Spring 2018: Math 112 Introduction to Analysis
Old Course Information
"Now many errors consist of this alone, that we do not apply names rightly to things. For when any one says that lines which are drawn from the centre of a circle to the circumference are unequal, he means, at least at the time, something different by circle than mathematicians. Thus when men make mistakes in calculation they have different numbers in their minds than those on the paper. Wherefore if you could see their minds they do not err; they seem to err, however, because we think they have the same numbers in their minds as on the paper. If this were not so we should not believe that they made mistakes any more than I thought a man in error whom I heard the other day shouting that his yard had flown into his neighbor's chickens, for his mind seemed sufficiently clear to me on the subject."
(Spinoza, Ethics II.XLVII)