The argument invalid. The middle term is not distributed (it should be). That's why you're able to construct a counter-example.

The argument invalid. The middle term is not distributed (it should be). That's why you're able to construct a counter-example. — TheMadFool

What is the middle term, and how should it be distributed? Where is the counter-example? Could you elaborate with more details and examples?

The problem is that you're comparing apples and oranges. You're comparing letters in the first example and comparing categories (animals) to elements of categories (cats and dogs) in the latter.

If a in the first example were a category, like animals, and c and d were elements of that category then c = d would be false too. Essentially, a, c and d are not being defined in the same way as animals and dogs and cats, so the relationship between the letters vs animals and dogs and cats are completely different.

As usual, it comes down to what the scribbles point to, or how they are defined.

You're comparing letters in the first example — Harry Hindu

Well, not "letters", but they are "objects".

comparing categories (animals) to elements of categories (cats and dogs) in the latter. Essentially, a, c and are being defined in the same way as animals and dogs and cats, so the relationship between the letters vs animals and dogs and cats are completely different. — Harry Hindu

But surely, cats and dogs themselves can be categories too?

According to your point, it sounds to me that you can only compare God with another God. Not logically possible task, is it?

Sure, but are a, c and d categories?

If you re-wrote the first example as

All c's are letters . (true)
All d's are letters. (true)
Therefore d's are c's (false)

Then it would be a fair comparison to your second example. In other words, you're comparing different types of entities in each example, so what works for one fails to work with the other.

Illicit minor

What is the middle term, and how should it be distributed? Where is the counter-example? Could you elaborate with more details and examples? — Corvus

1. All A are B
2. All C are B
Ergo, you feel
3. All A are C

A, B, and C are terms or classes/categories.

In 1, A is the subject term, B is the predicate term. 1 is making a claim about members of the subject term/class/category (A), specifically that ALL of them also belong to the predicate term/class/category (B). 2 is the exact same story but this time about C and B.

Remember this is categorical (term/class/category) logic developed I'm told by Aristotle.

The major premise contains the predicate term of the conclusion. In your argument, it's 2. The minor premise is the one that has the subject term of the premise viz. 1.

The middle term is the link between the subject term of the conclusion (A) and the predicate term of the conclusion (C) and is not found in the conclusion. The middle term is B.

The middle term has to be distributed i.e. there must be a premise that makes a claim about ALL the members of the middle term.

All X are Y type of statements are called a universal statements and the subject term (X) is distributed but, unfortunately, for your argument not the predicate term (Y).

As you can see all the premises (1, 2) are universal statements that have B as a predicate term i.e. The term/class/category B isn't distributed. That makes your argument invalid.

An intuition on why the middle term needs to be distributed is that it's the link between the subject term of the conclusion and the predicate term of the conclusion and the link needs to be as strong as possible and for that a premise must make a claim about ALL members of the middle term.

Sure. Great explanation. :up:
I also thought, it is possible for the arguments to come to the true conclusion, had the premises came up with the complete set of sufficient and necessary propositions, because obviously the deductive premises above has insufficient conditions for the conclusion.

It is just to show that simple traditional symbolic logic can be a bit inadequate for arriving at true conclusions, even if the arguments look valid and consistent.

And then you will get people claiming that his dog is a copycat, so the conclusion is right, when the others say it isn't. Or some will say that his dog is a hot dog. Hot dogs are not animals, because it doesn't move or breath etc, so that the premise is false etc.

There are a few books on logic I've read and the points you're discussing are part of what some have lovingly and condescendingly (reality's messy) called baby logic - you can imagine from that description alone how vast and deep as the mighty oceans of the world logic, in fact every single subject, really is. We are, as those who have come face to face with this seemingly obvious but usually ignored and frustrating truth know, barely scratching the surface. If you're anything like me, you'll despair. All I can say is, Aristotle would give you his nod of approval - the situation and the feeling are a perfect match! It's all a giant pile of shit I tell you and it doesn't matter where you are in a giant pile of shit, you're in shit! Rant alert!

Illicit minor — Michael

Great study material. Thanks :up:

I thought they are great practices in the Critical Argument studies. It is certainly helping me understanding the topics more.

It depends on from what angle you are looking at anything. If you feel sh*t, then everything looks sh*t. You can criticise anything, if you want. But it is just a psychology, not the objects out there.

I thought they are great practices in the Critical Argument studies. It is certainly helping me understanding the topics more.

It depends on from what angle you are looking at anything. If you feel sh*t, then everything looks sh*t. You can criticise anything, if you want. But it is just a psychology, not the objects out there. — Corvus

How right you are. The angle makes all the difference. From a certain angle, shit looks like shit, from another angle, shit looks like... :chin:

How right you are. The angle makes all the difference. From a certain angle, shit looks like shit, from another angle, shit looks like... :chin: — TheMadFool

I thought for the fact that you replied to this thread with the good write up, you must also be very much interested in the topic, but what made you feel that way, I am lost. :) But never mind. I hope you feel better.

I thought for the fact that you replied to this thread with the good write up, you must also be very much interested in the topic, but what made you feel that way, I am lost. :) But never mind. I hope you feel better. — Corvus

Ranting! Venting! Blowing off steam! Sorry you had to see this! By the way, did I say anything even mildly inappropriate? Apologies if I did.

On a more serious note, logic is logic's own worst enemy (it fails its own tests). That's the beauty!

Ranting! Venting! Blowing off steam! Sorry you had to see this! By the way, did I say anything even mildly inappropriate? Apologies if I did. — TheMadFool

No troublems. Logic had never been an interesting subject for me before, but since reading more forum discussions recently, my interest on logic seems have gone up. I will try to learn more about it through time with more practicing :D

On a more serious note, logic is logic's own worst enemy (it fails its own tests). That's the beauty! — TheMadFool

I would go with that. :grin:

Good luck. I hope you have better luck than me, Corvus.

All d -> a (true)
All c -> a (true)
Therefore c = d (true)

Above logical arguments look OK in the symbols. But when they are put in with the real objects in the world, it leads to the wrong conclusion.

All dogs are animals. (true)
All cats are animals. (true)
Therefore cats are dogs (false)

What are the actual problems here? — Corvus

The problems are:

(1) Your first example is not correct syntax, and even when corrected, it is irrelevant

Maybe you meant:

Ax(Dx -> Bx)
Ax(Cx -> Bx)
therefore Ax(Cx <-> Dx)

But the logical calculus doesn't permit that inference so your example is irrelevant.

Or more simply you might mean:

D -> B
C -> A
therefore C <-> D

Again, the logical calculus doesn't permit that inference so your example is irrelevant.

(2) Your second argument is not correct syntax, and even when corrected, it is irrelevant.

Maybe you mean:

Ax(Dx -> Nx)
Ax(Cx -> Nx)
therefore Ax(Cx -> Dx)

The logical calculus doesn't permit that inference so your example is irrelevant.

symbolic logic can be a bit inadequate for arriving at true conclusions, even if the arguments look valid and consistent. — Corvus

You gave examples of arguments that symbolic logic rules as invalid. That's not a problem for symbolic logic; it's only a problem for you if you think symbolic logic does rule those arguments as valid.

I will try to learn more about it through time with more practicing — Corvus

Its a good bet that, if you're not taking a class, then the best way to learn is from a good textbook.

'Logic: Techniques of Formal Reasoning' by Kalish, Montague, and Mar is the best introduction, in my opinion based on having looked at a lot of logic books.

The logical calculus doesn't permit that inference so your example is irrelevant. — TonesInDeepFreeze

I have started reading a couple of Introduction to Logic books, and still in the 1st chapter. It has not gone to the logical calculus chapter yet.

You gave examples of arguments that symbolic logic rules as invalid. That's not a problem for symbolic logic; it's only a problem for you if you think symbolic logic does rule those arguments as valid. — TonesInDeepFreeze

Sure it is not the symbolic logic issue as such you are right, but the traditional logic which often used by the God debaters seem have the problems like that. Even what looks like valid arguments could have traps of fallacies. Not suitable tool to rely on for more complicated cases, I was trying to prove. I was not trying to say that the OP argument is valid or correct. As TMF said, the enemy of logic is often, the logic itself.

Its a good bet that, if you're not taking a class, then the best way to learn is from a good textbook.

'Logic: Techniques of Formal Reasoning' by Kalish, Montague, and Mar is the best introduction, in my opinion based on having looked at a lot of logic books. — TonesInDeepFreeze

I have a couple of basic logic books, but they seem not great. I will see, if I could get hold of the book you recommended. Thanks.

the enemy of logic is often, the logic itself — Corvus

How so?

I have a couple of basic logic books, but they seem not great. — Corvus

Which books are those?

How so? — TonesInDeepFreeze

When logic is used in the debates, the debaters might get a false sense of security that they might arrive at true conclusions because they are using logical methods. But in many cases, it is not the case. Because logic can hide the traps. Just guessing :D

Which books are those? — TonesInDeepFreeze

Logic by Wilfrid Hodges
Introduction to Logic by Gensler

Both books are in Amazon, and the 1 star reviews explain the problems with the books in great detail.
I agreed with the reviewer about the books. (the same reviewer for the both books).

https://www.amazon.co.uk/product-reviews/0141003146/ref=acr_dp_hist_1?ie=UTF8&filterByStar=one_star&reviewerType=all_reviews#reviews-filter-bar

https://www.amazon.co.uk/product-reviews/0415996511/ref=acr_dp_hist_1?ie=UTF8&filterByStar=one_star&reviewerType=all_reviews#reviews-filter-bar

"This book, like other pseudo-logic texts of the type, does inform us that logical arguments require true premises. And of course, the vast majority of the book is focused upon technical logical rules designed to insure that we are able to spot obvious logical contradiction in an argument. Here's the problem with that;I know of no one who will believe an argument which they know is derived from untrue premises, or which contains obvious contradiction. The real problem is that via appeals to authority and emotion we tend to accept premises as true which are not supported by evidence or which are deceptively incomplete. (Very cleverly, Gensler and his ilk teach us what we we already know naturally.)"

When logic is used in the debates, the debaters might get a false sense of security that they might arrive at true conclusions because they are using logical methods. But in many cases, it is not the case. Because logic can hide the traps. — Corvus

Sure, people err, and abuse even simple logic. And logic is often not simple.

Logic by Wilfrid Hodges
Introduction to Logic by Gensler — Corvus

Thanks, I'll look at them out if I see them somewhere.

Quotes below are from a third party's comments on a book:

"This book, like other pseudo-logic texts of the type, does inform us that logical arguments require true premises."

'pseudo-logic' is mere and false characterization.

Good for those books. Logical arguments do not require true premises.

"technical logical rules designed to insure that we are able to spot obvious logical contradiction in an argument"

Wrong. The rules are to prevent non sequiturs, and to disallow inferring contradictions from consistent premises.

The writer of the review doesn't understand logic.

"I know of no one who will believe an argument which they know is derived from untrue premises, or which contains obvious contradiction."

The writer fails to understand the difference between evaluation of the validity of an argument and the truth value of the conclusion.

"The real problem is that via appeals to authority and emotion we tend to accept premises as true which are not supported by evidence or which are deceptively incomplete."

Appeals to emotion and authority are informal fallacies. Such fallacies are worth discussing, but they are not in the field of formal logic.

"Gensler and his ilk teach us what we we already know naturally."

Yeah, I don't think so. The writer doesn't even know the difference between inferential validity and factual truth and falsity.

You are quoting from someone who is ignorant.

You are quoting from someone who is ignorant. — TonesInDeepFreeze

I was not sure if she was ignorant or not, but there were parts that resonated with my feelings about the books. The reviewer didn't sound like a newbie (she has many Logic books, and read them all) for sure. I am the newbie :D

there were parts that resonated with my feelings about the books. — Corvus

You just quoted her about the ill-effects of emotion in arguments. Your feelings about the books don't make her arguments about them sound.

he reviewer didn't sound like a newbie (she has many Logic books, and read them all) — Corvus

Based on the quote you provided, she seems not to understand what she read, thus remaining ignorant.

I read both her posts. They're ignorant diatribes.

You just quoted her about the ill-effects of emotion in arguments. Your feelings about the books don't make her arguments about them sound. — TonesInDeepFreeze

I don't always quote or post sound arguments only. But the quoted parts are what I felt was good points. I used to believe that one must not start philosophical debates with inferred premises. I still do.

But the quoted parts are what I felt was good points. — Corvus

They're not. They reveal fundamental misunderstanding, confusions, and ignorance of the writer.