Let us be clear, now, about what doubt and certainty are, and make a couple of distinctions. First of all, certainty is the opposite of doubt, not "probability." We will have occasion to talk about probability and its laws much later; and it turns out that the "laws of probability" are not probable (still less dubious) but certain. But that is another topic.
What I mean by certainty is the knowledge that what one thinks is true is not mistaken; it is a conviction that what you think is true is in fact true. Now "subjective" certainty is this conviction when you don't have any objective grounds for it (any evidence for it); it is an emotional state of confidence that you're "right."
This emotional conviction may go along with objective certainty, which can give the factual grounds for knowing (i.e., the evidence) that you aren't mistaken. In the case in question, the mere statement that you are certain that there is something is the grounds for knowing that you are not mistaken, because that statement is (and is known to be) something.
"There is something," in other words, is absolutely self-evident, because the statement itself is evidence that the statement is true, because it is something. It cannot be denied without asserting it. Hence, the statement (or the thought, or whatever) gives one objective confidence that one knows in this instance what is true, and one cannot be mistaken.
The contradictory of certainty is doubt, which is the state of mind where one thinks that he might be mistaken. If you think you are mistaken, of course, you then are conscious of being in error, and you don't have a doubt. That is, if you as a reader held the view that it's never possible to be absolutely certain, and then you began to see that "There is something" can't be false from any point of view, you at some point realized that your view that absolute certainty is impossible was a mistaken view. You didn't doubt it any more; you now (I hope) know for certain that it is false that absolute certainty is impossible.
But there is also subjective doubt, which is the opposite of the pig-headed type of subjective certainty: the emotional and groundless fear that the thought you are now having might be mistaken. You are afraid that you might be mistaken, not because there is any reason to believe that you are mistaken, or even that there is any reason to believe that some fact might refute your position, but because, "Well, you never know..."
It is this kind of doubt which is so pervasive, and which is in fact a subjective certainty that objective certainty can't be attained. What I am saying when I ask you (if you have this fear) to look into yourself is to question whether this fear is groundless or not. If you still want to hold onto it, because, "Well, you never know..." I can't help you, and you might as well stop reading right here.
There are going to be a lot of things that we will find we can't be absolutely certain of; but this should not necessarily make us doubt them. The fact that it is conceivable that you could be mistaken is not grounds for thinking that you are mistaken, or even wondering whether you are or not. If you have reason to think you aren't mistaken and no reason to think you are, then (even if it isn't impossible for you to be mistaken), it would be precisely unreasonable for you to doubt. Why? Because you have reason not to doubt and no reason to doubt.
This means that there are certainties that are not absolute: you can be certain that in fact you are not mistaken, even though you recognize that it is not impossible for you to be mistaken. Descartes messed up the theory of knowledge by taking absolute certainty as the only certainty there is, and everything that was not known with absolute certainty was (according to his "method") to be assumed not only to be dubious but provisionally false unless it could be proved with absolute certainty from something that was absolutely certain.
But as Descartes himself saw, we are in fact certain of a number of things, because we can't really doubt them, except on his supposition of a malevolent demon who is tampering with our minds so that we can't help believing things which aren't true, such as that there is a real world and that we're not always dreaming, that (for instance) you're reading this page, and you didn't make it up, and so on.
Let me call "physical certainty" this level of certainty in which you can't prove it's impossible for you to be mistaken, but where you know that in fact you aren't mistaken. For physical certainty, you have to have objective facts to back up what you think is true and also no facts to indicate that it is not true. That is, there might (somewhere) be facts that contradict your view, but you have no knowledge that they exist. You then have reason to think that you are not mistaken, and no reason to think you are; though you can't prove that you can't be mistaken. You have physical certainty (you don't doubt), but not absolute certainty.
You may not have direct evidence of something and still have physical certainty. For instance, if someone you have reason to believe is an expert is telling you that something is a fact (and you have no reason to believe that he's lying or biased), then you have reason to think that what he says is a fact and no reason not to. Practically everything we learned in school is knowledge of this type, because even if we did experiments in the lab and "learned on our own," they were constructed with our education in mind, and we had to take the instructor's word for it that the experiment is valid.
At a still lower level is the type of certainty you have when you don't have any particular proof or solid evidence that what you think is the case is actually the case, but at the same time you have no hint of evidence that it's not the case. A great deal of our knowledge is on this level; hearsay from a non-expert when we simply have no reason to suspect that we are being lied to or the person telling us doesn't know what he's talking about or is biased is a case in point. This is moral certainty.
It really means that you simply have no reason to suspect that you are mistaken, not that you have any solid reason to show that you're not mistaken. It isn't doubt, because in fact we don't suspect that we are mistaken; but it's not at the level even of physical certainty, where we can give reasons.
People do, of course, lie to us without our suspecting it, or pass off ignorant opinions as knowledge or hearsay as if they knew the facts themselves, and often when we are certain at this level we are mistaken. But this does not alter the fact that we have no reason to doubt what we are told. So we are certain. It is unreasonable to go around cross-examining everything we are told, suspiciously asking, "Are you sure of that? Do you really have evidence of it?" as if we were the Counsel for the Defense. People who behave like this are quickly shunned by others, and made dupes of by those who resent their lack of trust and play upon it.
But to return to the point I was making above, not all certainty is just physical or moral. Absolute certainty is not only possible; we in fact are absolutely certain of some things; we are at least absolutely certain that there is something.
Absolute certainty only occurs when the denial of something implies its assertion.(1)
It should be obvious that this sort of thing gives absolute certainty, because (as we saw with "there is something") to think that it is false can't be done without admitting that it is true. And so it is simply not possible (supposing one understands the meaning of what one is asserting) to be mistaken.
There are some other statements like this, and we will see them shortly. Needless to say, they are supremely trivial, and all but contentless. Still, there are some.
Practically everything we know, however, is at the level of physical certainty, where we are relying on evidence for something and can't rule out either that there might be other evidence out there that would refute it, or (especially in complex cases) that there is not some flaw in our reasoning process. There are, of course, various degrees of this physical certainty, depending on how compelling the evidence is and what evidence we might have that there isn't evidence that could refute our assertion.
For instance, in this book, we will prove that there is a God (an infinite being), and show that every other explanation of the evidence we present involves some contradiction. But the evidence for the existence of God is very complex and intricate, and it is always possible either to have misread it, or to have made some mistake in reasoning to the conclusion from the evidence. Absent, however, any facts that would indicate that I have misread the evidence or committed some logical fallacy, then I am certain of the conclusion. I could be mistaken, but there is reason to believe I am not mistaken and no reason to believe that I am.Next
1. Note that this is the requirement for self-evidence, not something that everyone takes for granted as true. Jefferson, for example, considered it "self-evident" that "all men are created equal," but when you analyze this, it turns out in fact to be, far from self-evident, false.