MEPX
Chapter 4 of 10All chapters
  1. 1What an argument is
  2. 2Validity and soundness
  3. 3If, then
  4. 4All, some, none
  5. 5Necessary and sufficient
  6. 6Deduction against induction
  7. 7Formal fallacies
  8. 8Informal fallacies
  9. 9Logic puzzles
  10. 10Using it in real arguments

Chapter 4 of 10

All, some, none

Categorical reasoning.

What carries through

All A are B and all B are C gives all A are C. Some A are B and all B are C gives some A are C. Most other combinations give nothing.

  • Some means at least one, not most and not some but not all.
  • The negation of all A are B is at least one A is not B.

Draw it

Overlapping circles settle these questions faster than words. If you can draw a case where the premises hold and the conclusion fails, the argument is invalid.