Pythagoras taught that the universe is a single, living, conscious, intelligent, ensouled, Divine being, and that each of us is a part of this single being, which he called "Cosmos". Pythagoras also taught that the psyche/soul survives the physical death of the body, and, moreover, that we have all lived many lives before, and will live again many times in the future in different bodies. More specifically, Pythagoras taught that in many of our past lives we have not been human, but that we have rather inhabited every manner of animal body, and that we will do so again in the future. For this reason Pythagoras was a strong proponent of vegetarianism, even warning that those who eat meat could very well have the blood of their own deceased loved ones on their hands!
In addition to teaching panpsychism, pantheism, metempsychosis (reincarnation), and vegetarianism, Pythagoras was a scientific pioneer who championed the idea that the properties of the physical world can be expressed in mathematical formulas. Pythagoras also promoted the use of experimentation, especially in the field of harmonics, as a way to test and demonstrate theories about the physical world.
Socrates encouraged his friends to consult oracles, according to his life-long friend, Xenophon, who also tells us that Socrates would meet with his friends to discuss various oracular pronouncements in order to try to discover their meaning. Another close life-long friend of Socrates, Chaerephon (who was one of Athen's most famously outspoken radical democrats) once traveled to Delphi to ask the Oracle of Apollo the following question: "Is there anyone more wise than Socrates?" To which the Oracle simply answered "No." When Socrates was later accused of impiety and put on trial for his life, he explained that all of his philosophizing among the Athenians had been conducted in an effort to understand this sacred pronouncement from the God Apollo. Socrates insisted that just as he had never abandoned his post, even when his life was at risk, when he served in the Athenian army as a hoplite, just so would he never abandon his philosophical "post", and he would therefore continue, regardless of the consequences, to engage in what he saw as his sacred duty to conduct his philosophical investigations.
Socrates' most famous student, Plato, founded the first educational institution in Western history, the Academy. And just a generation after Plato, the Platonic philosopher Euclid would provide the model upon which the very concept of "proof" is based in the Western mind (a model that few who speak of "proof" ever live up to). The Pythagorean/Socratic tradition of advances in mathematics and science would later culminate in the figure of Ptolemy, who developed a sophisticated theoretical framework for the design, conduct, and analysis of scientific experiments in the second century AD.
All of those named above, and many others whose names could be added to the list (from Aristotle to Poseidonius to Hypatia) were all Pagans, and as such they were all believers. They believed in the Gods, and they participated in the traditional worship of the Gods, including both small-scale household rituals and grand city-wide (or wider) festivals and other ceremonies, gatherings, Mysteries, etc.
Anyone who claims to be more rational, more scientific, more skeptical, more intellectually sophisticated, etc., than the great Pagan philosophers of the ancient world simply cannot be taken seriously. Anyone who claims that there is some conflict between traditional Pagan beliefs and sound reasoning knows nothing about either one.
P.S. If you have no idea what I am on about, here are some links to provide some context:
What Do I Believe Anyway? Jason
Saepe sub nomine pacis bellum latet Sannion
The Philosopher’s Dilemma Sufenas
Humanist Paganism on the rise? Brendan
And here are some relevant posts (of mine) from the past:
- Sceptical Scepticism (5/6/09)
- The Religion of Socrates (5/31/09)
- Ancient Pagans and Theology: did they, or didn't they? (6/14/09)
- Pythagoreanism: the personal is cosmological (7/14/09)
- Thomas Taylor on the Religion of Socrates (7/22/09)
- "detached from the masses and usually disempowered" (7/22/09)
- Thinking Like a (Pagan) Scientist (8/4/09)
- "that all our knowledge is a knowledge of states of consciousness." (12/17/09)
- Children of the Gods: Stoic Theology from a Modern Pagan Perspective (4/30/10)
- "When you enter a village, swear by its Gods." (5/26/10)
- The Socratic Logos in Plato's Republic (9/2/10)
- Hypatia (10/30/10)
- More on Hypatia (11/1/10)
- Six Degrees of Charles Darwin (11/21/10)
- The Eleusinian Mysteries & The Evolution of Species (11/28/10)
- Vergil's Cosmology and Modern Paganism (12/13/10)
- Let Us Pray (5/20/11)
- What Is Paganism? Some Reliable Sources (6/1/11)
- Undervaluing Non-Harming: On Brendan Myers on the Wiccan Rede (6/6/11)
- Shedding Light on Cosmopolitan Paganism: Of Particles, Waves, and Egyptian Mysteries (6/8/12)
- Defining Paganism: "Where your treasure is, there is your heart also." (8/30/12)