An Investigation of the Laws of Thought: On which are Founded the Mathematical Theories of Logic and ProbabilitiesWalton and Maberly, 1854 - 424 σελίδες |
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Σελίδα 8
... involved in the premises . 8. Now this being premised , the requirements of a general method in Logic seem to be the following : - 1st . As the conclusion must express a relation among the whole or among a part of the elements involved ...
... involved in the premises . 8. Now this being premised , the requirements of a general method in Logic seem to be the following : - 1st . As the conclusion must express a relation among the whole or among a part of the elements involved ...
Σελίδα 9
... involved in it . Or we might form the conception of some thing or class of things , involving more than one of the elements of the conclusion , and require its expression in terms of the other elements . Again , suppose the elements ...
... involved in it . Or we might form the conception of some thing or class of things , involving more than one of the elements of the conclusion , and require its expression in terms of the other elements . Again , suppose the elements ...
Σελίδα 25
... in subjection to fixed laws dependent upon their mutual interpre- tation . 3. Let us consider the particulars involved in the above de- finition separately . ( 1. ) In the first place , a sign CHAP . II . ] 25 SIGNS AND THEIR LAWS .
... in subjection to fixed laws dependent upon their mutual interpre- tation . 3. Let us consider the particulars involved in the above de- finition separately . ( 1. ) In the first place , a sign CHAP . II . ] 25 SIGNS AND THEIR LAWS .
Σελίδα 26
... involved in the definition of a sign , viz . , its subjection to fixed laws of combination depending upon the nature of its interpretation . 4. The analysis and classification of those signs by which the operations of reasoning are ...
... involved in the definition of a sign , viz . , its subjection to fixed laws of combination depending upon the nature of its interpretation . 4. The analysis and classification of those signs by which the operations of reasoning are ...
Σελίδα 40
... involved in the mode of their state- ment . They contain an element of truth which no ulterior cri- ticism upon the nature , or even upon the reality , of the mind's operations , can essentially affect . Let it even be granted that the ...
... involved in the mode of their state- ment . They contain an element of truth which no ulterior cri- ticism upon the nature , or even upon the reality , of the mind's operations , can essentially affect . Let it even be granted that the ...
Άλλες εκδόσεις - Προβολή όλων
An Investigation of the Laws of Thought: On which are Founded the ... George Boole Πλήρης προβολή - 1854 |
An Investigation of the Laws of Thought: On which are Founded the ... George Boole Προβολή αποσπασμάτων - 1961 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a₁ algebraic application assume babilities c₁ C₂ cause chapter cloth coefficients conception conclusion condition connexion constituents deduce definition deliberative assembly denoted determine DIONYSIUS LARDNER disjunctive proposition Edition elements elimination equa equal events whose probabilities exist expression F. W. NEWMAN factor Fcap function given Hence hypothesis indefinite independent interpretation involved laws of thought logical equation M₁ method minor limit natural evils nature necessary object observed occur p₁ P₂ particular phænomenon premises present preventive of pain primary propositions principle Prob problem processes productive of pleasure Prop question reasoning reduced relation represent respect result second member secondary propositions simple events sition solution supposed syllogism system of equations t₁ t₂ theory of probabilities things tion treatise true truth universe universe of discourse V₁ whence καὶ
Δημοφιλή αποσπάσματα
Σελίδα 212 - Those things which have nothing mutually in common with one another cannot through one another be mutually understood, that is to say, the conception of the one does not involve the conception of the other.
Σελίδα 212 - I understand the affections of substance, or that which is in another thing, by which thing also it is conceived. 6. By God, I understand the Being absolutely infinite, that is the substance consisting of infinite attributes, each of which expresses an eternal and infinite essence.
Σελίδα 24 - That Language is an instrument of human reason, and not merely a medium for the expression of thought, is a truth generally admitted. It is proposed in this chapter to inquire what it is that renders Language thus subservient to the most important of our intellectual faculties. In the various steps of this inquiry we shall be led to consider the constitution of Language, considered as a system adapted to an end or purpose; to investigate its elements; to seek to determine their mutual relation and...
Σελίδα 27 - ... 1st. Literal symbols, as x, y, drc., representing things as subjects of our conceptions. 2nd. Signs of operation, as + , — , X , standing for those operations of the mind by which the conceptions of things are combined or resolved so as to form new conceptions involving the same elements.
Σελίδα 6 - There is not only a close analogy between the operations of the mind in general reasoning and its operations in the particular science of Algebra, but there is to a considerable extent an exact agreement in the laws by which the two classes of operations are conducted.
Σελίδα 1 - The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation to establish the science of Logic...