And, making a digression at this stage on the subject of light, I expounded at considerable length what the nature of that light must be which is found in the sun and the stars, and how thence in an instant of time it traverses the immense spaces of the heavens, and how from the planets and comets it is reflected towards the earth.
However, this weakness of spaces delimited by human rules rather than by natural laws is at the same time their strength: we can build them ourselves, change them and develop them according to our experience and finally reach incredibly impressive edifices.
To say that an expression means thus and so is essentially to say that it ought to be used in a certain way. Thus, meanings are 'beyond the natural, causal order', but, at the same time, are not 'supernatural' in any abstruse or esoteric sense.
I have ever remained firm in my original resolution to suppose no other principle than that of which I have recently availed myself in demonstrating the existence of God and of the soul, and to accept as true nothing that did not appear to me more clear and certain than the demonstrations of the geometers had formerly appeared; and yet I venture to state that not only have I found means to satisfy myself in a short time on all the principal difficulties which are usually treated of in philosophy, but I have also observed certain laws established in nature by God in such a manner, and of which he has impressed on our minds such notions, that after we have reflected sufficiently upon these, we cannot doubt that they are accurately observed in all that exists or takes place in the world and farther, by considering the concatenation of these laws, it appears to me that I have discovered many truths more useful and more important than all I had before learned, or even had expected to learn.
How linguists became philosophers I've puzzled for a long time about what the difference is between certain kinds of philosophy and certain kinds of linguistics and finally decided that the main difference lies in whether you're embarrassed about not knowing about a paper in 'Linguistic Inquiry' or the 'Journal of Philosophy' Bach (1985, p.
Linguists, of course, have been in pursuit of meaning - in their own way - since the very time linguistics came into being; some of them, the semanticians, being even the specialists.
At the same time it is futile to see semantics as parasitic upon a psychology of language use. Semantics is primarily neither a matter of relating words with things, or of words with thoughts, it is a matter of displaying a certain kind of structure of language.
Finally, if there be still persons who are not sufficiently persuaded of the existence of God and of the soul, by the reasons I have adduced, I am desirous that they should know that all the other propositions, of the truth of which they deem themselves perhaps more assured, as that we have a body, and that there exist stars and an earth, and such like, are less certain; for, although we have a moral assurance of these things, which is so strong that there is an appearance of extravagance in doubting of their existence, yet at the same time no one, unless his intellect is impaired, can deny, when the question relates to a metaphysical certitude, that there is sufficient reason to exclude entire assurance, in the observation that when asleep we can in the same way imagine ourselves possessed of another body and that we see other stars and another earth, when there is nothing of the kind.
This nature of infinity has been repeatedly pointed out - probably for the first time by Aristotle, and more recently by several of the most outstanding 9 mathematicians and philosophers of this century - but many theoreticians simply ignore it. However, if there are no real infinite sets beyond those grounded in a finite number of generating rules, then there are also no functions with infinite domains beyond functions defined via finite rules.
From the latter point of view it may indeed be conceded (if only for the sake of argument) that rationality is involved in the meaning of the word 'man' while two-leggedness is not; but two-leggedness may at the same time be viewed as involved in the meaning of 'biped' while rationality is not.