# What exactly does 'Some' mean in Logic?

If the argument

(1) Some dogs are carnivores.
(2) Some dogs are mortal.
(c) Some dogs that are carnivores are mortal.

is given, do those 'some dogs' refer to two different groups (dogs might or might not be carnivores and mortal at the same time) or the same (all of the 'some dogs' are automatically both carnivores and mortal). Or more simply, is the statement valid?

• Google search, 5 seconds: cas.umkc.edu/philosophy/vade-mecum/3-1.htm another page search for "some", 3 seconds, reading the sentence, 5 seconds: Answer in less than 20 seconds. Writing this question took more, I guess? – Philip Klöcking Oct 26 '16 at 16:26
• @PhilipKlöcking there's no need to belittle user23907 with your abductive reasoning. Don't you remember what you said about philosophy and being humble?? Perhaps that was merely an ad hoc rationalization in lieu of a counter-example, eh? – Mr. Kennedy Oct 26 '16 at 16:34
• Compare with : (1) Some numbers are odd. (2) Some numbers are even. (therefore ???) Some numbers that are odd are even. – Mauro ALLEGRANZA Oct 26 '16 at 18:22

The deduction is not valid.

The modern translation of 'Some X are...' is 'There exists an (meaning at least one) X such that...'

So, in modern parlance, you are saying: There exists a vegetarian dog. There exists a carnivorous dog. Therefore, there exists a vegetarian, carnivorous dog.

The latter statement is false, since a being cannot be both vegetarian and carnivorous. But the premises are both true. (Sadly so, for the poor vegetarian dog.) Any syllogistic form with a real counterexample can't be valid. So this one is not a reliable form.

And, yes, those three phrases all refer to different groups, represented by different choices that satisfy the 'exists' statement. You know the first two don't coincide because the dog that represents one group cannot be in the other, and therefore the third group is empty.

• sorry, i think this is wrong. the reason the inference fails is because of the form of the syllogism, not because of the meanings of the terms. "Some dogs are that are carnivores are vegetarians" is an invalid conclusion. it does not follow that no dogs are carnivorous vegetarians. just replace "carnivores" and "vegetarians" with X and Y and it becomes obvious. – user20153 Oct 26 '16 at 19:43
• Paragraph 4, I read it as stating "the conclusion is false due to the fact that the words carnivorous and vegetarian refer to disjoint sets" presumably by virtue of their meaning; whether or not this is true is irrelevant for the logical structure of the OP's question. – Dave Oct 27 '16 at 19:20
• Ok, then since several readers miss that point, it might be better if you made it explicit in the main body. – Dave Oct 27 '16 at 19:46
• @Dave I have now gone out of my way to state the obvious, for those who want to read more into the statement than it can possibly actually be taken to mean by any careful reader. – user9166 Oct 27 '16 at 20:20

The argument is: "(1) Some dogs are carnivores. (2) Some dogs are vegetarians. (therefore) Some dogs that are carnivores are vegetarians."

No valid conclusion follows; neither premise distributes the middle term (dogs). In a valid syllogism the middle term must be distributed in at least one premise.

Note also that because "dog" is a middle term, it is going to disappear in the conclusion. When you revise the premises and get to a valid conclusion, it will say nothing about dogs.

"Some" just means a sub-set with at least one member.

If "all dogs" are thought of visually (like a Venn diagram) as a circle, then "some dogs that are carnivorous" would be a smaller circle inside the "all dogs" circle. Likewise, "some dogs that are vegetarian" would also be a smaller circle inside the "all dogs" circle.

Do the two smaller circles inside the "all dogs" circle overlap?

Well, if we take carnivorous to mean "eats meat" and vegetarian to mean "eats vegetables" in an exclusive sense of "eats only meat" and "eats only vegetables" then they do not overlap. If we take carnivorous and vegetarian to describe the predominant diet, then they could overlap at different times of at least one dogs life, but this is stretching things a bit far to make a contradiction plausible. Also, where they might overlap, would we not say the dog is omnivorous?

As for whether or not each premise is true, there is significant evidence supporting the claim that some dogs are indeed carnivorous. While dogs are generally considered to be omnivorous, I don't think there are many considered vegetarian, tho it is certainly arguable that there is at least one instance of a vegetarian dog somewhere.

So, if we take premise one to be true and premise two to be true, are we correct in deducing that there is a dog that is both vegetarian and carnivorous? In the exclusive sense of "only eats meat" or "only eats vegetables" this is obviously a contradiction, so no, the two smaller circles do not overlap. In the loose sense of "predominant diet" then the truth value is still relative to the time of evaluation and predominance implies that one diet or the other is the main source of nutrition, so, again, no: there are no dogs that are both carnivorous and vegetarian.

Of note, exclusively vegetarian diets are not at all a good idea for your doggy. Please talk to a licensed veterinarian for nutritional guidelines and breed risk assessment if you are feeding your dog like so.

As for logic, if you dig this kind of stuff, check out Logic-Cola by Harry Gensler - it is a fun companion to his book, Introduction to Logic.

Let's look at your initial premises:

Premise 1) Some X are A (i.e. at least one X is A)

Premise 2) Some X are B (i.e. at least one X is B)

Here I think you might want an additional step, stating the relationship of A and B.

Premise 3) All A are not B (i.e. No A is B)

Therefore your

Conclusion) Some X are A and B (i.e. at least one X is A and B)

is false because it contradicts the third premise.

the reasoning is fallacious. if you want to know why, google "term logic", and pay attention to the "square of opposition" and the 4 types of proposition (A, I, E O). For a contemporary treatment search for Fred Sommers.

the point being that "some" has no place in modern logic. it comes from traditional Aristotlean (i.e. term) logic.

see section 4.3 of http://plato.stanford.edu/entries/aristotle-logic/

square of opposition: http://plato.stanford.edu/entries/square/

note that Aristotlean "some" is not equivalent to modern existential quantification. there is no quantification in Aristotlean logic. of course we can come up with quantificational representations of Aristotlean reasoning, but it does not follow that his logic was quantificational.

Clarification

It's important to be clear about the differences between logical validity, truth, and the meanings of terms. Syllogisms (inferences, arguments) may be valid, but true and false to not apply to them. Similarly statements may be true or false, but neither valid nor invalid. In determining the validity of an argument, only its form is taken into consideration, not the meanings of its extra-logical terms like "dog" and "carnivorous". If a syllogism is invalid, its conclusion may yet be either true or false. Similarly, a syllogism could be valid, yet its conclusion still either true or false, as in the case where a premise is false but the reasoning is valid. If the premises are true and the reasoning is valid then the conclusion must be true (this is often called a "sound" argument to distinguish it from a merely valid one.)

So your premises are probably true (that's for empirical science to determine), but the syllogism is invalid, so the conclusion - "Some dogs that are carnivores are vegetarians" - may be either true or false as a matter of logic, where the meanings of "dogs", "carnivores", and "vegetarians" are irrelevant. It may be false as a matter of science, based on the meanings of those terms, but that is a separate question that has nothing to do with logic.

• There is no reference to Aristotle in the OP, and 'Some' is a word in the English language that is reasonably represented via quantification. So this technical rant is totally irrelevant to the question. – user9166 Oct 27 '16 at 20:56