Two cases must be clearly distinguished, for a considerable number of our ideas, viz., all complex ideas except those of substances, make no claim to represent things, and consequently cannot represent them falsely.  For mathematical and moral ideas and principles, and the truth thereof, it is entirely immaterial whether things and conditions correspondent to them exist in nature or not.  They are valid, even if nowhere actualized; they are “eternal truths,” not in the sense that they are known from childhood, but in the sense that, as soon as known, they are immediately assented to.[1] The case is different, however, with simple ideas and the ideas of substances, which have their originals without the mind and which are to correspond with these.  In regard to the former we may always be certain that they agree with real things, for since the mind can neither voluntarily originate them (e.g., cannot produce sensations of color in the dark) nor avoid having them at will, but only receive them from without, they are not creatures of the fancy, but the natural and regular productions of external things affecting us.  In regard to the latter, the ideas of substances, we may be certain at least when the simple ideas which compose them have been found so connected in experience.  Perception has an external cause, whose influence the mind is not able to withstand.  The mutual corroboration furnished by the reports of the different senses, the painfulness of certain sensations, the clear distinction between ideas from actual perception and those from memory, the possibility of producing and predicting new sensations of an entirely definite nature in ourselves and in others, by means of changes which we effect in the external world (e.g. by writing down a word)—­these give further justification for the trust which we put in the senses.  No one will be so skeptical as to doubt in earnest the existence of the things which he sees and touches, and to declare his whole life to be a deceptive dream.  The certitude which perception affords concerning the existence of external objects is indeed not an absolute one, but it is sufficient for the needs of life and the government of our actions; it is “as certain as our happiness or misery, beyond which we have no concernment, either of knowing or being.”  In regard to the past the testimony of the senses is supplemented by memory, in which certainty [in regard to the continued existence of things previously perceived] is transformed into high probability; while in regard to the existence of other finite spirits, numberless kinds of which may be conjectured to exist, though their existence is quite beyond our powers of perception, certitude sinks into mere (though well-grounded) faith.