## Anticipations

The principle result that I announce here - the existence of synthetic logic - has been anticipated in the universal characteristic of Leibniz, and in the concept of the synthetic a priori of Kant.

In the early C20th Henri Poincare opposed the tide in favour of the mathematical logic of Peano and Russell by advocating that mathematical induction was not reducible to that logic. In recent times John Lucas proposed that Godel's theorem was non-algorithmic, a view that Roger Penrose has also defended.

Another anticipation is the deployment of an intensional logic based on phenomenology, which may be found in the work of Bradley, Bosanquet, Husserl and Loetze. The C19th regarded logic as the science of judgement, as opposed to the study of extensions advocated initially by Russell, and subsequently taken up by the academic philosophers as a means to thrust their dialectical adversaries into oblivion.

In the early C20th Henri Poincare opposed the tide in favour of the mathematical logic of Peano and Russell by advocating that mathematical induction was not reducible to that logic. In recent times John Lucas proposed that Godel's theorem was non-algorithmic, a view that Roger Penrose has also defended.

Another anticipation is the deployment of an intensional logic based on phenomenology, which may be found in the work of Bradley, Bosanquet, Husserl and Loetze. The C19th regarded logic as the science of judgement, as opposed to the study of extensions advocated initially by Russell, and subsequently taken up by the academic philosophers as a means to thrust their dialectical adversaries into oblivion.

## Related articles

## Towards the universal characteristic

Chapter 15 of a work entitled "Poincare's thesis" of October 2011.

## A neo-Kantian philosophy of mathematics

Chapter 16 of "Poincare's thesis" of October 2011.

## Expressive power of formal languages

Chapter 13 of "Poincare's thesis" of October 2011.

Demonstrates that formal first-order languages are not capable of expressing all the propositions of mathematics.

Demonstrates that formal first-order languages are not capable of expressing all the propositions of mathematics.

Detail from

*Nigredo*by Peter Paul Fekete