Descartes' Epistemology - SEP
I distinguish the two as follows: there is conviction [persuasio] when there remains some reason which might lead us to doubt, but knowledge [scientia] is conviction based on a reason so strong that it can never be shaken by any stronger reason. (24 May 1640 letter to Regius, AT 3:65, CSMK 147)
I shall now expound for a second time the basis on which it seems to me that all human certainty can be founded.
First of all, as soon as we think that we correctly perceive something, we are spontaneously convinced that it is true. Now if this conviction is so firm that it is impossible for us ever to have any reason for doubting what we are convinced of, then there are no further questions for us to ask: we have everything that we could reasonably want. … For the supposition which we are making here is of a conviction so firm that it is quite incapable of being destroyed; and such a conviction is clearly the same as the most perfect certainty. (AT 7:144f, CSM 2:103)
SEP - "These passages (and others) suggest an account wherein doubt is the contrast of certainty. As my certainty increases, my doubt decreases; conversely, as my doubt increases, my certainty decreases."
All models are wrong, but some are useful.
In a bivalent logic model, certainty and doubt are mutually exclusive. There is either certainty or there is doubt. But they do not co-exist or overlap in the model. This is called the excluded middle.
In a fuzzy logic model, certainty and doubt overlap. There are degrees of certainty and doubt where increasing certainty diminishes doubt and increasing doubt diminishes certainty.
Baruch Spinoza describes the relationship between pleasure and pain using the fuzzy logic model. He says intense pleasure drives out pain and intense pain drives out pleasure.
Recognizing and Quantifying Uncertainty
People view uncertain events as knowable in principle (epistemic uncertainty), as fundamentally random (aleatory uncertainty), or as some mixture of the two.
To quantify aleatory uncertainty mathematicians, scientists, and other experts apply the conventional methods of probability and statistics. To quantify epistemic uncertainty experts use more recently developed methods associated with the fields of data science, machine learning, and artificial intelligence.
Bayes' Theorem - SEP
Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology.
Nobody doubts that he exists, though he may doubt the existence of God. If he finds out the truth about himself and discovers his own source, this is all that is required.
Book of Job
"When the sons of God gathered before the Lord, Satan also came among them! God said, "From whence do you come?" Satan replied, "From roaming the earth and patrolling it!"
The question then is: why can’t we be certain, for example, in the fact that unicorns do not exist.
Because it is reasonable to doubt the assertion that unicorns do not exist. This doubt can be based on the vague human perceptions of what is or is not a unicorn (goat, rhino, horse); or on the fact that many creatures in the past and present roam and patrol the earth undetected by humans when we roam the earth and patrol it.