On the Analyticity of Mathematics — Philosophy
A point which is not sufficiently brought out by Russell, if indeed it is recognized by him at all, is that every logical proposition is valid in its own right. Its validity does not depend upon its being incorporated in a system, and deduced from certain propositions which are taken as self-evident. The construction of systems of logic is useful as a means of discovering and certifying analytic propositions, but it is not in principle essential even for this purpose. For it is possible to conceive of a symbolism in which every analytic proposition could be seen to be analytic in virtue of its form alone. The fact that the validity of an analytic proposition in no way depends on its being deducible from other analytic propositions is our justification for disregarding the question whether the propositions of mathematics are reducible to propositions of formal logic, in the way that Russell supposed (1919, chap. 2). For even if it is the case that the definition of a cardinal number as a class of classes similar to a given class is circular, and it is not possible to reduce mathematical notions to purely logical notions, it will still remain true that the propositions of mathematics are analytic propositions. They will form a special class of analytic propositions, containing special terms, but they will be none the less analytic for that. For the criterion of an analytic proposition is that its validity should follow simply from the definition of the terms contained in it, and this condition is fulfilled by the propositions of pure mathematics.
philosophy is a department of logic
In other words, the propositions of philosophy are not factual, but linguistic in character — that is, they do not describe the behaviour of physical, or even mental, objects; they express definitions, or the formal consequences of definitions. Accordingly we may say that philosophy is a department of logic. For we will see that the characteristic mark of a purely logical enquiry, is that it is concerned with the formal consequences of our definitions and not with questions of empirical fact.
Alfred JulesAyer
Alfred Jules Ayer-This person…look how he complicates the word proposition.he z rather promoting the effects of the word proposition by bringing out a redundancy in the word proposition.its indeed a new proposition to propose the word proposition by highlighting the word proposition many times though out a sentence by typing propostion and concioulsy trying to catch the attention of the viewer in to the word propositon. He has tried to connect all the situation that he tries to explain with the word proposition and here I too have done a part of what he couldn’t contribute..does this proposition make any sense with what I have written here..can this also called as philosophy?no its surely projecting a kind of obscure mind here.
Well this is what I call as timepass….but I do love it.
Bear with me:)
A point which is not sufficiently brought out by Russell, if indeed it is recognized by him at all, is that every logical proposition is valid in its own right. Its validity does not depend upon its being incorporated in a system, and deduced from certain propositions which are taken as self-evident. The construction of systems of logic is useful as a means of discovering and certifying analytic propositions, but it is not in principle essential even for this purpose. For it is possible to conceive of a symbolism in which every analytic proposition could be seen to be analytic in virtue of its form alone. The fact that the validity of an analytic proposition in no way depends on its being deducible from other analytic propositions is our justification for disregarding the question whether the propositions of mathematics are reducible to propositions of formal logic, in the way that Russell supposed (1919, chap. 2). For even if it is the case that the definition of a cardinal number as a class of classes similar to a given class is circular, and it is not possible to reduce mathematical notions to purely logical notions, it will still remain true that the propositions of mathematics are analytic propositions. They will form a special class of analytic propositions, containing special terms, but they will be none the less analytic for that. For the criterion of an analytic proposition is that its validity should follow simply from the definition of the terms contained in it, and this condition is fulfilled by the propositions of pure mathematics.
philosophy is a department of logic
In other words, the propositions of philosophy are not factual, but linguistic in character — that is, they do not describe the behaviour of physical, or even mental, objects; they express definitions, or the formal consequences of definitions. Accordingly we may say that philosophy is a department of logic. For we will see that the characteristic mark of a purely logical enquiry, is that it is concerned with the formal consequences of our definitions and not with questions of empirical fact.
Alfred JulesAyer
Alfred Jules Ayer-This person…look how he complicates the word proposition.he z rather promoting the effects of the word proposition by bringing out a redundancy in the word proposition.its indeed a new proposition to propose the word proposition by highlighting the word proposition many times though out a sentence by typing propostion and concioulsy trying to catch the attention of the viewer in to the word propositon. He has tried to connect all the situation that he tries to explain with the word proposition and here I too have done a part of what he couldn’t contribute..does this proposition make any sense with what I have written here..can this also called as philosophy?no its surely projecting a kind of obscure mind here.
Well this is what I call as timepass….but I do love it.
Bear with me:)
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