Rationalism in Mathematics Enters Shaky Ground
During the Enlightenment, the world was viewed as an orderly place in which everything operated in accordance with precise mathematical principles. Beginning with the Romantic backlash, however, and unfolding into the early 20th century, both rationalism in mathematics and the concept of absolute truth were called into question. Discover how the quest to improve Euclid’s system of geometric propositions further disrupted the philosophy of rationalism.
- The Divide Between the Arts and the Sciences -
The early 20th century sat at an interesting intellectual crossroads. The Enlightenment of the 17th and 18th centuries upheld reason as the defining characteristic of humanity and saw the advance of knowledge as the hallmark of human progress.
The romantic movement of the 19th century was a backlash against what it saw as the arrogance and naiveté of the reduction of the human to its brain. As such, there was a divide in the intellectual world between the sciences and the arts.
The sciences largely bought into the Enlightenment presuppositions of a well-behaved world, regulated by absolute laws that were accessible to human reason through rigorous processes of observation and logic. Acquiring an understanding of these laws was paramount in striving to move forward as a species.
The practitioners of the arts and letters, on the other hand, saw themselves as the loyal opposition, obligated to correct what they saw as the overreach of the sciences, which seemed to miss the beauty, the joy, and the experience of being human. The heart was as important as the brain and the fetish that scientists held for knowledge limited their true understanding.
But this divide was not impermeable; there were important influences in both directions.
Sometimes art and science influence each other, sometimes not. A tension existed between the Enlightenment-influenced rationalists and the romantically-inclined thinkers.
- Mathematics as Absolute Truth -
Mathematical propositions were self-evident and true beyond question. Those who doubted these propositions revealed themselves either to be lacking in understanding, mentally deficient, or just trying to be irascible.
It was worrisome when, in the 19th century, the very foundations of mathematics came into serious doubt.
Continued
https://www.thegreatcoursesdaily.com/rationalism-in-mathematics-enters-shaky-ground/
During the Enlightenment, the world was viewed as an orderly place in which everything operated in accordance with precise mathematical principles. Beginning with the Romantic backlash, however, and unfolding into the early 20th century, both rationalism in mathematics and the concept of absolute truth were called into question. Discover how the quest to improve Euclid’s system of geometric propositions further disrupted the philosophy of rationalism.
- The Divide Between the Arts and the Sciences -
The early 20th century sat at an interesting intellectual crossroads. The Enlightenment of the 17th and 18th centuries upheld reason as the defining characteristic of humanity and saw the advance of knowledge as the hallmark of human progress.
The romantic movement of the 19th century was a backlash against what it saw as the arrogance and naiveté of the reduction of the human to its brain. As such, there was a divide in the intellectual world between the sciences and the arts.
The sciences largely bought into the Enlightenment presuppositions of a well-behaved world, regulated by absolute laws that were accessible to human reason through rigorous processes of observation and logic. Acquiring an understanding of these laws was paramount in striving to move forward as a species.
The practitioners of the arts and letters, on the other hand, saw themselves as the loyal opposition, obligated to correct what they saw as the overreach of the sciences, which seemed to miss the beauty, the joy, and the experience of being human. The heart was as important as the brain and the fetish that scientists held for knowledge limited their true understanding.
But this divide was not impermeable; there were important influences in both directions.
Sometimes art and science influence each other, sometimes not. A tension existed between the Enlightenment-influenced rationalists and the romantically-inclined thinkers.
- Mathematics as Absolute Truth -
Mathematical propositions were self-evident and true beyond question. Those who doubted these propositions revealed themselves either to be lacking in understanding, mentally deficient, or just trying to be irascible.
It was worrisome when, in the 19th century, the very foundations of mathematics came into serious doubt.
Continued
https://www.thegreatcoursesdaily.com/rationalism-in-mathematics-enters-shaky-ground/