By intuition we get the first principles, on which everything else is based.
Let us remember that in this book we are considering the five ways that we get at truth. We care about truth because we care about whether our actions are true to our moral character; we care about being true to ourselves.
A "first principle" is something which is true. For example, for everything which happens, something causes it to happen -- that is true. And by "true" we mean "that which is so" more than "something which is not false". So we can say that "water is wet" is something that is true in the way in which a child "knows" that it is so, and less like something that is a scientific fact.
Now, we want to know how we come to have first principles, so let us consider which of the five ways we can use to get at that kind of truth. Again, the five ways are (1) science, (2) art, (3) practical wisdom, (4) philosophic wisdom, and (5) intuitive reason. Let us go through each of them, in turn, and figure out which it is, starting with science.
Well, scientific knowledge (episteme) comes from first principles. While we may remember some thing which agrees with our scientific knowledge (e.g. that thunder comes from lightening), the scientific knowledge itself we remember based on those first principles. For instance, that for each effect there is a cause; so from that we know that there is something that causes the thunder. We see that lightening always comes before thunder and we conclude that lightening is the cause of the thunder. But if our minds could not get "cause and effect", then we could not get that lightening causes thunder. "Cause and effect" comes first.
Yet the first principles themselves are not scientific knowledge. You cannot demonstrate a first principle (e.g. that effects have causes). The other person has to have experience of certain things in order to "get it". You cannot demonstrate that water is wet. You can tell someone that "water is wet" (in your own language, for instance), but they have to first have seen the water and had the feeling of wetness in order to know what you mean. From there, there is nothing more to be demonstrated: one gets it or not. So, it is not science by which we get first principles.
We also know that the first principles cannot come from art or practical wisdom. Art and practical wisdom deal with things which could come out in different ways, based on what is needed. First principles are not based on anything else.
But with art, it is based on whatever the product is wanted for. Clothes can be made to measure according to the person and their style.
And with practical wisdom, it is based on whatever is good for that person. People can eat healthy, but that does not mean everyone eats the same thing. Yet first principles cannot be anything other than what they are. Water cannot not be wet. Things happening must come from some cause.
But could first principles come from philosophizing (e.g. from philosophic wisdom)? After all, we ask "what is truth?" and "what is the soul?" If things like truth and soul are first principles, then they must come from asking what they are? This may seem to be the case, but it is not so. For us even to be able to talk about "truth" and "soul" we must first have a sense of what they are. From there the philosopher will take it a step further, but we start from the sense we already have of true and false, right and wrong and then go to what those things mean, what follows from them. In order to ask "what is the meaning of life?" we have to already basically "get" what life is. We cannot get first principles from philosophy.
So that leaves only one other way of thinking: intuitive reason. Intuitive reason is what gets us the first principles. Intuitive reason is that by which we feel and know that this truly is a thing and that it is different from other things. One can see that there is water and then feel that it is wet and intuitively grasp that "water has wetness".
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