by the unfortunate notion that its method is dogmatically to indicate premises which are severally clear, distinct, and certain; and to erect upon those premises a deductive system of thought. But the accurate expression of the final generalities is the goal of discussion and not its origin. Philosophy has been misled by the example of mathematics [...]." (PR 8)

And:

"[...] the method of philosophy has [...] been vitiated by the example of mathematics. The primary method of mathematics is deduction: the primary method of philosophy is descriptive generalization. Under the influence of mathematics, deduction has been foisted onto philosophy as its standard method, instead of taking its true place as an essential auxiliary mode of verification whereby to test the scope of generalities." (PR 10)

The confrontation of the Bradley quotes with the Whitehead quotes reopens the question: "Can Whitehead's speculative philosophy be considered as a generalized mathematics?" And yet, I agree with Bradley that the answer to this question is "Yes." In this paper I defend that what Bradley writes only apparently contradicts the passages in Whitehead's writings he refers to, and hence, that the yes-answer is indeed justified.

"It is no accident that Whitehead describes philosophy as 'imaginative generalization' (PR 5), and sees his thought as a 'generalized mathematics' (ESP 109). [...] What he means by this is evident throughout Process and Reality (1929), which is the revision and the culmination of his earlier mathematical and philosophical work, in particular his collaboration with Russell in Principia Mathematica (1910-1912). For in Process and Reality and subsequent writings, Whitehead builds on the brilliant success of the Frege-Russell generalization of the mathematical function and develops his philosophy on that basis." (Tijdschrift voor filosofie, 64/2002, p.254.)

A year later, in a similar paper, "Whitehead and the analysis of the propositional function," Bradley repeats:

"It is no accident that Whitehead calls his speculative philosophy a "generalized mathematics" (ESP 109). For in Process and Reality (1929), as the revision and culmination of his work in Principia Mathematica (1910-1912), he builds on the brilliant success of the Frege-Russell generalization of the mathematical function as the propositional function." (In: George W. Shields (ed.), Process and Analysis, SUNY, 2003, p.145.)

However, if we consult Whitehead's Essays in Science and Philosophy (ESP 109), we discover that he utilizes the expression "generalized mathematics" to stress that mathematics evolved from the specific study of numbers and quantities to the general study of patterns: "The essence of this generalized mathematics is the study of the most observable examples of the relevant patterns; and applied mathematics is the transference of this study to other examples of the realization of these patterns." (ESP 109-110) Whitehead does not explicitly link generalized mathematics to speculative philosophy (on page 109 of ESP). Moreover, if we consult the first chapter on "Speculative Philosophy" in Process and Reality, we do read that "the study of philosophy is a voyage towards the larger generalities" (PR 10), but also:

"Philosophy has been haunted by the unfortunate notion that its method is dogmatically to indicate premises which are severally clear, distinct, and certain; and to erect upon those premises a deductive system of thought. But the accurate expression of the final generalities is the goal of discussion and not its origin. Philosophy has been misled by the example of mathematics [...]." (PR 8)

And:

"[...] the method of philosophy has [...] been vitiated by the example of mathematics. The primary method of mathematics is deduction: the primary method of philosophy is descriptive generalization. Under the influence of mathematics, deduction has been foisted onto philosophy as its standard method, instead of taking its true place as an essential auxiliary mode of verification whereby to test the scope of generalities." (PR 10)

The confrontation of the Bradley quotes with the Whitehead quotes reopens the question: "Can Whitehead's speculative philosophy be considered as a generalized mathematics?" And yet, I agree with Bradley that the answer to this question is "Yes." In this paper I defend that what Bradley writes only apparently contradicts the passages in Whitehead's writings he refers to, and hence, that the yes-answer is indeed justified.

Originele taal-2 | English |
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Titel | Chromatikon IV - Yearbook of Philosophy in Process |

Redacteuren | Michel Weber, Pierfrancesco Basile |

Uitgeverij | Presses Universitaires de Louvain |

Pagina's | 37-49 |

Aantal pagina's | 13 |

Volume | IV |

ISBN van geprinte versie | 978-2-87463-137-5 |

Status | Published - 2008 |

### Publicatie series

Naam | Chromatikon IV - Yearbook of Philosophy in Process |
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