Rationalism

Since the Enlightenment, rationalism is usually associated with the introduction of mathematical methods into philosophy, as in Descartes, Leibniz, and Spinoza. This is commonly called continental rationalism, because it was predominant in the continental schools of Europe, whereas in Britain empiricism dominated.
Rationalism is often contrasted with empiricism. Taken very broadly these views are not mutually exclusive, since a philosopher can be both rationalist and empiricist. Taken to extremes the empiricist view holds that all ideas come to us through experience, either through the five external senses or through such inner sensations as pain and pleasure, and thus that knowledge is essentially based on or derived from experience. At issue is the fundamental source of human knowledge, and the proper techniques for verifying what we think we know (see Epistemology).

Proponents of some varieties of rationalism argue that, starting with foundational basic principles, like the axioms of geometry, one could deductively derive the rest of all possible knowledge. The philosophers who held this view most clearly were Baruch Spinoza and Gottfried Leibniz, whose attempts to grapple with the epistemological and metaphysical problems raised by Descartes led to a development of the fundamental approach of rationalism. Both Spinoza and Leibniz asserted that, in principle, all knowledge, including scientific knowledge, could be gained through the use of reason alone, though they both observed that this was not possible in practice for human beings except in specific areas such as mathematics. On the other hand, Leibniz admitted that "we are all mere Empirics in three fourths of our actions" Rationalism is predicting and explaining behavior based on logics.

Empiricists

The term "empirical" was originally used to refer to certain ancient Greek practitioners of medicine (Empiric school) who rejected adherence to the dogmatic doctrines of the day (Dogmatic school), preferring instead to rely on the observation of phenomena as perceived in experience. The notion of tabula rasa ("clean slate" or "blank tablet") dates back to Aristotle, and was developed into an elaborate theory by Avicenna and demonstrated as a thought experiment by Ibn Tufail. The doctrine of empiricism was later explicitly formulated by John Locke in the 17th century. He argued that the mind is a tabula rasa (Locke used the words "white paper") on which experiences leave their marks. Such empiricism denies that humans have innate ideas or that anything is knowable without reference to experience.

According to the empiricist view, for any knowledge to be properly inferred or deduced, it is to be gained ultimately from one's sense-based experience. As a historical matter, philosophical empiricism is commonly contrasted with the philosophical school of thought known as "rationalism" which, in very broad terms, asserts that much knowledge is attributable to reason independently of the senses. However, this contrast is today considered to be an oversimplification of the issues involved, because the main continental rationalists (Descartes, Spinoza, and Leibniz) were also advocates of the empirical "scientific method" of their day. Furthermore, Locke, held that some knowledge (e.g. knowledge of God's existence) could be arrived at through intuition and reasoning alone. Similarly, Robert Boyle, a prominent advocate of the experimental method, held that we have innate ideas.

Some important philosophers commonly associated with empiricism include Aristotle, Alhazen, Avicenna, Ibn Tufail, Robert Grosseteste, William of Ockham, Francis Bacon, Thomas Hobbes, Robert Boyle, John Locke, George Berkeley, David Hume, John Stuart Mill, Gilles Deleuze and Félix Guattari.

Jung's Analytical Psychology

A 37 year old Carl Jung in 1912.

In Carl Jung's analytical psychology, he contrasted a rational, decisive logos with an emotional mythos. Jung contrasted the critical and rational faculties of logos and with the emotional, non-reason oriented and mythical elements of mythos. In Jung's approach logos vs mythos can be represented as "science vs mysticism", or "reason vs imagination" or "conscious activity vs the unconscious".

For Jung, logos represented the masculine principle of rationality, in contrast to its female counterpart, eros:

Woman’s psychology is founded on the principle of Eros, the great binder and loosener, whereas from ancient times the ruling principle ascribed to man is Logos. The concept of Eros could be expressed in modern terms as psychic relatedness, and that of Logos as objective interest.
Jung attempted to equate logos and eros, his intuitive conceptions of masculine and feminine consciousness with the alchemical Sol and Luna. Jung commented that in a man the lunar anima and in a woman the solar animus has the greatest influence on consciousness. Jung often proceeded to analyze situations in terms of "paired opposites", e.g. by using the analogy with the eastern yin and yang and was also influenced by the Neoplatonics.

In his book Mysterium Coniunctionis Jung made some important final remarks about anima and animus:

In so far as the spirit is also a kind of "window on eternity"... it conveys to the soul a certain influx divinus... and the knowledge of a higher system of the world, wherein consists precisely its supposed animation of the soul.

And in this book Jung again emphasized that the animus compensates eros, while the anima compensates logos

The Incompleteness Theorem

The Incompleteness Theorem

In 1931 and while still in Vienna, Gödel published his famous incompleteness theorems in "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme" (called in English "On formally undecidable propositions of Principia Mathematica and related systems"). In that article, he proved for any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers (e.g. the Peano axioms or ZFC), that:

If the system is consistent, it cannot be complete.

The consistency of the axioms cannot be proven within the system.

These theorems ended a half-century of attempts, beginning with the work of Frege and culminating in Principia Mathematica and Hilbert's formalism, to find a set of axioms sufficient for all mathematics. The incompleteness theorems also imply that not all mathematical questions are computable.

In hindsight, the basic idea at the heart of the incompleteness theorem is rather simple. Gödel essentially constructed a formula that claims that it is unprovable in a given formal system. If it were provable, it would be false, which contradicts the idea that in a consistent system, provable statements are always true. Thus there will always be at least one true but unprovable statement. That is, for any computably enumerable set of axioms for arithmetic (that is, a set that can in principle be printed out by an idealized computer with unlimited resources), there is a formula that obtains in arithmetic, but which is not provable in that system. To make this precise, however, Gödel needed to solve several technical issues, such as encoding statements, proofs, and the very concept of provability into the natural numbers. He did this using a process known as Gödel numbering.

The Power to Integrate....

Wittgenstein, who ... looked back nostalgically on a well-ordered world where everyone had his place, found modernity uncultured because it had lost its power to integrate, and left individuals in a state of confusion. The only ones who can keep their balance and personal creativity are those whom Nietzsche calls the strong men, that is the most moderate, who need neither convictions nor religion, who are able not only to endure, but to accept a fair amount of chance and absurdity, and are capable of thinking in a broadly disillusioned and negative way without feeling either diminished or discouraged (p. 296).by Jacques Le Rider’s (1993)

What is the Use of Studying Philosophy?

What is the use of studying philosophy if all that it does for you is enable you to talk with some plausibility about some abstruse questions of logic, etc., and if it does not improve your thinking about the important questions of everyday life .... You see, I know that it is difficult to think well about “certainty”, “probability”, “perception”, etc. But it is, if possible, still more difficult to think, or try to think, really honestly about your life and other people’s lives.-Wittgenstein

Compassion

Compassion (from Latin: "co-suffering") is a virtue —one in which the emotional capacities of empathy and sympathy (for the suffering of others) are regarded as a part of love itself, and a cornerstone of greater social interconnectedness and humanism —foundational to the highest principles in philosophy, society, and personhood.

There is an aspect of compassion which regards a quantitative dimension, such that individual's compassion is often given a property of "depth," "vigour," or "passion." More vigorous than empathy, the feeling commonly gives rise to an active desire to alleviate another's suffering. It is often, though not inevitably, the key component in what manifests in the social context as altruism. In ethical terms, the various expressions down the ages of the so-called Golden Rule embody by implication the principle of compassion: Do to others what you would have them do to you.