There are five ways, or modes, of thinking by which the mind can get to truth. They are: (1) science, (2) art, (3) wisdom about everyday things (i.e. practical wisdom), (4) wisdom about theoretical things (i.e. philosophic wisdom), and (5) intuitive thinking. We might have included (6) judgement and (7) opinion, but we excluded them instead, because they may lead us to what is false, as they can be mistaken. The others, if we reason correctly, will always lead us to truth.

Let us start with science. We feel like we really know that something is so when there is no way that it could be otherwise (i.e. that it could be anything other than what it is). For example, we know that things dropped in water always fall slower than things dropped in air, because water is denser than air. There is no way that you could take something, drop it in the air, and then take the very same thing, and drop it in water, and then it falls faster. But for other things, if we are not certain about them, then we may look away, and then look back and find that the thing has changed or disappeared. It never was necessary that the thing be so in the first place, and if doesn't have to be what it is, then it can be something different. For example, in cities with violent political factions, a traveller may visit one day, and the laws have the city be a democracy, and then that person may return a month later, and find that the laws are changed, and it is now an aristocracy. Even though the city may happen to have this or that form of government, it does not have to have it. Scientific knowledge, on the other hand, is about things being the way they are, because they have to be that way: they cannot be otherwise. A scientific law does not change, but describes Nature as it is and as it will always be. There never was a beginning for a scientific law, such that there was an earlier time when the scientific law did not hold true. So we know, that there was never a time when things fell faster in water than in air, nor will there ever be a time when that is so.

Now, how can we get scientific truth? We can discover them ourselves or we can learn them from a teacher. All the sciences can be taught and learned. And how is that? Well, whoever discovers something about Nature does something (e.g. makes an investigation) in order to learn that thing. They can then turn around, do the same thing, and then show how they discovered it to another person. When the discoverer does that, then the other person may learn the same thing (i.e. learn the same scientific truth) in the much same way as it was discovered. This is called teaching by demonstration. The teacher demonstrates that the thing is true, and if the learner is able to follow the demonstration, then they will now have the scientific knowledge of the teacher. If the learner does not follow the demonstration, then they might, incidentally, know that the thing is true (i.e. they can remember having heard it said), but they will not have scientific knowledge of it. They will not know why it is so. For instance, someone may know that when there is a lunar eclipse (which happens at night), the Earth is between the Moon and the Sun. They may know this as a fact, but not as a scientific truth if they have not followed through the reasoning, from the start, all the way to an end point. If they know the thing as a scientific truth, then they know (1) the light of the Moon is a reflection of the rays of the Sun, (2) a body in front of a source of light casts a shadow, (3) the Earth is a body, (4) the Sun is a light source, (5) a lunar eclipse is a shadow. The shadow must come from some body, the only body which comes between the Moon and the Sun is the Earth, therefore it must be the case that the Earth is between the Sun and the Moon, and it is causing the shadow of the eclipse. So, we can see that this scientific knowledge of the fact is very different from a bare remembering of the fact.

All teaching starts off as something that is already known by the learner, and then goes to something that is new. This teaching can go in two ways: (1) by syllogism and (2) by induction. Syllogism is showing how if we know that two things (A and B) are true, then we also know that a third thing (C) must also be true. For instance, if (A) all humans are mortal, and (B) Socrates is a human, then (C) Socrates is mortal. That is called a syllogism. But suppose that we want to know whether all animals eat food, how can we know that? This is where we use induction. Induction means taking one of each kind of a thing, and finding that something is true for each of them, and then concluding that the thing must be true for every single one of them, generally speaking, because that is part of what it means for it to be that thing. Part of being human is dying. That is true of Socrates, and it is true of Solon, and it is true of all humans. We may do an induction like this: (1) Socrates was human and was mortal, (2) Solon was human and was mortal, (3) All humans are mortal. For any other human, we can say about them that they are mortal and will die, and we can say this without first having to observe them die to know that it is so. We do not have to check that every single person does die in order to know, scientifically, that every single person will die. Again, this is because we made the induction that all humans are mortal.

But is two cases enough for an induction? Not necessarily. Suppose instead that we take cattle and humans, and we find that each of them is an animal and it walks on legs. Can we then induce that all animals walk on legs? We could, but we would be wrong, and it would not be a very good induction. To be an animal is to be a living thing that moves. There are ways for things to move other than walking. We might first consider this before making an induction, and then we might think of fishes or snakes as animals which do not walk on legs.

But suppose that we were among a people that had never seen a fish or a snake, but had only seen animals which walk on legs. Is it right there for us to use an induction? And when it is right for us to use an induction, generally speaking? What we should try to do is take enough particulars to cover whatever is the essence of that thing (i.e. what it means for it to be that very thing and not something else). For animals, their essence is to be a living thing which moves. Now, there are many animals we may have seen getting their food, from lions to ants. But, when, for each different kind of animal, we observe that it gets food for itself, it is not as though each one has a separate reason why it gets food, as being that specific thing (rather than because it is an animal). A lion does not get food because it is a lion, and then an ant also gets food, but for a different reason: because it is an ant; that is not the case, and it is no coincidence that both get food. We rather induce that all animals get food because they are animals. We can do this without going over each and every animal that exists. Now suppose that we see a kind of animal, perhaps a bird, but we have not yet seen it getting food. Still, because it is an animal, and because we made the induction that all animals get food, we know that this animal gets food, even though we do not know what food it gets. From there we may ask what kind of food it gets, how it gets it, and then do an investigation to find out those things.

To know that: "All animals get food" or that "The Earth is between the Moon and the Sun in a lunar eclipse", and to know it because you did an induction or made a syllogism is what it means to have scientific knowledge of it. If you can truly go through an induction or syllogism and get to a scientific truth, then you have the ability to demonstrate, to teach it to someone else. If you cannot teach it by doing a demonstration, then you do not really know it scientifically.

And, so we can see that scientific knowledge does not include such a thing which a person may happen to know, and it really is true, but that person never really thought it through, to make sure that it definitely must be true. One may know that a yard of silk is costs more than a measure of flour, but yet that is not necessarily true, and so it is not a scientific truth. After all, in a time of famine, a measure of flour may cost more than a yard of silk (because people are starving to death). Again, what is scientifically true is always and necessarily true.

Scientific knowledge also requires that a person know what they are talking about when they are talking about something. Suppose that someone were to know that (1) salmon are fish, (2) fish breathe through gills, and then reason that (3) salmon breathe through gills (because salmon are fish). But suppose also, that the person in question does not know just what gills are (perhaps they cannot even identify them on a fish) and they do not know what "breathe through gills" really means. Such a person cannot be said to know that "salmon breathe through gills" is true scientifically (even though that really is true). This is because "fish breathe through gills" is a starting point, but, again, the person in question does not grasp that starting point, because they do not know what gills are. And if a person does not grasp the starting points scientifically, then they cannot be said to grasp the conclusion scientifically. In order to know things scientifically, we must first grasp those starting points on which we base the scientific demonstrations (i.e. the inductions and the syllogisms).

We do need to get some truths from induction in order to have a place to start from. It is true that many truths may be got at deductively (e.g. that Socrates is mortal), but we still need to get the starting points inductively (e.g. that all humans are mortal).

And here, at this point, we wrap up on all we have to say in this book about what scientific knowledge is, and what it means for a person to have scientific knowledge.