considered as representations, are symbols, that is, signs which are at least potentially general. But the rules of logic hold good of any symbols, of those which are written or spoken as well as of those which are thought. They have no immediate application to likenesses or indices, because no arguments can be constructed of these alone, but do apply to all symbols. All symbols, indeed, are in one sense relative to the understanding, but only in the sense in which also all things are relative to the understanding. On this account, therefore, the relation to the understanding need not be expressed in the definition of the sphere of logic, since it determines no limitation of that sphere. But a distinction can be made between concepts which are supposed to have no existence except so far as they are actually present to the understanding, and external symbols which still retain their character of symbols so long as they are only capable of being understood. And as the rules of logic apply to these latter as much as to the former, (and though only through the former, yet this character, since it belongs to all things, is no limitation,) it follows that logic has for its subject-genus all symbols and not merely concepts. We come, therefore, to this, that logic treats of the reference of symbols in general to their objects. In this view it is one of a trivium of conceivable sciences. The first would treat of the formal conditions of symbols having meaning, that is of the reference of symbols in general to their grounds or imputed characters, and this might be called formal grammar; the second, logic, would treat of the formal conditions of the truth of symbols; and the third would treat of the formal conditions of the force of symbols, or their power of appealing to a mind, that is, of their reference in general to interpretants, and this might be called formal rhetoric.

There would be a general division of symbols, common to all these sciences; namely, into,

1° Symbols which directly determine only their grounds or imputed qualities, and are thus but sums of marks or terms;

Herbart says: "Unsre sämmtlichen Gedanken lassen sich von zwei Seiten betrachten; theils als Thätigkeiten unseres Geistes, theils in Hinsicht dessen, was durch sie gedacht wird. In letzerer Beziehung heissen sie Begriffe, welches Wort, indem es das Begriffene bezeichnet, zu abstrahiren gebietet von der Art und Weise, wie wir den Gedanken empfangen, produciren, oder reproduciren mögen." But the whole difference between a concept and an external sign lies in these respects which logic ought, according to Herbart, to abstract from.

2° Symbols which also independently determine their objects by means of other term or terms, and thus, expressing their own objective validity, become capable of truth or falsehood, that is, are propositions ; and,

3° Symbols which also independently determine their interpretants, and thus the minds to which they appeal, by premising a proposition or propositions which such a mind is to admit. These are arguments. And it is remarkable that, among all the definitions of the proposition, for example, as the oratio indicativa, as the subsumption of an object under a concept, as the expression of the relation of two concepts, and as the indication of the mutable ground of appearance, there is, perhaps, not one in which the conception of reference to an object or correlate is not the important one. In the same way, the conception of reference to an interpretant or third, is always prominent in the definitions of argument.

In a proposition, the term which separately indicates the object of the symbol is termed the subject, and that which indicates the ground is termed the predicate. The objects indicated by the subject (which are always potentially a plurality, — at least, of phases or appearances) are therefore stated by the proposition to be related to one another on the ground of the character indicated by the predicate. Now this relation may be either a concurrence or an opposition. Propositions of concurrence are those which are usually considered in logic; but I have shown in a paper upon the classification of arguments that it is also necessary to consider separately propositions of opposition, if we are to take account of such arguments as the following:

Whatever is the half of anything is less than that of which it is the half;

A is half of B:

.. A is less than B.

The subject of such a proposition is separated into two terms, a "subject nominative" and an "object accusative."

In an argument, the premises form a representation of the conclusion, because they indicate the interpretant of the argument, or representation representing it to represent its object. The premises may afford a likeness, index, or symbol of the conclusion. In deductive argument, the conclusion is represented by the premises as by a general sign under which it is contained. In hypotheses, something

like the conclusion is proved, that is, the premises form a likeness of the conclusion. Take, for example, the following argument:—

M is, for instance, P, P", P, and Piv;

S is P', P", P!", and Piv:

S is M.

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Here the first premise amounts to this, that " P' P", P'"', and Piv" is a likeness of M, and thus the premises are or represent a likeness of the conclusion. That it is different with induction another example

will show.

S', S", S'", and Siv are taken as samples of the collection M;

S', S", S'"', and Siv are P:

.. All M is P.

Hence the first premise amounts to saying that "S', S", S"", and Siv " is an index of M. Hence the premises are an index of the conclusion.

The other divisions of terms, propositions, and arguments arise from the distinction of extension and comprehension. I propose to treat this subject in a subsequent paper. But I will so far anticipate that, as to say that there is, first, the direct reference of a symbol to its objects, or its denotation; second, the reference of the symbol to its ground, through its object, that is, its reference to the common. characters of its objects, or its connotation; and third, its reference to its interpretants through its object, that is, its reference to all the synthetical propositions in which its objects in common are subject or predicate, and this I term the information it embodies. And as every addition to what it denotes, or to what it connotes, is effected by means of a distinct proposition of this kind, it follows that the extension and comprehension of a term are in an inverse relation, as long as the information remains the same, and that every increase of information is accompanied by an increase of one or other of these two quantities. It may be observed that extension and comprehension are very often taken in other senses in which this last proposition is not

true.

This is an imperfect view of the application which the conceptions 38

VOL. VII.

which, according to our analysis, are the most fundamental ones find in the sphere of logic. It is believed, however, that it is sufficient to show that at least something may be usefully suggested by considering this science in this light.

Five hundred and eighty-third Meeting.

May 28, 1867.- ANNUAL MEETING.

The PRESIDENT in the chair.

The following Report of the Council upon the changes which had occurred in the Academy during the past year was presented.

IN surveying the events of the past year, as respects the membership of the Academy, the Council would first call attention to the losses which we have sustained, and would put upon record some brief tribute to the memory of our deceased associates. We have lost six Fellows, two Associate Fellows, and one Foreign Honorary Member, — nine in all.

Four of the six taken from our immediate circle, Messrs. Hayward, Mussey, Swett, and Jenks, were well advanced in years; two, Dr. Gould and Dr. Bryant, were suddenly removed from active life and stations which they might have been expected much longer to adorn. All have left names and memories to be affectionately cherished by this society.

JAMES HAYWARD was born in Concord, Massachusetts, in the year 1786, and died July 27, 1866. His youth was passed on his father's farm, first in Concord, and afterwards in Plainfield, Hampshire County, to which place his father removed when James was eight years old. Anxious to obtain a liberal education, he left his home at the age of eighteen, in the hope of finding in Boston employment that would give him the means of accomplishing his purpose. After three years of fruitless effort he returned to his old home, and took the management of his father's farm, teaching school in winter, and studying at intervals. It was not until 1815, when he was twenty-nine years old, that he was able to carry out his purpose of entering college at Cambridge. Graduating in 1819, he entered the Divinity School, and went through its course, having been appointed tutor in mathematics in the Col

but

lege in 1820, he continued in that office until 1826, when he became Professor of Mathematics and Natural Philosophy. The very next year, however, he resigned his professorship, to devote himself to Civil Engineering; and the same year he was appointed a member of the State Board of Internal Improvements, and also engineer to this Board.

His first work appears to have been a survey, made in 1827, of a line from Boston to Providence for a railroad to be worked by horse-power. This was followed by a survey of a line from Plymouth to Wareham. In 1829 he visited Pennsylvania and Maryland, and made a report on the internal improvements of those States. These and similar labors give him an honorable place among those who introduced the railway system into Massachusetts. Subsequently (1836 to 1845) he was engineer of the Boston and Maine Railroad, the greater part of which was built by him. He was President of this road from 1853 to 1856. Mr. Hayward also took an early interest in the preservation of the harbor of Boston, and was a member of the first Board of Harbor Commissioners. Besides the extended surveys then made, and others ten years later, as a Commissioner on the third Board he was consulted, in 1850, by a Committee of the Legislature on the Harbor, and in 1853 by a Commitiee of the City Government on the Harbor, and made reports to both these bodies. In the former of these reports he recommended the building of a sea-wall along the northern border of the South Boston flats to Fort Independence, which is one of the main features in the present plans for improving the harbor. Mr. Hayward was elected into this Academy in 1834.

At the close of his long and useful career, Mr. Hayward testified his love of science and his interest in the elevation of his fellow-men by many noble bequests. Among the most important of these were three of $20,000 each to the Observatory at Cambridge, to the Massachusetts Institute of Technology, and to the Unitarian Association, for the support of foreign missions.

DR. REUBEN DURRAND MUSSEY died in Boston on the 21st of June, 1866, at the age of eighty-six years, having been born at Pelham, New Hampshire, June 23, 1780. His childhood was passed in different country towns of New Hampshire, in which his father successively resided, until, at the age of twenty-one, he entered the Junior class at Dartmouth College. He pursued his medical studies at the same institution, under the tuition of the celebrated Professor Nathan Smith, and afterwards at the University of Pennsylvania, from which