Traditional versus Modern Logic

[upperhappy]

Mr. Cothran,

I am previewing the Traditional Logic DVDs this summer in preparation to teach it to my 7th grade son. I am having a wonderful time learning through your clear and well-laid out curriculum. I have also read some of the articles posted on the memoria press web site. In one on Logic and Math, you stated that Modern Logic, first posited by Bertrand Russell, is easily recognizable because of its forms, such as the Venn Diagram, which are widely in use today. I have just finished the 8th chapter of Traditional Logic I where you discuss distributed and undistributed terms and I think you are also making use of Venn Diagrams. These are very helpful to visualize the concept, but I am wondering why you clumped them with Modern Logic and yet use them in the Traditional Logic presentation. Perhaps I am not versed in exactly what the definition of a Venn Diagram is. Any insights you can offer would be most appreciated.

Thanks

Jenny

[spiland]

upperhappy,

I think I'll jump in for Mr. Cothran here, if he doesn't mind . I teach some logic courses for him here at the Online Academy, and I think I can help you. The diagrams that Mr. Cothran is using are called Euler diagrams rather than Venn diagrams.

One main difference betwee Euler diagrams and Venn diagrams are the different philosophical assumptions behind them. Leonhard Euler formulated his diagrams with the same philosophical assumptions held by traditional logicians, namely that the categorical statements (I and O) assume some sort of existential import (that the the classes represented by the terms actually exist in some sense). Euler's system of diagrams were strictly to illustrate the relationship between the classes stated in a given premise. In traditional logic you could say that since,

[I]All dogs are brown[/I]

then

[I]Some dogs are brown [/I]

follows from this

You cannot infer this from the modern system. In the modern system (represented by Venn diagrams) just because [I]All dogs are brown[/I] is true (these statements don't postulate existence) it doesn't mean that [I]Some dogs are brown[/I] is true (because this statement assumes that [I]at least one [/I]brown dog exists, when in fact we don't know this). Venn diagrams, however, do not asume that anything actually exists. That is why you have certain categorical statements that traditional logicians deem valid yet modern logicians deem invalid.

Hopefully this helps.

For a helpful, yet technical article about the difference between Euler and Venn diagrams, see:

[URL="http://plato.stanford.edu/entries/diagrams/#venn"]http://plato.stanford.edu/entries/diagrams/#venn[/URL]

Mr. Piland
Logic Instructor