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An Introduction To Non-aristotelian Systems And General Semantics.

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152 IV. STRUCTURAL FACTORS IN A LANGUAGES
lation, and therefore most probably the form of the reaction, and we know already that different intensities of the same stimulus can be differentiated very accurately, one definite intensity being connected with excitation and another with inhibition. (394)                                                    I. p. pavlov
Whoever studies Leibniz, Lambert and Castillon cannot fail to be convinced that a consistent calculus of concepts in intension is either immensely difficult or, as Couturat has said, impossible. (3ao>          c. I. lewis
The relation between intensions and extensions is unsymmetrical, not symmetrical as the medieval logicians would have it. (300)           C. I. lewis
The old "law" of _ formallogic, that if a is contained in 0 in extension, then is contained in a in intension, and vice versa, is false. The connection between extension and intension is by no means so simple as that.
(300)                           '                                                                                        c. I. LEWIS
I do not suggest explicit confusions of this sort, but only that traditional elementary logic, taught in youth, is an almost fatal barrier to clear thinking in later years, unless much time is spent in acquiring a new technique.
(457)                                                                                                    BERTRAND RUSSELL
Section A. Undefined terms.
We can now introduce a structural non-el term which underlies not only all existing mathematics, but also the present work. This bridging term has equal importance in science and in our daily life; and applies equally to 'senses' and 'mind'. The term in question is 'order', in the sense of 'betweenness'. If we say that a, b, and c are in the order a, b, c, we mean that b is between a and c, and we say, further, that a, b, c, has a different order from c, b, a, or b, a, c,. .The main importance of numbers in mathematics is in the fact that they have a definite order. In mathematics, we are much concerned with the fact that numbers represent a definite ordered series or progression, 1, 2, 3, 4,.
In the present system, the term 'order' is accepted as undefined. It is clear that we cannot define all our terms. If we start to define all our terms, we must, by necessity, soon come to a set of terms which we cannot define any more because we will have no more terms with which to define them. We see that the structure of any language, mathematical or daily, is such that we must start implicitly or explicitly with undefined terms. This point is of grave consequence. In this work, following mathematics, I explicitly start with undefined important terms.
When we use a series of names for objects, 'Smith, Brown, Jones'., we say nothing. We do not produce a proposition. But if we say 'Smith kicks Brown', we have introduced the term 'kicks', which is not a name for an object, but is a term of an entirely different character. Let us call it a 'relation-word'. If we analyse this term, 'kicks', further, we will find that we can define it by considering the leg (objective) of Smith (objective), some part of the anatomy of Brown (objective), and,