Seeing Deduction with OR happen

with Interactive Diagrams

from logic tutorial .com


logic diagram one
Captions for logic diagrams

OR

logic diagram two
Captions for logic diagrams

means


logic diagram three
Captions for logic diagrams


Click within the first two diagrams to create the third.



Again we can watch deduction happen by clicking on and altering the first two statements (diagrams). Here the "first statement OR the second statement" yields our third statement, which says exactly as much, no more and no less than the first two statements do when joined by an OR. That is, the first diagram ORed with the second diagram, is logically equivalent to the third diagram.

An area in the third diagram is black (excluded from consideration/possibility) if only if both previous statements (one and two) exclude it (have it colored black.) Thus the third diagram represents not just a deduction from the first two, but is logically equivalent to "A OR B".

Again, as with "AND" deduction with "OR" is not an any way mysterious. It's a mechanical process as well; where what is meant by "or" is just what we exclude on both sides of the "or". That is, whatever both statements exclude from consideration, "A OR B" excludes.

Notice that "the contradiction" joined to any other statement by "OR" just yields the other statement, since "not contradiction" is true.

Here we're using the "inclusive or": "this OR that OR both". Arguably, in ordinary English, "or" is more usually meant as an "exclusive or": "this OR that but NOT both" - for example, what a mother means when she tells a child "You may have one orange or one apple." She doesn't mean you can have one of each. But when early logicians tried out the mathematics and mechanics of deduction, the inclusive OR turned out to be much easier to work with, so that's what formal logicians mean by OR today. It would be possible of course to create a similar page showing deduction with the exclusive OR, which would have somewhat different results - but since logicians don't use the exclusive OR, this hasn't been done here.

Again, what "meaning" means turns out to be straightforward enough. What is meant by the first statement OR the second, is just whatever both statement exclude from consideration or possibility. Therefore we can determine area by area within the diagrams what areas both exclude, and mechanically create/deduce the third diagram ourselves if we wish, without the computer's help.



  • NEXT: A discussion of meaning as exclusion.
      

  • So our minds work by exclusion? Not so fast!
      

  • Relevant Buddhist philosophy of logic.
      

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