Formulas for Propositions: Principle of Assertion and Logical Equivalences

如果你也在线性代数linearalgebra这个学科遇到相关的难题,请随时添加vx号联系我们的代写客服。我们会为你提供专业的服务。 linearalgebra™长期致力于留学生网课服务,涵盖各个网络学科课程:金融学Finance,经济学Economics,数学Mathematics,会计Accounting,文学Literature,艺术Arts等等。除了网课全程托管外,linearalgebra™也可接受单独网课任务。无论遇到了什么网课困难,都能帮你完美解决!

All the formulas which we have hitherto noted are valid alike for propositions and for concepts. We shall now establish a series of formulas which are valid only for propositions, because all of them are derived from an axiom peculiar to the calculus of propositions, which may be called the _principle of assertion_.This axiom is as follows:Ax. 10\[(a=1)=a.\]P. I.: To say that a proposition a is true is to state the proposition itself. In other words, to state a proposition is to affirm the truth of that proposition.58We can see at once that this formula is not susceptible of a conceptual interpretation (C. I.); for, if \(a\) is a concept, (\(a=1\)) is a proposition, and we would then have a logical equality [identity] between a concept and a proposition, which is absurd._Corollary_:\[a^{\prime}=(a^{\prime}=1)=(a=0).\]P. I.: The negative of a proposition \(a\) is equivalent to the affirmation that this proposition is false.By Ax. 9 (SS0.20), we already have\[(a=1)(a=0)=0,\]”A proposition cannot be both true and false at the same time”, for(Syll.)\[(a=1)(a=0)

发表回复

您的电子邮箱地址不会被公开。 必填项已用 * 标注