Aristotle's Logic

[dekoi]

In what [major] ways is Aristotle's logic flawed? I am referring to his notions of immediate inference and syllogistic reasoning.

Would anyone have any specific examples of flawed versions of syllogistic reasoning -- or is it practically flawless?

Is there degrees of difficulty in syllogistic reasoning examples? Would anyone mind offerring some examples of difficult syllogistic logic?

Thank you. :smile:

[MathematicalPhysicist]

his categorical logic was mainly constructed by two premises sentences and a one conclusion.
we can ofcourse argue for more data and therefore the complexity will increase (more premises lengthy sentences, etc).
from what i read aristotle's logic lacked diassociation and association, i.e it didnt used the "or" "and" etc in its reasoning.

[dekoi]

his categorical logic was mainly constructed by two premises sentences and a one conclusion.
we can ofcourse argue for more data and therefore the complexity will increase (more premises lengthy sentences, etc).
from what i read aristotle's logic lacked diassociation and association, i.e it didnt used the "or" "and" etc in its reasoning.

How would you define Disassociation and Association in the subject of logic?

Also, in the syllogistic reasoning example:
All Potatoes Have eyes.
Dana's head has eyes.
Therefore, Dana is a potatoe.
We can conclude that the conclusion is false, since the premise is a specific one, in that it states "All potatoes have eyes" and not "All eyes are on potatoes."

Am i correct in this reasoning?

[MathematicalPhysicist]

disassociation is using the "or" option- "it will rain or it wont rain tomorrow"
association uses "and"- "if im sick and tired i wont go to work"

aristotle didnt use these words in his syllogisms and therefore it was limited (not flawed) in comparison to nowadays.

about the example i dont know what you mean by the word "specific", but you are correct that the conclusion doesnt follow its premises.

all you need to know is to confine the objects into symbols and then there is the chain rule that if you have a->b b->c then a->c (follow the arrow).

[chronon]

Note that when Aristotle said 'All x are y' he made a hidden assumption that some x exist. This problem wasn't noticed for about two millennia, when Boole found that it made more sense to allow 'All x are y' to be true if no x existed. You can find more on the web page:

www.cut-the-knot.org/LewisCarroll/syllogism.shtml

[dekoi]

all you need to know is to confine the objects into symbols and then there is the chain rule that if you have a->b b->c then a->c (follow the arrow).

Right.
But when we have the example:
"All potatoes have eyes" --> "x=y"
"Dana's head has eyes." --> "d=y"
"Dan's had is a potatoe." --> "x=d"

But the conclusion is false. Therefore, the confining of the objects to symbols does not work in this case.

This rule is called, "Distributing the middle term". The middle term being 'y' in that case. But i am not sure what "distributing" means in this context.

[MathematicalPhysicist]

when you put them in an equation you may think that it doesnt matter how you read it because they are equivalent, this is exactly why i put them on arrows, there is a meaning to the arrow (as you will progress in logic you will something like this "<->" if you havent already seen) you should it read there is a which is b, i.e a->b it ofcourse doesnt mean that every b is a! which is ofcourse very important.

i suggest searching in this forum for tom's thread about logic, i believe that the basics of logic is dealt in his thread. (btw it's Tom Mattson the super duper mentor o:) ).

[meyer_lev3]

The Syllogism you have presented in your post...

dekoi wrote:

All Potatoes Have eyes.

Dana's head has eyes.

Therefore, Dana is a potatoe.


...suffers from the Informal Fallacy of Equivocation: :bugeye: :smile:

The following definition/description is from Philosophy Pages-Garth Kemerling.
The home page link is...
http://www.philosophypages.com/

The quote below is from Fallacies of Ambiguity page at this link...
http://www.philosophypages.com/lg/e06c.htm

Garth Kemerling wrote:

Equivocation
An equivocation trades upon the use of an ambiguous word or phrase in one of its meanings in one of the propositions of an argument but also in another of its meanings in a second proposition.

1. Really exciting novels are rare.
2. But rare books are expensive.
3. Therefore, Really exciting novels are expensive.

Here, the word "rare" is used in different ways in the two premises of the argument, so the link they seem to establish between the terms of the conclusion is spurious. In its more subtle occurrences, this fallacy can undermine the reliability of otherwise valid deductive arguments.


The result of this fallacy is that there are four terms instead of three which is of course illegal in this type of syllogism.

terms:
a. potatoes
b. potatoe "eyes"
c. Dana
d. human eyes

The PhylosophyPages website cited above is by far the clearest site I have found on the internet when it comes to explanations on the basics of Logic. From the home page click on Logic in the menu up top.
It is highly recomended! :approve:
Enjoy!

c ya!

[dekoi]

The Syllogism you have presented in your post...

dekoi wrote:


...suffers from the Informal Fallacy of Equivocation: :bugeye: :smile:

The following definition/description is from Philosophy Pages-Garth Kemerling.
The home page link is...
http://www.philosophypages.com/

The quote below is from Fallacies of Ambiguity page at this link...
http://www.philosophypages.com/lg/e06c.htm

Garth Kemerling wrote:


The result of this fallacy is that there are four terms instead of three which is of course illegal in this type of syllogism.

terms:
a. potatoes
b. potatoe "eyes"
c. Dana
d. human eyes

The PhylosophyPages website cited above is by far the clearest site I have found on the internet when it comes to explanations on the basics of Logic. From the home page click on Logic in the menu up top.
It is highly recomended! :approve:
Enjoy!

c ya!
I thank you for taking the time to write that.
I read a little more on Aristotle's Logic and Logical Fallacies, and discovered the flawed nature of my above example. It said exactly what you suggested.

Thank you.

[meyer_lev3]

dekoi wrote:

Thank you.


You're welcome.

[NanoTech]

The compromise Aristotle developed - and it's a clever one - was to say that infinity both existed and didn't exist... http://www.firstscience.com/site/articles/infinity1.asp The Informal Fallacy of Equivocation be used to explain Aristotle's flaw in his logic reasoning and ideas of Infinity.

[MathematicalPhysicist]

but the categorical syllogisms which are usually regarded as aristotle's logic in itself as a tool arent wrong, the way he used it to prove scientific issues was wrong because it didnt have the empirical info, as the data galileo established by his experiments.

[honestrosewater]

1) All potatoes have eyes.
2) Dana's head has eyes.
3) Therefore, Dana is a potatoe.
-
As a general rule, use variables to make the form of the argument clearer.
-
1) All A have B.
2) C has B.
3) Therefore, C is A.
-
meyer_lev3 has made a nice contribution, but it is not the problem with your argument. "Common sense" says two things that share a certain property are not necessarily equal, which is what the conclusion claims. I'm not used to dealing with syllogisms (and there are specific rules for evaluating them) but I can tell you the problem is with the form of the argument. See for yourself:
_
1) All dogs have hair.
2) My cat has hair.
3) Therefore, my cat is a dog.
_
Bad form.
If you find an explanation with As, Es, Is, and Os, you're on the right track.
Happy thoughts,
Rachel

[honestrosewater]

Okay, I found it. It's called the Undistributed Middle (Term)
google for more.

[NanoTech]

Could you also use statistical reasoning to prove aristotle's logical method wrong. For example, in the context of Infinity, his thinking that " association of 2 or more variables is equal to the relationship of 2 or more variables, which is Infinity exists and Infinity doesn't exist." When in fact, Correlation is not equal to causation. Association is a statistical pattern of co-variation among two or more variables. Relationship is only a cause-effect linkage between the variables.

[honestrosewater]

NanoTech,
Can you explain more about the quote you use? It isn't clear that Aristotle is arguing that correlation implies causation. The quote hardly makes any sense to me as an argument.

[loseyourname]

Aristotelian logic isn't really flawed. It can be used to evaluate any argument. It just require that an argument be translated into a series of syllogism in order to be evaluated - an undertaking that can be cumbersome, time-consuming, and difficult at times. Symbolic and quantificational logic are much easier to use because they focus instead on logical connectives and the internal structure of propositions, eliminating the need for syllogisms.

[Jeebus]

Aristotle's system is mostly seen as of historical value now (though there is some current interest in extending term logics), regarded as made obsolete by the advent of calculus.

Also, Aristotelian logic runs into serious trouble when one or more of the terms involved is empty. Meaning, if you say "all drug traffickers will be prosecuted" will imply the existence of at least one drug trafficker.