Does transposition of the premises preserve validity in categorical syllogisms?

This morning I've stumbled upon this doubt to which I couldn't find a clear answer.
I intuitively myself that yes, it does preserve validity because as long as you don't change the premises the conclusion should not change.

• With "transposition" do you mean interchange the order of major and minor premises ? If so, the answer is YES. Commented Dec 4, 2017 at 10:37
• Usually, this is transposition. Commented Dec 4, 2017 at 10:38
• @MauroALLEGRANZA yes I mean interchanging the order of the major and minor premises. In fact i read that a syllogism is told to be in normal form only if the subject of the conclusion is in the second premise, otherwise it's said to be transoposed. So I had this stupid doubt ahah. Thank you as always for clearing me up Commented Dec 4, 2017 at 10:48
• I also read somewhere that is considered a rule of inference and it sometimes called mutatio Commented Dec 4, 2017 at 10:49
• Syllogisms in standard categorical form require a specific format as you describe. The major premise must contain the predicate of the conclusion and the minor premise must be the subject of the conclusion. What is not in the conclusion is the middle term. So you should see formally this process is specific. Any other variation is not transposition but the syllogism is not in standard categorical form. Commented Dec 5, 2017 at 0:06

Transposing the premises does not change the validity of the syllogism. This action does alter the normal format of a syllogism, where the predicate of the conclusion appears in the first premise (the major premise). But validity is unaffected.

Compare:

(1) All emeralds are green.This gemstone is an emerald. Therefore this gemstone is green.

(2) This gemstone is an emerald. All emeralds are green. Therefore this gemstone is green.

Example (1) shows the usual order of the premises. But both are valid.

• Can you apply this to any figure and mood configuration? Commented Dec 4, 2017 at 23:37

What you are referring to is the mood and figure of a syllogism. Yes the order does matter. Consider an A A A in the fourth figure: it is invalid via Venn diagram but reversing the premise order allows validity.

If what you state is true I should be able to change the order of the premises and still not change validity without any exceptions. If anyone finds a syllogism that is valid as written and after the transposition of the premise order the validity disappears you know your method is not valid. Validity requires 100% results that do not vary.

Consider this example: All women are human beings. All human beings are mortal beings. Therefore all mortals beings are women. Invalid as written & Not sound fourth figure and mood A A A. Commits a formal fallacy. Know which one?

All human beings are mortal beings. All women are human beings. Therefore all women are mortal beings. Valid and sound in the first figure and mood A A A

• The first example is invalid because if a term (mortal beings) is distributed in the conclusion, it must be distributed in the premises. Not true here. That said, the examples are not on point, because their conclusions are different. Commented Dec 5, 2017 at 0:45
• Even if the conclusions were both all women are mortal beings there would still be problems. A fallacy still because some term in the conclusion would be distributed and not distributed in the premise. My point was that figure and mood can alter the order of terms in the conclusion and alter being valid or invalid. Perhaps some arguments can change the order and follow conclusively. But all argument forms can't do this so the method is not valid. Perhaps valid is being used here in a different context you may think. Validity refers to a form 100% not some cases. Commented Dec 5, 2017 at 1:10
• If the first conclusion were “all women are mortal beings”, then “women” would be distributed in both the conclusion and in the first premise. Can you cite an example where inverting the major and minor premises, but altering nothing else, produces an investment syllogism? Commented Dec 5, 2017 at 1:42
• My point was you would be breaking rules to keep the same conclusion as the difference in mood and figure would require different conclusions. You can't have it that way and follow the standard categorical rules. I will try to come up with a counter example as well. One way can be valid whereas the other way would be invalid based on figure and mood. Commented Dec 5, 2017 at 1:57
• To be specific here I tried only valid arguments with this theory and it seems to hold that distribution does not change while keeping the conclusion the same and changing the order of the premises of a valid argument. Standard categorical syllogisms do not allow the conclusions to be identical though. Furthermore this opens the possibility where you can start with a sound argument and go into an unsound argument by keeping the conclusion identical. Commented Dec 5, 2017 at 2:16