enter image description hereBritannica.com/biography/John-Venn says the rings on the left are a Venn diagram of the syllogism “Some mammals are carnivores; all mammals are animals; therefore, some animals are carnivores” but ignoring the mysterious “X”, that doesn’t seem quite so.

“Some mammals are carnivores” but isn’t the second premise of the diagram not “all…” but rather “some mammals are animals”?

Shouldn’t “all mammals are animals” be shown as set M fully enclosed by set A, as in the rings on the right?

Doesn’t the difference matter quite a lot?

  • 2
    The shaded areas in the left type of diagram are supposed to be excluded areas, i.e. there can be no objects in those areas, so that diagram does show the only objects in the non-shaded part of the 'mammals' circle must be in the 'animals' circle. Sometimes the reverse convention is used and the shaded areas are allowed objects while the white areas are excluded, see here.
    – Hypnosifl
    Jul 26 at 19:59
  • @Hypnosifl Thanks and I don't see the shading as relevant, nor how that diagram does show the only objects in the non-shaded part of the 'mammals' circle must be in the 'animals' circle could matter. How am I mistaken in thinking “all mammals are animals” requires the set of mammals to be not merely intersecting, but wholly enclosed by the set of animals? Jul 26 at 20:08
  • 1
    Well, that's what the shading means in that type of diagram--those areas are excluded, the set "mammals" only consists of the non-shaded areas in that diagram. So, the set "mammals" is wholly contained within the set "animals", the way the sets are defined in that diagram.
    – Hypnosifl
    Jul 26 at 20:28
  • @Hypnosifl Then if we drop the set C and the mysterious X, the remaining shaded M and unshaded A express not an intersection but a total inclusion… or did I miss something? Jul 26 at 20:34
  • 1
    The X is not shaded, it's not meant to be dropped. I think the X area represents "some mammals are carnivores", and since that area is also part of "animals", it shows that "some mammals are animals" must be true. And why do you mention dropping the set C? Only the shaded areas are supposed to be dropped, most of C is non-shaded.
    – Hypnosifl
    Jul 26 at 21:14

The difference matters. Venn diagrams are intended for the representation of all logically possible relations, not merely actual ones. A subtle, but logically significant difference: The syllogism states that all mammals are animals, not that mammals constitute a subset of animals.

  • There I thought I was starting to get it, and now how is there a difference between "all mammals are animals" and "mammals constitute a subset of animals." Jul 27 at 16:27
  • @Robbie Goodwin Spend some time on this issue: According to the usual conception of formal languages, '(for) all' is a logical quantifier, whereas 'element of' (hence, 'subset of') is a non-logical (set-theoretical) predicate. Don't be dispirited, even many professional philosophers miss such distinctions. Jul 27 at 17:27
  • Thanks and where did '(for) all' or 'element of' come into this? Aug 11 at 22:55

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