## Testing the validity of syllogism argument

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I came across a validation method for testing the validity of a syllogistic argument which seems quite easier to grasp:

For example:

To test the argument:

no P is B
some C is B
Therefore, some C is not P


1.) Star premise letters that are distributed and conclusion letters that aren't distributed.

2.) Then the syllogism is VALID if and only if every capital letter is starred exactly once and there is exactly one star on the right-hand side.

It becomes:

no P* is B*
some C is B
Therefore, some C* is not P


Now, we can say that the argument is valid because it meets the requirements for it to be valid but I don't exactly understand what is the proof behind this star test method.

Such as where does the validation ideas come from and what is the answer to:

Why or what makes it valid when there is exactly one star on the right hand side?
Why or what makes it valid when a capital letter is starred exactly once?

@cpx Did you ever find an answer to this question? – Mark Andrews – 2019-10-28T00:55:23.970

The originator of the star test, Harry Gensler, still teaches and has a web page. https://harryhiker.com/ Maybe you could contact Prof Gensler directly.

– Mark Andrews – 2019-10-28T18:43:57.193

The stat test works because every valid syllogism has an anti syllogism or aka anti logism. That is the proof is what is called reduction to the absurd proof. You modify a premise to see if you can make a valid argument form while the new modified conclusion is the contradiction to the original conclusion before it was modified. You can look up antilogism to read for yourself. – Logikal – 2020-08-27T18:05:48.773

You have to study the original article defining the method ...

– Mauro ALLEGRANZA – 2014-10-01T06:18:06.040

I just took a look at it. It presents various methods for testing validation but it doesn't exactly explain why do you need to follow the steps in method in order to prove the validity. E.g. it tells me "Star the letters in premises and count the stars etc." but doesn't say why am I doing this. – cpx – 2014-10-01T06:45:34.097

I haven't read it; but I think that he has "simply" find a simple way to apply the traditional "meta-theoric" rules. See Aristotle's Logic : 5.5 Metatheoretical Results, e.g. : "1. No deduction has two negative premises. 2. No deduction has two particular premises", etc.

– Mauro ALLEGRANZA – 2014-10-01T07:47:05.523

But these are also the rules or result. Is it possible I can know where do these come from or what is the proof that "no deduction has two negative premises". – cpx – 2014-10-01T10:18:57.867

Basically, form Aristotle's Prior Analytics (e.g. a modern edition with commentary) or from a detailed modern exposition of it. There are some books : Jan Lukasiewics, Gunter Patzig. – Mauro ALLEGRANZA – 2014-10-01T10:22:36.173

1The "technique" used by Aristotle is a "standard" one: counter-examples. In modern term, you show by a counter-example that from "some C is B" and "some B is D" you cannot conclude anything about C and D, like e.g. "some C is D". – Mauro ALLEGRANZA – 2014-10-01T11:33:18.490

For a modern brief formal exposition, see Jan von Plato, Elements of Logical Reasoning (2013), Ch.14.1 Aristotle’s deductive logic, page 220-on.

– Mauro ALLEGRANZA – 2014-10-01T14:30:27.110