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Is Aristotle's logic sufficient to model human reasoning?

If not, why not?

Are there counter-examples, certain cases where we reason differently?

Let's assume we're talking about sound reasoning, or the reasoning of the ideal human reasoner.

EDIT: I'm asking here about our decision-making procedure, not that part of human thought that has no need of logical systems. I should have been more specific and asked whether we need more than the 'laws of thought' to perform our calculations in philosophy.

EDIT 2: I'm not asking about syllogisms. I'm asking about the essential logical rules that allow us to construct syllogisms and other arguments.

  • Aristotle's logic is too weak to even express most human thoughts, let alone reason about them. It does not have connectives, multi-place relations or iterated quantifiers. You can not even use it to conclude that if X is less than Y, and Y is less than Z, then X is less than Z, as de Morgan pointed out. – Conifold May 18 at 19:11
  • Relevant question: philosophy.stackexchange.com/questions/42558/…. The first answer contains some examples that should be relevant to your question. – Eliran May 18 at 19:44
  • @Eliran Another seemingly related question: "Can all mathematical reasoning be translated into traditional logic?" – Geremia May 18 at 23:27
  • @Conifold I'm afraid I don't understand your comment. I can work out your puzzle easily enough using the laws of thought. A logic that couldn't cope with your example wouldn't be much use for anything. In respect of 'most human thought' I'll add an edit to cover this. – PeterJ May 19 at 9:41
  • @PeterJ I agree, and Aristotle's syllogistic was not. I suspect that what you mean by "Aristotle's logic" is more along the lines of natural deduction. – Conifold May 19 at 9:44
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If you are considering Aristotle's Syllogistic, the answer is clearly : NO.

Syllogism is Monadic predicate calculus which is a subset of predicate logic.

A well-know example (due to Augustus De Morgan) of valid inference that cannot be accounted for by syllogism is the following :

“All horses are animals. So, all horse tails are animal tails.”


Having said that, we have a more general issue : is deductive logic sufficient to model human reasoning?

Also in this case the answer is (presumably) : NO.

We have to consider at least inductive reasoning.



Rgarding dialectic, see Top., Bk.I, 100a25 :

Now a deduction is an argument in which, certain things being laid down, something other than these necessarily comes about through them. It is a demonstration, when the premisses from which the deduction starts are true and primitive, or are such that our knowledge of them has originally come through premisses which are primitive and true; and it is a dialectical deduction, if it reasons from reputable opinions.

  • "Syllogism is […] a subset of predicate logic." Logic isn't a subset of mathematics, though. Also, how is your example a "valid inference that cannot be accounted for by syllogism"? – Geremia May 18 at 23:26
  • Thanks. I'm struggling to see how your example is a problem. – PeterJ May 19 at 9:37
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    @PeterJ - it is quite simple. A's Syllogism uses unary predicates : Human(x), Mortal(x), etc. This means that it is (in modern terms) Monadic predicate logic. To formalize the above example we need the unary predicates Horse(x) and Animal(x), but we have also the need to express a binary relation : "z is the tail of w" and in A's Syllogism there is no binary predicate Tail(z,w). – Mauro ALLEGRANZA May 19 at 12:18
  • Okay. But I'm not askihg about syllogisms. I'm asking about his dialectical logic. . – PeterJ May 21 at 9:11
  • @PeterJ - I've linke SEP's entry dedicated to A's Logic and added also a comment about A's dialectic : "Aristotle often contrasts dialectical arguments with demonstrations. The difference, he tells us, is in the character of their premises, not in their logical structure: whether an argument is a sullogismos is only a matter of whether its conclusion results of necessity from its premises. The premises of demonstrations must be true and primary. The premises of dialectical deductions, by contrast, must be accepted." – Mauro ALLEGRANZA May 21 at 9:50
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I think there is something of a general misconception about Aristotle's work on logic.

Aristotle had a definite empirical outlook. For this reason, I don't believe he focused at all on his own introspective capabilities. I suspect he never considered his own logical intuition (he discussed intuition in relation to discovering scientific principles). His syllogistic, rather, was based on his observation of empirical facts.

What Aristotle did essentially was to identify a small number of forms of arguments regularly used by other people. He probably did it from reading philosophical works available to him. I suspect he benefited greatly in his effort from the extensive debate over the Paradox of the Liar that had started a few decades before him, and which must have made philosophers in particular more sensitive to the question of truth and falsity, and thereby to that of logic generally.

So, as I see it, he didn't think of his own syllogistic as an introspection-based formalisation of the laws of thought but rather as an empirical formalisation of proper argumentation as routinely practised by philosophers.

Thus, in respect of his syllogistic, Aristotle's logic was limited by the empirical evidence available to him to a small set of logical truths. Logical truths should be seen as a by-product of the "laws of thought" proper. In effect, Aristotle only thought to look at the by-product, and then only a small part of it, rather than at the source of it.

However, he also offered a definition of a syllogism that was also, if only implicitly, a definition of logical validity. It just happened that his definition was so formulated as to being completely general. As such, it applies perfectly, without any modification, to all deductively valid inferences that the logical tradition has discovered since. So, in effect, his definition should be seen as the best we have in terms of identifying a law of thought. And it has proved itself universal by standing the test of time over a period of 2,500 years.

Further, by recasting the notion of consequence as the central one in logic, modern logicians have also ipso facto shown Aristotle's definition of validity as the most important for our understanding of logic and therefore of the laws of thought.

Most people focus on his syllogistic to argue Aristotle's limitations, and rightly so. Yet, they forget to look at the concept of validity he effectively articulated, and which is still the best we have today.


Aristotle's definition of a syllogism

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.

Prior Analytics, Book I, Translated by A. J. Jenkinson, published by eBooks@Adelaide, The University of Adelaide Library, University of Adelaide https://ebooks.adelaide.edu.au/a/aristotle/a8pra/book1.html

  • Thanks for this overview. At this time I cannot grasp why everybody is talking about syllogisms here. A syllogism is one of a number of forms of argument. I'm asking about the dialectic and the laws of thought, not this or that form of argument. . – PeterJ May 21 at 9:16
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    @PeterJ I assume you were talking about assertoric logic and indeed deductive logic. I'm not sure why you talk now of dialectic, which I see as a method for debating and an application of logic to the rules of debate, which seems to go beyond the narrow question of the laws of thought. – Speakpigeon May 21 at 14:08
  • This is the clearest exposition of your views so far. I'd add the definition you mention to the post for completeness. It would also be an interpretation of what the OP's "laws of thought" might be. – Conifold May 22 at 10:08
  • @Conifold I'm sure it's not a law of thought as such because it's a bit too vague. But that's the closest thing we seem to have to one, or even merely pointing to one. The crucial point is that it is truly universal, at least as far the human mind is concerned. – Speakpigeon May 22 at 17:02
  • By the way, Azzouni has some thoughts on the empirically observed "implicit logic" of mathematicians that you may find interesting, see his Foundations paper, pp. 33-39. – Conifold May 23 at 5:32
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I would say that the original intent of Aristotle's deductive reasoning skill was to match concept with reality. That is the intent of all arguments was for a user to have true premises --NOT assumptions as Mathematical logic must have to operate. So there must be a few distinctions made here because there has been a drastic shift how the same terms have come to mean differnt things when people allegedly talk about "Logic".

For Aristotelian logic to work the whole notion of knowledge would need to be at the very least mentioned. Deductive reasoning as Aristotle used the original purpose of what propositions are was to focus only on SOUNDNESS and --Not validity as Mathematical logic does. So let's talk about KNOWLEDGE.

For me to make a proposition, any proposition, an average person or one heavy into science will enquire how I know my proposition. I will use a famous example: the proposition "All Swans are White" is stated BY ME in this case to HOLD a truth VALUE of TRUE. (Yes, I know that Black Swans have been discovered already to make the proposition literally false now.) Anybody, I mean anybody like one of you readers for instance will ask "How do you KNOW that is true?" Even if I say I know this is true by the theory of universal bifuricants you will then ask the same question "How do you know that is true?" Regardless how I answer you will always have the come back "how do you know . . .?" Ad infinitum. No answer I give will ever suffice. It is at this point I might add how ironic this obvious fact is inconsistent with the claim Mathematical logic is NOT about truth but VALIDITY. I would like to point out the very definition of VALIDITY from Mathematical logic mentions that if the premises ARE TRUE that the conclusion must also be TRUE. We now have a problem: when I make a proposition as I did in an earlier example, " you would ask me how do you know." This already implies every proposition is an assumption as I would never be able to PROVE any non semantic proposition to any scientist for every case. Only sematical propositions that have specific definitions called analytical terms would work such as all bachelors are unmarried males. So the million dollar question is why can't I do the famous " how do you know . . ." on the conclusion of YOUR Mathematical proposition? Well it seems that all of your propositions would also be assumptions themselves or self referencing propositions via semantics. It seems amusing that if the premises were true is a really difficult task to justify. How can we then KNOW with certainty that the proposition in the conclusion MUST ALSO BE TRUE when the term TRUE is not so easily defined?

Deductive reasoning was broken into phases. Aristotle likely knew other animals were capable of reasoning seductively. He knew humans used different forms of reasoning and some were deductive while others weren't deductive. Then he noticed when humans used deceptive tactics to persuade another human being to do something the person would not regularly do something clicked!

He noticed PATRERNS OF THOUGHT during the interaction. These patterns seemed to repeat in the real world and not just in his mind. Now to the notion of truth at least workable context would be to notice instances of an event or an action. WAS this event or action (I will call variable X) always true or sometimes true. Notice how truth matters here. Before I even pucker my lips to Express a proposition I should know what truth value the proposition may hold. Even if I am mistaken the proposition has a truth value objectively. Objective in the sense meaning the truth value whatever that is must be permanent and never change. This distinction rules out science and its contexts of knowledge or truth. Science must be falsifiable for instance.

So to make a rational and practical use of deductive reasoning one should know what propositions are and they are not PHYSICAL. We dont see, hear, smell, etc propositions. They are mental images that are EXPRESSED into our real world. Secondly they must be meaningful as in the sense a scientific enquiry would be as stated before "How do know . . . This implies use of the human senses. The human senses is what we use to scientifically use and practically use to determine or describe TRUTH. In this sense when I say my All swans are white proposition I am aware that PHYSICALLY all the ones I could verify with my senses were indeed white in color. Thus truth now has to have multiple context and not just one!

Contingent truths differ from objective truths. Aristotelian logic is originally intended to be OBJECTIVE or UNIVERSAL and not contingent where the same proposition would hold a true value in New York and the same proposition would hold a False value in Alabama. This would not be useful or practical if any logic system did that!

So far we have propositions that had rules or explanations of ALREADY BEING TRUE being used in accordance with rules of syntax in a pattern. This is deductive reasoning. By true we mean objective. That is, for example a figure one syllogism will always be valid FOREVER. Any objective claim is a FOREVER CLAIM and must have the same truth value. There is no need to worry about where I am standing and testing to see if the claim is true. So this means my proposition ought to be objectively true. These objective propositions combined with other related objective true propositions will form a syllogism. Not just any syllogism but a SOUND SYLLOGISM. That is the argument must be valid and the premises must be objectively true to HAVE PRACTICAL USE in reality. You have all seen nonsense argument premises with a nonsensical conclusion but yet the argument was VALID. People tend not to mention this misuse makes the topic useless. For how am I to know if the validity applies to reality if you remove the connection with truth? If some thing could be valid but untrue what good is it? You also have an argument that is objectively valid sound and useful. Okay we now have a system if knowledge that is about 50 - 50 in results. This is not impressive. What I defined is now known as epistemology and not logic as used today.

  • Thanks for your thoughts and some interesting observations. – PeterJ May 23 at 10:02
  • Thanks for you interest. I wanted to write an answer that did not directly address how syllogisms work as did the Mathematical respondents did. There is a huge difference today in the same concepts & terms than let us say 60 years ago. Too many people define a logical term "proposition" amongst other terms incorrectly. This is because to those people all logic is logic and they are never told any distinctions -- until they meet someone like me. The whole idea of logic was What is now deemed EPISTEMOLOGY. people try to hide this fact. Logical form mattered but also content mattered. – Logikal May 23 at 13:18
  • "Deductive reasoning as Aristotle used the original purpose of what propositions are was to focus only on soundness - and not validity as Mathematical logic does." WRONG. See A's Topics (ref in my answer) : "Now a deduction is an argument in which, certain things being laid down, something other than these necessarily comes about through them. It is a demonstration, when the premisses from which the deduction starts are true and primitive." – Mauro ALLEGRANZA May 23 at 14:48
  • Thank you for the reply. However the issue is still how do you know what is TRUE. If you say X is a fact in every case how do you know this in reality? I don't see how you can people in Mathematical logic can consistently tell other humans that logic is purely about form and NOT about truth when this same topic of TRUTH arises when the conclusion of a valid argument is stated to be a certain. How do you move from every proposition is an assumption but your valid argument conclusion is CERTAIN? This seems inconsistent no? It shows indeed logic does involve truth. – Logikal May 23 at 15:07
  • @Logikal There's no part of logic that tells you how to decide whether particular premises are true or false. Not in mathematical logic, not in Aristotle's logic, not in the Stoics' logic, not in the Scholastics' logic. So, clearly, logic is not about the truth of your premises. You makes an argument? Fine, then you take responsibility for asserting the premises as true. Taking the responsibility means you answer questions like "How do you know the premises are true?". So, the truth of the premises is not decided by any method of logic. – Speakpigeon May 23 at 16:47

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