**Table of Contents**

#### Absolute Idealism

- Science progressed in the 19th century, developing the atomic theory, the theory of electromagnetism, thermodynamics, and the theory of evolution. Mathematics also made progress, led by Gauss, Riemann, and Poincare. But philosophy, with a few exceptions, regressed.
- Absolute Idealism, the philosophical school that dominated the century, is characterized by the following principles, according to the Britannica:
- “The common everyday world of things and embodied minds is not the world as it really is but merely as it appears in terms of uncriticized categories.”
- “The best reflection of the world is not found in physical and mathematical categories but in terms of a self-conscious mind.”
- “Thought is the relation of each particular experience with the infinite whole of which it is an expression, rather than the imposition of ready-made forms upon given material.”

- German Absolute Idealism dominated the first half of the century, led by Georg Wilhelm Friedrich Hegel, Johann Fichte, and Friedrich Schelling.
- British Absolute Idealism, championed by T. H. Green, Bernard Bosanquet, and F.H. Bradley, dominated the last half.

#### A Taste of Absolute Idealism.

- In his major work, Appearance and Reality: A Metaphysical Essay (1893), F.H. Bradley tries to prove that aspects of the everyday world are contradictory and therefore not real.
- He argues, for example, that space is not real, but only a “contradictory appearance” on the grounds that:
- If space is real, space is not a mere relation
- If space is real, space is nothing but a relation.
- Therefore, space isn’t real.

- To give a feel for how he reasoned, here’s Bradley’s argument for his first premise:

#### Exceptions

###### John Stuart Mill

- Mill, “the most influential English language philosopher of the nineteenth century,” was an empiricist, utilitarian, and liberal. His important works are:
*A System of Logic*(1843)*On Liberty*(1859)*Utilitarianism*(1861)*An Examination of Sir William Hamilton’s Philosophy*(1865)*The Subjection of Women*(1869)

###### Gotlob Frege

- Toward the end of the century, Gotlob Frege developed
*Predicate Logic*, the foundation of modern symbolic logic. - Here’s an example of a proof in Predicate Logic, the proof of the validity of the argument that:
*If a first integer is greater than a second, the second is not greater than the first*.- Therefore,
*no integer is greater than itself*.

- Proof
- (x)(y)(Gxy → ~Gyx)
- For any integers x and y, if x > y then it’s false that y > x.

- (y)(Gay → ~Gya)
- Gaa → ~Gaa
- ~Gaa
- (x)~Gxx
- ~(∃x)Gxx
- It’s false that there at least one integer x such that x > x.

- (x)(y)(Gxy → ~Gyx)