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How is the inference WB <-some->F validly made? Doesn't it involve linking two "some" statements, which never yields a valid inference?

Also, on a more general note, when using the "some" and "most" trains to make inferences, is it always necessary to begin with a "some" or "most" statement to make a valid inference? Could you start with an "all" or "none" statement and then use a "some" or "most"?
 Robert Carroll
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I see only one "some" statement present, the first statement, so I don't see a danger of combining two such here.

The first statement means that some things are simultaneously birds and mammals. All birds (so specifically these) have feathers, and all mammals (so specifically these) are warm-blooded. So those birds that are mammals are both feathered and warm-blooded, so some things are both feathered and warm-blooded, which is what the inference claims.

You can make some inferences using "none" and a "some" or "most" train. The Formal Logic info from which this drill is drawn discusses that when discussing the trains. For instance:

"No empiricists are libertarians"

"Some libertarians are atheists"

I get from this:

E :dblline: L :some: A

I can infer:

A :dblline: E (some atheists are not empiricists)

So a "none" and "some" can lead to an inference.

Robert Carroll
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 Dave Killoran
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Hi Forumuser,

Let me add to the above that #12 is a very tough one, and it forces you to recycle inferences and plug them back into the original diagram. So, consider the following:

  • Initial diagram:

    ..... WB :larrow: M :some: B :arrow: F

    We know one of the inferences there is B :some: WB, which is the same as WB :some: B. Well, plug that back into the diagram, to get:

    ..... WB :some: B :arrow: F

    Now that "super inferences" of WB :some: F is much easier to see!

Note that I can take a different route as well:

  • Initial diagram:

    ..... WB :larrow: M :some: B :arrow: F

    We know one of the inferences there is M :some: F. Well, plug that back into the diagram, to get:

    ..... WB :larrow: M :some: F

    That "yields the "super inferences" of F :some: WB, which is the same as WB :some: F.

It's like mountain climbing: there can be several different routes to get to the "top" here :-D


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