## What are the differences between an argument and a syllogism?

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What are the differences between an argument and a syllogism?

I would like to get examples where i can comprehend the differences along with definitions and usages.

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See the well-known counter-example, due to A.De Morgan (1847) of a deductive relational inference that is not syllogistic: "Every man is an animal; therefore, every head of a man is the head of an animal."

– Mauro ALLEGRANZA – 2021-01-25T19:04:31.067

@MauroALLEGRANZA "Every man is an animal; therefore, every head of a man is the head of an animal." - is surely not a valid argument. animal and head of animal are two different identities and thus that violates the law of identity. Correct me if I am wrong. I was looking for a valid argument which is not a syllogism specifically. – Sazzad Hissain Khan – 2021-01-25T20:12:54.263

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The modern use of the term "syllogism" without qualifiers is rather narrow, it only covers 4 figures with one place predicates, A, E, I, O. But there is more expansive use, e.g. "Every man is an animal; therefore, every head of a man is the head of an animal" is called oblique syllogism, and there are also hypothetical, relational, modal and temporal ones. One can, in principle, use the word broadly enough to cover any valid argument, but it is uncommon today.

– Conifold – 2021-01-25T21:04:35.683

"animal and head of animal are two different identities and thus that violates the law of identity. Correct me if I am wrong. " Yes, you are wrong: animal is a term (i.e. a "class" of objects) and head of animal is a part of an animal, i.e. an object. – Mauro ALLEGRANZA – 2021-01-29T13:42:51.087

@Mauro if so this is a valid argument. But why it is not a syllogism could you please describe more? – Sazzad Hissain Khan – 2021-01-29T14:23:20.767

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A syllogism is a logically valid argument.

Any logically valid argument is a syllogism. This follows from the definition given by Aristotle himself:

A syllogism is discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so. I mean by the last phrase that they produce the consequence, and by this, that no further term is required from without in order to make the consequence necessary. -- Aristotle, Prior Analytics, Book I

A few examples of syllogisms...

A circular argument:

God exists; Therefore, God exists.

A syllogism some people are wrong to believe that it is not a syllogism:

P and if P, then Q; therefore Q.

Fake Old News:

If Oswald didn't kill Kennedy, somebody else did; Oswald didn't kill Kennedy; Therefore, somebody else did.

"every logical valid argument is a syllogism" Not true. – Mauro ALLEGRANZA – 2021-01-25T18:55:03.520

1Modus Ponens is NOT a syllogism. – Mauro ALLEGRANZA – 2021-01-25T19:05:24.040

1"Syllogism" is not used today in the broad sense of Aristotle and scholastics. Arguments involving what Aristotle called "relatives" are not called "syllogisms", nor are even simple propositional forms like conjunction introduction or double negation elimination. Stoics introduced non-syllogistic inferences already in Aristotle's time. – Conifold – 2021-01-25T20:56:37.870

1@Conifold "Syllogism" is polysemic. Aristotle gave a clear definition and many people, including professional logicians, use this sense. Dictionaries also give this sense. Further, it is by far the most interesting definition. Essentially, a syllogism is a logically valid inference. An argument is something else. Further, the way mathematicians try to speak about logic is irrelevant to logic. Correction: the Stoics discovered new forms of syllogisms. And modus ponens is of course a syllogism. Its conclusion follows from its premises. – Speakpigeon – 2021-01-26T11:20:47.207

@Conifold I just discovered that like me, John Corcoran (who just died, by the way, Jan. 8) uses the word "syllogism" in the same sense as defined by Aristotle, -- See Aristotle's natural deduction system, in Ancient logic and its modern interpretations, proceedings of the Buffalo Symposium on modernist interpretations of ancient logic (1972)..Isn't that you (lol) who referred me to this document? – Speakpigeon – 2021-01-27T14:50:58.813

You can discover fresher papers than the one from 1974 where the authors use Aristotle's meaning when writing about Aristotle. But "syllogism" is rarely used outside of historical contexts, especially in broad sense. Are you warming up to mathematical logic now that Corcoran uses it to interpret Aristotle? – Conifold – 2021-01-27T20:45:03.247

@Conifold No, it is a sordid fact of the history of scholastic academia that mathematical logic is dead as a dodo. It is as fundamentally wrong as could possibly be. Corcoran came to do much more than interpret Aristotle through the paradigm of mathematical logic but I wouldn't expect him to have understood how wrong mathematical logic was. Logic is still hasn't done it Copernican revolution. You are all doing epicycles. Des ronds dans l'eau. – Speakpigeon – 2021-01-28T10:51:15.177

@Conifold Yes, the word syllogism is rarely used in its original sense nowadays. So what? Most of the literature on logic is premised on the false idea that mathematicians are the experts in formal logic. What they do is not even logic. It is mathematics. – Speakpigeon – 2021-01-28T10:54:12.083

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A syllogism is a simplified form of argument, mainly used for pedagogical purposes to demonstrate valid and invalid moves in argumentation. If I may make a chess analogy, syllogisms are like a description of how individual pieces can move — part of the rules of the game — while an argument is an actual game being played.

A syllogism is a logical unit that shows how properties of categories are transferred across two propositions. To use the classical example:

All men are mortal
Socrates is a man
∴ Socrates is mortal (where ∴ is a symbol meaning 'therefore')


We have the category 'men', a property 'mortality' that inheres in that category, and an object 'Socrates' that is a member of that category. Generalized, this looks like:

Category C has property P
Object O is a member of category C
∴ Object O has property P


... or in English, that any member of a category shares any properties that are inherent to that category. A syllogism makes explicit and procedural something that we might normally consider to be mere common sense, but syllogisms are useful because they allow us to manipulate the symbols to discover what are and are not valid moves. For instance, if I switch things up a bit and write the following:

Socrates is mortal
Socrates is a man
∴ All men are mortal


We can easily see that this logical unit does not work (technically, an illicit minor term fallacy). Why should everyone be mortal just because Socrates is? We've made an invalid move by asserting that the property of an individual must necessarily inhere in the category the individual belongs to. It doesn't matter that in fact all men are mortal (that the conclusion is 'true'); what matters is that the process by which we came to that 'true' conclusion was flawed.

So, syllogisms spell out the basic valid and invalid logical units. However, it's rare that any real-world debate can be reduced to a simple syllogism. I mean, occasionally you'll find someone who makes the kind of false induction presented in that last (illicit minor) syllogism. This is particularly salient in prejudice, where people have an unfortunate tendency to judge entire groups by the perceived or imagined behavior of their worst members. But generally speaking arguments normally rest on numerous premises — some spoken and some unspoken — that are combined in various complex ways to produce a number of far-end conclusions. We cannot normally even reduce an argument to a simple sequential chain of syllogistic units; arguments are rarely so linear.

For instance, if we consider the ever-present debates about 'free will' that can found on this site, we'll find various arguments resting on diverse presumptions: the presence or absence of metaphysical entities such as a 'soul', physical determinism vs cultural determinism vs psychological determinism vs various forms of conditioned or unconditioned indeterminism, differences in choice models between libertarian, spiritual, and phenomenological perspectives, etc. One group might argue that the divine spark allows us to make free choices within the determinism of God's plan; another might say that we have only the illusion of free will as part of a fully deterministic order, a third might say that we have a presumptive capacity for free will and that the underlying reality is indeterminate. All of these positions make complex argument in their own favor and against the other positions. We might pick out some particular syllogisms, e.g.:

All men have free will
Sam Harris is a man
∴ Sam Harris has free will


(which, incidentally, Sam Harris might disagree with). But this syllogism merely opens the door for new questions:

• Do all men have free will?
• How is the category 'man' defined here?
• How is the property 'free will' defined?

The syllogism is valid as given (in a simplistic, 'yeah-yeah-sure' sort of way), but it doesn't answer any of the properly philosophical questions, which must be explored through argumentation.

Is this sense, syllogisms become a limitation on what claims one can make in an argument — no one (and certainly no philosopher) wants to get called out for making a boneheaded error transferring a property improperly — but syllogisms rarely define and never resolve philosophical arguments.

Could you please give two examples with premises and conclusion? – Sazzad Hissain Khan – 2021-01-24T19:32:10.313

@SazzadHissainKhan: I don't understand what you mean. premises and conclusions are parts of a syllogism; an argument is more complex than that simplified structure. – Ted Wrigley – 2021-01-25T01:54:03.247

What do you mean by more complex? Thats what I need to be clarified. Could you please give me an example of both? – Sazzad Hissain Khan – 2021-01-25T16:54:19.433

1@SazzadHissainKhan: updated and expanded. Hope this helps. – Ted Wrigley – 2021-01-26T20:35:44.533