Kant (number and Time):

In his Critique of Pure Reason (1781 and 1787) Kant states:

“The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience”.

He gives 2 expositions of space and time: metaphysical and transcendental.  These 2 expositions are concerned with clarifying how those intuitions are known independently of experience.  The forms of human sensibility, space and time, provide the basis from which to derive synthetic and a priori mathematical judgments.  Kant argues that time is a pure a priori intuition that renders mathematics possible.  These arguments, together with the details of his account of the synthetic and a priori nature of all mathematical judgment, provide an answer to the question of the possibility of mathematics.

 

the Eleatic (problem of motion): * see EndNote<A>

a pre-Socratic school of philosophy founded by Parmenides early 5th century BC in Elea (Greek colony in S. Italy); included Zeno of Elea & Melissus of Samos.  Evolved in opposition to theories of the early physicalist philosophers (who explained existence in terms of primary matter) and Heraclitus, who declared that existence consisted of perpetual change.  They maintained that truth lay in the conception of a universal unity of being; the senses cannot cognize this unity, as their reports are inconsistent; only by thought can one eschew false senses & arrive at the truth that "All is One".  There is no creation, being cannot come from non-being; errors here arose from the ambiguous use of the verb to be, which implies physical existence when it was in reality but a linguistic copula connecting subject & predicate.  Among other things they denied the reality of motion (see Zeno’s paradoxes).

 

copula:

noun, something that connects or links together; also a linking verb (be, seem, or look) connecting or establishing an identity between subject & complement; in logic. a word that acts as a connecting link between the subject & predicate of a proposition.

 

Kirchhoff:

(1824-1887) German physicist, pioneer in understanding of electrical circuits, spectroscopy & the emission of black-body radiation by heated objects (a term he coined in 1862).  there are a number of "Kirchhoff's laws", concerning black-body radiation & spectroscopy, electrical circuits & thermochemistry.   In 1857 he calculated that an electric signal in a resistance less wire travels at the speed of light.  In 1859 he proposed his law of thermal radiation, proving it 1861.  With Bunsen he invented the spectroscope.  He used it to pioneer the identification of the elements in the Sun; in 1859 he showed the Sun contains sodium.  He & Bunsen discovered caesium and rubidium in 1861.  He contributed to the field of spectroscopy by formalizing 3 laws that describe the spectral composition of light emitted by incandescent objects (spectrum analysis).  He also contributed to optics, solving the wave equation to provide a solid foundation for Huygens' principle.