Something I wrote about ten years ago.
The following is, admittedly, 99% drawn from Ayn Rand. After thirty years of reading, and wandering all over the religious and philosophical MAP, I have decided that, on the ABC fundamentals I cover below, she was right. I have larger disagreements with her on ethics and politics. -JBH
What is philosophy?- The word "philosophy" comes from Greek roots meaning "the love of wisdom." Philosophy is the effort to answer those questions that everyone MUST answer.
What is real, what is not real, what kind of world am I living in? - Metaphysics.
How can I know what's true? How do I separate the true from the false? - Epistemology. (Includes logic, mathematics, and the methods of science.)
What should I do? What's good, what's right? What's it all for? - Ethics.
How do I deal with other people? How can we live together in peace, what should we fight over, and how shall we fight? - Politics.
What's beautiful, what's essential, what's meaningful, what's insightful, what's inspiring? - Aesthetics.
Everybody MUST have and use SOME answers to these questions, to live their lives. Lots of people get their answers by just "picking them up"... they hear answers from other people, but never think too hard about them. The love of wisdom is what motivates the effort to make all your answers consistent with each other, to know where they come from and what they are based on.
FIRST THINGS FIRST
Everything else in philosophy is based on the answers in metaphysics and epistemology: "What do I know?" and "How do I know it?"
What can you know for CERTAIN? Exactly three things. (1) You exist. (2) You are conscious, you are aware of something. (3) Whatever may exist, whatever thing you may be aware of, it is what it is, it has the characteristics that it has. To be, is to be something in particular; existence is identity. A thing cannot both have a particular characteristic and not have it at the same time in the same way.
Why can we be certain of these three things? Because you cannot deny them without first assuming them true. If you say "I do not exist", who is speaking? If you say "I am not conscious", how can you speak? (Of anything?) If you say that a thing is not itself, then what are you speaking of?
Why are these three things important? If things are what they are, then contradictions cannot exist in reality. Every part of reality is what it is, and so is the whole Universe at once; the whole cannot contradict itself, the parts cannot contradict the whole. All the parts necessarily fit together.
If we are conscious, then we are conscious OF something. We receive sensations from our eyes, ears, fingers, and so forth. We then INTERPRET those sensations; we use imagination to form a mental model of the world that we are sensing. Our minds do some of this automatically; we sense areas of brown, some straight lines and angles, and we "see" a wooden table. Some interpretations are NOT automatic; we have to work deliberately, think about what we have seen, to make a mental model that fits all we have seen.
Why can NOT we be certain of anything else, besides those three things? Because we can make mistakes, and sometimes do; we are not infallible. We get sensations, from our eyes, ears, fingers, and so forth, but sometimes we make errors, mistakes, in interpreting what our senses tell us. We make mistakes in our thinking about what we have seen, and our memory is also sometimes mistaken.
SCIENCE is the practice of eliminating contradictions between our mental models and what we observe with our senses. We say what we expect to see, if our mental model is correct; we make a "testable hypothesis", we predict what we ought to see, and (by implication) what we would NOT expect to see (anything strongly different from what we predict.) We then go and look, to TEST our hypothesis. If we see what we expect, our mental model survives; if we see something NOT consistent with our model, we have a problem; our mental model must be adjusted, or perhaps thrown out and replaced with a different model altogether.
LOGIC is the practice of eliminating contradictions in our thinking; it is the practice of making all of our mental models, of all parts of the world, consistent with each other. Since there can be no contradictions in reality, then we know that if we have contradictions in our mental models, we must have made some mistakes somewhere. Reality must be consistent with itself, so if we want our mental models to reflect reality, our mental models must also be consistent with themselves.
Though we cannot be CERTAIN of anything beyond those three things stated above, testing our mental models justifiably makes us more confident that they reflect reality. The more testing our models have survived, the more confidence we can have in them. We can make mistakes, we can also remove mistakes by changing our mental models and doing more testing. Models that have survived a LOT of testing, which reliably predict new observations, can be regarded as "practically certain".
SO: What do we know, and how do we know it? We are, we are aware, we are aware of the world. The world is itself; there are no contradictions in reality. We learn about reality by applying imagination and logic to the evidence of the senses, and testing to find and remove our mistakes.
MORE ABOUT LOGIC
Logic is the practice of finding and eliminating contradictions in our thinking. It does this by assuming some statements to be true "for the sake of argument", then working out what else MUST be true if those are true. Logic goes from the assumed "premises" to new "conclusions" by "rules of inference", rules which by thorough testing have been found to "preserve truth". If we assume some premises, and derive a contradiction, then at least one of the premises MUST be false.
If the statements assumed to be true "for the sake of argument" contain any contradictions between themselves, then ANYTHING AT ALL can be proven from them. For example:
(1) sentence A is true. [assumption]
(2) sentence A is false. (Sentence NOT-A is true) [assumption, contradicting the first]
(3) Either sentence A is true, or sentence X is true. [This follows from (1).]
(4) Therefore: Sentence X is true. [This follows from (3) and (2).]
If we allow ourselves to hold contradictory beliefs, then logically ANYTHING FOLLOWS; we cannot rule out anything; we cannot predict anything, because the opposite may just as easily be true. If we hold contradictory premises, our means of understanding the world is short-circuited and blown.
If our mental model of the world contains internal contradictions, then we cannot make predictions about what we will and will not observe. The model will just as easily predict NOT-X as X, so the model is not testable. Untestable models are useless; the entire purpose of our mental models is to tell us what we can expect to happen, and what we can expect NOT to happen, when we try to do something in the world.