The argument in question is the following:

Penguins are black and white Some old tv shows are black and white Therefore, some penguins are old tv shows.

I believe this is an example of the undistributed middle fallacy. I've been told it's still valid. Is this true or not?

  • Maybe change the title to indicate you are asking about a particular argument and fallacy? There are deductive fallacies, and arguments utilizing them as inferences will be invalid. But, more commonly, people have in mind so-called "informal fallacies" and there is no general connection between those fallacies and the validity of a deductive argument. Typically they'll be appealed to as reasons to believe the premises are true, so they are more likely to call into question a deductive argument's soundness than validity.
    – Dennis
    May 14, 2017 at 19:04

1 Answer 1


This is not valid.

You can see by formalizing it:

  1. All P are BW
  2. Some T are BW
  3. Therefore, Some P are T.

We cannot infer the conclusion. For a graphical proof with venn diagrams, see AII - form two from this link.

  • Thank you. I have another question. I'm also being told "inductive premises can't give a deductive conclusion". Is that true?
    – user26403
    May 14, 2017 at 3:24
  • The wording is a bit strange on that, but I'd say that's probably true. (deductive and inductive are two forms of arguments -- rather than types of premises and conclusions -- properly speaking, but it's fair to say that an inductive argument's conclusion never has the properties we associate with deductive argument's conclusion).
    – virmaior
    May 14, 2017 at 3:28
  • Sorry if it wasn't clear. Is the premise "All men are mortal" not inferred from through inductive reasoning, but the conclusion "Socrates is a man" through deductive reasoning?
    – user26403
    May 14, 2017 at 3:35
  • As used in the standard argument "All men are mortal. Socrates is a man. Socrates is mortal", "all men are mortal" is a premise a in deductive argument. / If instead we are inferring (inductively) that all men are mortal, then it could be the conclusion of an inductive argument "A was a man and died. B was a man and died. C was a man and died ... Ergo, All men are mortal." But whether something is inductive or deductive refers to the form of the argument -- not tot the statement itself.
    – virmaior
    May 14, 2017 at 3:44
  • "all men are mortal" seems to be claim whose truth rests on an empirical determination, but this does not mean it cannot be premise in a deductive argument. It merely means we cannot know merely deductively whether the premise is true.
    – virmaior
    May 14, 2017 at 3:45

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