The Problems of Philosophy · Chapter
How a Priori Knowledge Is Possible explained
This chapter explores the nature and possibility of a priori knowledge, particularly in mathematics and logic.
What happens
This chapter explores the nature and possibility of a priori knowledge, particularly in mathematics and logic. Russell critiques Kant's solution that such knowledge arises from the mind's contribution to experience, arguing that this view fails to account for the certainty and universality of a priori truths. He proposes that a priori knowledge concerns entities like relations, which exist in a non-mental, non-physical world.
Themes in this chapter
A Priori Knowledge
The entire chapter is dedicated to examining how a priori knowledge, especially in mathematics and logic, is possible. Russell critiques Kant's solution and offers his own view that such knowledge concerns relations in a non-mental, non-physical world.
Knowledge and Certainty
Russell discusses the certainty of a priori truths like 'two and two are four' and contrasts them with empirical generalizations, questioning how we can have certain knowledge about things we have not yet experienced.
The Existence of Matter
The chapter touches on the distinction between physical objects and sense-data, and Kant's concept of the 'thing in itself' as unknowable, which relates to the problem of matter's existence.
Characters to notice
- Immanuel Kant
Kant's critical philosophy and his theory of a priori synthetic knowledge are the central focus of the chapter. Russell discusses Kant's views on space, time, causality, and the distinction between phenomena and noumena.
- Hume
Hume is mentioned as a precursor to Kant, who argued that the connection of cause and effect is not a priori and cannot be logically deduced, challenging rationalist assumptions.
Key passages
“two and two are four. And no fact about the constitution of our minds could make it true that two and two are four.”
The truth of 'two and two are four' does not depend on the structure of our minds.
Russell argues that a priori truths are objective and not merely mental constructs.
“The thing to be accounted for is our certainty that the facts must always conform to logic and arithmetic. To say that logic and arithmetic are contributed by us does not account for this.”
The real puzzle is why we are certain that reality always follows logic and math; claiming we impose them doesn't explain that certainty.
Russell's key objection to Kant: the mind's contribution cannot guarantee the constancy of a priori truths.
“It might happen, if Kant is right, that tomorrow our nature would so change as to make two and two become five.”
If Kant were correct, our mental nature could change tomorrow, making two plus two equal five.
Russell highlights the instability of Kant's solution, as it relies on the constancy of human nature.