Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave nether room nor demand for a theory of probabilities.
Meaning of the quote
Probability is what we expect to happen based on the information we have. But if we knew every single detail that could affect an event, we would be certain about what will happen, and there would be no need to use probability to make guesses.

About George Boole
George Boole was an influential English mathematician, philosopher, and logician who made significant contributions to the field of logic and laid the foundations for the Information Age. He served as the first professor of mathematics at Queen’s College, Cork in Ireland and is best known for developing Boolean algebra, a fundamental concept in binary logic that paved the way for modern computer science.
More quotes from George Boole
No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful.
English mathematician, philosopher and logician (1815-1864)
It is not of the essence of mathematics to be conversant with the ideas of number and quantity.
English mathematician, philosopher and logician (1815-1864)
To unfold the secret laws and relations of those high faculties of thought by which all beyond the merely perceptive knowledge of the world and of ourselves is attained or matured, is a object which does not stand in need of commendation to a rational mind.
English mathematician, philosopher and logician (1815-1864)
Of the many forms of false culture, a premature converse with abstractions is perhaps the most likely to prove fatal to the growth of a masculine vigour of intellect.
English mathematician, philosopher and logician (1815-1864)
Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave nether room nor demand for a theory of probabilities.
English mathematician, philosopher and logician (1815-1864)