The Language of Argument
1 4 3 C o n d i t i o n a l s “E & B.” Their truth-functional equivalence is too obvious to need proof. Similar oddities ari ...
1 4 4 C H A P T E R 6 ■ P r o p o s i t i o n a l L o g i c Both arguments are instances of the valid argument form “p; ∴ q ⊃ p. ...
1 4 5 C o n d i t i o n a l s or false. Yet it can be misleading to use a conditional on the basis of this logi- cal feature. Fo ...
1 4 6 C H A P T E R 6 ■ P r o p o s i t i o n a l L o g i c the first sentence is symbolized as follows: H ⊃ B Notice that in th ...
1 4 7 C o n d i t i o n a l s We can next look at sentences of the form “p if and only if q”—so-called biconditionals. If I say ...
1 4 8 C H A P T E R 6 ■ P r o p o s i t i o n a l L o g i c McCain will lose the election unless he carries the South. This sent ...
1 4 9 C o n d i t i o n a l s You can be a success if you are the only one who tries. (S, O) Unless there is a panic, stock pri ...
1 5 0 C H A P T E R 6 ■ P r o p o s i t i o n a l L o g i c The Democrats will win the election. Therefore, they will win the e ...
1 5 1 Categorical Logic In Chapter 6, we saw how validity can depend on the external connections among propositions. This chapte ...
1 5 2 C H A P T E R 7 ■ C a t e g o r i c a l L o g i c connective. In fact, if we properly translate the above argument into th ...
1 5 3 C a t e g o r i c a l P r o p o s i t i o n s We then shade out the portions of the circles in which nothing exists, ac- c ...
1 5 4 C H A P T E R 7 ■ C a t e g o r i c a l L o g i c for we are not saying that all spies are aliens. Saying that some aliens ...
1 5 5 C a t e g o r i c a l P r o p o s i t i o n s These forms are called categorical forms, and propositions with these forms ...
1 5 6 C H A P T E R 7 ■ C a t e g o r i c a l L o g i c Using just the four basic categorical forms, indicate what information i ...
1 5 7 C a t e g o r i c a l P r o p o s i t i o n s if our logical apparatus could be applied only to propositions with the expl ...
1 5 8 C H A P T E R 7 ■ C a t e g o r i c a l L o g i c is a man” as the A proposition “All things that are Socrates are men.” S ...
1 5 9 C a t e g o r i c a l P r o p o s i t i o n s Contradictories Once we understand A, E, I, and O propositions by themselves ...
1 6 0 C H A P T E R 7 ■ C a t e g o r i c a l L o g i c But for the corresponding I proposition to be true, there must be someth ...
1 6 1 C a t e g o r i c a l P r o p o s i t i o n s Existential Commitment It might also seem that an A proposition (with the fo ...
1 6 2 C H A P T E R 7 ■ C a t e g o r i c a l L o g i c Validity for Categorical Arguments We have introduced Venn diagrams beca ...
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