I am new to a philosophy course and recently learned about validity and soundness of an argument. In this exercise:

Premise 1: All humans are mortal.

Premise 2: Socrates is mortal.

Conclusion: Socrates is human.

It is asked to find if this argument is sound or not.

From the definition of soundness of an argument, it needs to be valid and the premises need to be true. Hence, I think this one is a sound sentence. (Though intuitively it seems the argument is not correct. Here, I am not talking about validity. By not being correct I mean this is not a good argument.)

But, the answer is - "This argument has all true premises (and a true conclusion) but it it is invalid. So it is not sound."

I am not getting how this is invalid (and hence, not getting how it is an unsound argument). Can anyone explain to me how this argument is invalid?

  • 1
    I made some edits which you may roll back or continue editing. You can see the versions by clicking on the "edited" link above. Welcome to this SE! Commented Sep 29, 2018 at 20:48
  • It is invalid becuase there are otehr cases of the some "pattern" that have true premises and false conclusion : "All fishes live in water. Whales live in water. Therefore, whales are fishes." Commented Sep 30, 2018 at 8:59
  • trying syllogisms out with examples helped me learn them etc.. try and find a counter example!
    – user35983
    Commented Jan 17, 2019 at 21:22

4 Answers 4


Hence, I think this one is a sound sentence.

Soundness is not a property that applies to sentences, but rather to arguments as whole. A sound argument is one that is valid and has all true premises. Since this argument is invalid, it is not sound, even though all the sentences in the argument happen to be true. My sense is that the fact that all these sentences happen to be true is what's throwing you off.

The argument you give is an instance of affirming the consequent, a paradigm example of an invalid argument. It is easier to see the invalidity when you convert the sentence "all humans are mortal" into the form of a conditional statement. Note that saying "all humans are mortal" is logically equivalent to saying, "if something is a human, then we can conclude that it is mortal". So you have:

  1. If human, then mortal.
  2. S is mortal.

Therefore, S is human.

More abstractly:

  1. If P then Q.
  2. s is Q.

Therefore, s is P.

This form of argument is not truth-preserving, because it is possible to for this form of argument to have true premises and a false conclusion. Notice:

  1. If human, then mortal.
  2. My friend's dog is mortal.

Therefore, my friend's dog is human.

You can clearly see that this argument has all true premises and yet the conclusion is false. Hence it it is an invalid form of argument (and note that it has the very same form as the argument you are considering).

More intuitively, we say that the conclusion doesn't follow from the premises. All you know from premise 1 is that anything that is a human is mortal. This licenses you to conclude from something's being human to its being mortal, but it precisely does not license you to conclude from something's being mortal to its being human. There could be any number of other things that are mortal. So knowing that s is mortal does not tell you that he is human. More technically, what you have is that being mortal is a necessary condition of being human. But being mortal is not a sufficient condition for being human (all other animals are mortal as well).

  • 5
    Shortcut: Have your friend name their dog Socrates. :)
    – cHao
    Commented Sep 30, 2018 at 1:15
  • You can clearly see that this argument has all true premises and yet the conclusion is false - yeah when we change the Socratis to anything else then the conclusion will be false, but, in this case how I can conclude that the conclusion is false? Is it the case that argument is invalid if the logical abstraction is false? Though as I have mentioned, in answer they have said that the conclusion also correct. Commented Sep 30, 2018 at 6:14
  • 2
    @taritgoswami The problem isn't that the conclusion is false (the conclusion that Socrates is human is true in this case), the problem is that the argument is invalid because the conclusion doesn't follow from the premises. In this example, to show that the conclusion follows from the premises you'd have to show that everything that is mortal is also human, which doesn't follow from the premises (and is, incidentally, also false). Note that even if all mortal beings were human, the argument would still be invalid because this doesn't follow from the premises.
    – Cubic
    Commented Sep 30, 2018 at 13:25
  • Shortly put: human->mortal doesn't imply mortal->human. It's not a "=" sign. Commented Oct 1, 2018 at 14:11

Premise 1: All humans are mortal.

Premise 2: Socrates is mortal.

Conclusion: Socrates is human.

This reasoning is unsound because the middle term (mortal) is undistributed. Thus there is no idea which links the two premises; together they cannot add up to any broader conclusion.

The general form of both premises is an A statement: All P are Q. "All P", by definition, says something about every member of the set P. There is no similar statement about set Q, and so Q remains undistributed. A valid syllogism requires at least one premise which distributes the middle term.

The syllogism is AAA in the second figure.

Incidentally, AAA-2 is the fallacious reasoning that supports guilt by association.


The argument is not sound because there could be things named Socrates that are mortal that are not human- for instance, my cat is named Socrates, and he's definitely not human. A sound argument would be the inverse:

Socrates is human All humans are mortal Socrates is mortal

  • Your response is NOT why the syllogism is invalid. You are substituting one word to say the whole argument is unsound. Terms have specific meaning in syllogisms. Playing with words is not the answer. The answer has to do with the middle term placement. The middle term is human. If anything you should have played word games with that term. The middle term repeats in the premises. The syllogism is an AAA-2 mood and figure. Mood and figure have much to do with soundness and validity.
    – Logikal
    Commented Jan 22, 2019 at 19:31

Premise 1: All humans are mortal.

Premise 2: Socrates is mortal.

Conclusion: Socrates is human.

We know Socrates is human, so we throw in the tacit knowledge rather readily into the melting pot of our analysis:

All humans are mortal, a bumble bee is mortal, therefor a bumble bee is human.

Seems less likely to confuse.

I would say also that this doesn't draw an inference. It simply makes a statement out of the blue. The word "conclusion" is therefore illicit. There is no conclusion here.

It's like if someone would say: 1. A house is a built thing. 2. The Mosque at Isfahan is a built thing. 3. "Moo" is the differentia by which one recognizes a cow's essence.

There is no link, simpliciter, between the premises and the output. Which is, anyway, I suppose, the meaning of an "unsound" syllogism. Sylogisms, unlike enthymemes, are meant to truly link. I would add: Perhaps there would even be someone who would find this a good argument, and with reasons, I wouldn't discount that, but it is a bad syllogism.

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