An interesting question, but I am a lazy person, so without research I will just point out one common fallacy which occurs too often in Wikipedia and other forums: namely, the assertion that Euclid's Postulate 5 and the parallel postulate are logically synonymous. This is easily disproved by pointing out that a negation of the parallel postulate (within the Euclidean context) does not entail a negation of Postulate 5.

The highest concentration of fallacious arguments in one location which I have ever come across is not in a speech by a politician or reality-show imposter, but in the Wikipedia article summarising all of the supposed proofs that 0 is an even number. I have seldom encountered so dense an intellectual fog within the compass of a single essay, even from a first-year student.

common fallacy which occurs too often in Wikipedia and other forums: namely, the assertion that Euclid's Postulate 5 and the parallel postulate are logically synonymous. — alan1000

I hate when people do that! :nerd: (or at least I would if I knew what it meant. Will look it up).
Thanks for your reply! :up:

I don’t think it’s a fallacy, but the biggest logical disconnect in politics is when millionaire candidates ask their poor followers for money.

Lewis Carroll would have trouble writing a satire of our times.
Truth became stranger than fiction a long time ago…

Logical fallacies committed by philosophers are ubiquitous. The greatest of all, and the the most damaging of all, is the idea that metaphysical problems are formal dilemmas. Anyone who knows Aristotle's rule for contradictory pairs will know this is not demonstrable, but still the idea is commonplace among philosophers.

The greatest of all, and the the most damaging of all, is the idea that metaphysical problems are formal dilemmas. — FrancisRay

Interesting! Could you expand on that a little? :smile:

one common fallacy which occurs too often in Wikipedia and other forums: namely, the assertion that Euclid's Postulate 5 and the parallel postulate are logically synonymous. — alan1000

Common fallacy? It occurs too often in Wikipedia???
It's the first time I hear about "Euclid's Postulate 5"! And I'm a fan of Math and paradoxes ...

We meet fallacies quite often. Most of the time in places like this one. Of course, since making philosophical and logical arguments is at the core of the discussions that are taking place in such places.

But there are different kinds of 'em. My favorite ones are those "hidden" in paradoxes, which for that reason --i.e. because they contain fallacies-- I call them pseudo paradoxes. So here's one. Find why Zeno's Achilles and the Tortoise is such a pseudo paradox ...

nteresting! Could you expand on that a little? :smile: — 0 thru 9

Despite its;crucial importance for philosophy this is a quite simple issue.

Aristotle's rules for the dialectic include the rule for legitimate contradictory pairs. This states:

Of every contradictory pair one member is true and one false

This is the input rule for his system, and when it is violated the entire system breaks down. It would be a case of 'garbage in garbage out.'.

If you examine any purported metaphysical dilemma you'll find you cannot be quite sure that its two horns obey this rule. In this case, you cannot know it is a dilemma. It is possible that both are false,or that both are unrigorous and neither quite true of false. . .

It is for this precise reason that metaphysicians cannot refute the nondual doctrine of mysticism for which all the extreme answers for metaphysical questions are incorrect, rendering them undecidable. It obeys the laws of logic so cannot be refuted. All the seeming dilemmas of metaphysics may be explained as abuses of the rule for contradictory pairs. It's an easy mistake to make but the consequences for philosophy are utterly catastrophic.

It might be the most significant logical mistake in all of human history.

Of every contradictory pair one member is true and one false — FrancisRay

Let's see ...
1) Man is white. 2) Man is not white.
Which is true and which is false? Or can they both be true? Or are they both false?
What is it that decides about their truthfulness or falseness?
Context. Geography. Logic.

Concering context and geography:
Referring to people in Europe we can safely say that "People are white". This does not exclude though that there are people who are not white (elsewhere in the world). Because, referring to people in Africa we can equally safely say that "People are not white".

Concerning logic:
Both statements are false. Saying that "Man is white" is false, because there are places where Man is not white. And the other way around: Saying that "Man is not white" is false, because there are places where Man is white.

This is the input rule for his system, and when it is violated the entire system breaks down. — FrancisRay

Based on the above, has the system been violated? How can a rule be violated if it its validity is not established?

What's fun here is how few folk on a philosophy forum understand what a fallacy is.

If we ask whether we have won or lost the lottery then the answer will be yes or no.

If we ask whether two plus two equals three or five then we are abusing the rule for legitimate pairs.

If we ask whether the universe begins with something or nothing then we are assuming one of the answers is correct but do not know this. Logic tells us that neither answer is correct. So we have a choice, Our assumption creates a dilemma and renders metaphysics incomprehensible, If we follow the logic and assume both answers are incorrect then there is no dilemma. This second assumption is necessary for the Perennial philosophy.and renders metaphysics comprehensible.

In metaphysics the second assumption is generally considered to break the laws of logic. This is a technical error, since we do not know that there is not a third answer.

Philosophers often see this logical point in relation to the freewill/determinism question and adopt compatabilism, thus doing away with the dilemma. Nothing prevents us from taking the same approach to all metaphysical questions because It is not possible to prove that the opposed answers to such questions exhaust the possibilities.

If we make the wrong assumption in such cases this is either a fallacy or a basic mistake. For sound reasoning we must know that a contradictory pair of propositions are mutually exclusive and exhaust the possibilities. We never know this for metaphysical questions. .
. .

.

If we ask whether we have won or lost the lottery then the answer will be yes or no.. — FrancisRay

Of course.

If we ask whether two plus two equals three or five then we are abusing the rule for legitimate pairs. — FrancisRay

This is not about contratictory pair --of the kind of Aristotle's "Of every contradictory pair one member is true and one false"-- that I commented on. It's about alternatives.

If we ask whether the universe begins with something or nothing then we are assuming one of the answers is correct but do not know this. — FrancisRay

OK, but something and nothing are too vague and abstact. So, I don't think that this can be used as an example in our case, either. Your first example (lottery) was good.

Logic tells us that neither answer is correct. — FrancisRay

I don't think that logic can enter in the above example. As I said, the contrassting elements are too abstract to be considered as evidence for truth or falseness. So, saying that neither answer is correct has no meaning.

In metaphysics the second assumption is generally considered to break the laws of logic. — FrancisRay

What is the "second assumption"? That the universe begins with nothing? If so, what rule exactly does it break and why? And what about the first assumption, i,e, that the universe begins with something? Why's not that breaking the rule?

If we make the wrong assumption in such cases this is either a fallacy or a basic mistake. — FrancisRay

It's just a mistake. Lack of knowledge. A false statement. Not a fallacy. A fallacy is an unsound argument. A single assumption alone cannot consist argument. it can only be part of an argument. "I assume that you are English" is not an argument. An argument would be "The name "Francis" is English. So you must be English."

For sound reasoning we must know that a contradictory pair of propositions are mutually exclusive and exhaust the possibilities. We never know this for metaphysical questions. . — FrancisRay

Right. But why are you mentioning that? In my example of "1) Man is white. 2) Man is not white" the two elements are mutually exclusive. In a most explicit and direct way.

But I have explained and described in detailed the factors and difficulties that are involved in such contraditory pairs. How could you miss all that? And how couldn't you comment on any single thing I have written? :gasp:

In fact, it looks like you have hardly read my message ...


.

I don't think that logic can enter in the above example. As I said, the contrassting elements are too abstract to be considered as evidence for truth or falseness. So, saying that neither answer is correct has no meaning. — Alkis Piskas

Yes. Just as saying both answers exhaust the possibilities is guesswork. This is my point. You cannot prove there is such a thing as a metaphysical dilemma. .

You;re right - I don't understand your comments. They seem to miss the point. As yet you've said nothing that would count as an objection. I fear we are misunderstanding each other. .

You;re right - I don't understand your comments. They seem to miss the point. — FrancisRay

I would respect your opinion if it weren't evasive and meaningless: "I don't undestand your comments" means nothing. There's a big difference between us in how we handle comments and debating in general. You would thrive as a (Greek) politician! :smile:
Anyway, it's better this way. We'll both avoid wasting more time.

I would respect your opinion if it weren't evasive and meaningless: "I don't undestand your comments" means nothing. There's a big difference between us in how we handle comments and debating in general. You would thrive as a (Greek) politician! :smile:
Anyway, it's better this way. We'll both avoid wasting more time. — Alkis Piskas

I'm sorry that you've not understood my posts but it's a bit cheeky to blame it on me.

I can only assume you have no relevant objection to what I said in the first place.

More wasted time ...Bye, bye for good now.

What's fun here is how few folk on a philosophy forum understand what a fallacy is. — Banno

A fallacy is what results when the fallible philosophise. Fortunately, we have enough gods among us to keep us from failing and falling into fallacy when it matters. (excuse my effing).

↪FrancisRay

More wasted time ...Bye, bye for good now. — Alkis Piskas

Hmm. No argument then. What was wrong with what I said at the start? .

You invited people to participate to your discussion.
Basic courtesy demands that you reply to someone who has responded. Even with just a "Thanks" ...

I've decided not to just leave it, but you can ignore this if you want.

I said that metaphysical dilemmas and antinomies are examples of a faulty use of logic. Specifically, they break the rule for legitimate contradictory pairs.

What is your objection? I didn't see an objection in your previous posts so wondered what point they were making.

You invited people to participate to your discussion.
Basic courtesy demands that you reply to someone who has responded. Even with just a "Thanks" ... — Alkis Piskas

Umm, thanks? :wink:
I was following your conversation with @FrancisRay. I was just trying to make sense of what was being said, and how to possibly respond. Was drawing a blank. But carry on…
Thanks!

I was talking about my response to your topic. What the hell has @FrancisRay to do with it?
That's totally crazy.

I was talking about my response to your topic. What the hell has FrancisRay to do with it?
That's totally crazy. — Alkis Piskas

This side conversation could be fascinating, but I’ll try to steer the discussion back to the OP (which is giving examples of bad logic and informal fallacies, and then explaining).

Find why Zeno's Achilles and the Tortoise is such a pseudo paradox ... — Alkis Piskas

Sorry, I have no answer for this yet. You may ask everyone again, or give the answer if you’d like.

Find why Zeno's Achilles and the Tortoise is such a pseudo paradox ... — Alkis Piskas

What passes as a rigorous explanation for why Zeno's paradox isn't a paradox? One can race a man against a turtle and see that men and turtles traverse finite distances over time.

The length of every half distance to reach the finish line infinitely diminish within the finite distance because it is imagined so. This is the dream of some mathematician, who introduces infinity as a problem to a real world scenario. If a finite distance is infinitely divisible in the realm of maths, so be it, but it doesn't apply in a way that makes motion in time impossible.

At last! A response to my challenge! Even after one week.
I can't believe it's a difficult challenge for this place. In fact, expected a lot of responses, since the subject is very well known. However, it's @0 thru 9 who actually invited people in this "game", not me. And think that not even he responded!
So thanks for responding! :smile:

What passes as a rigorous explanation for why Zeno's paradox isn't a paradox? — Nils Loc

It is actually very simple. (Describing it sounds more complicated though. :smile:)
Zeno assumes falsely --but I believe for us only, not for himself-- that time and space are finite and have a discrete (discontinuous) form, and so they are divisible. But this is a fallacy. They are not; they are infinite and continuous, so they are indivisible. Time and space have no start or end or middle or any point. So, his argument or description falls apart as an argument or description if one just realizes this basic logic, truth, knowledge about time and space.

Now, a paradox is a statement, argument or description that sounds impossible or self-contradictory or absurd but in reality it expresses a possible truth. Also, to be valid, it must be based on sound arguments or, at least, apparently sound. And Zeno's "paradoxes" neither express a possible truth nor are based on sound arguments. That's why I call them "pseudo-paradoxes", together with a lot of other that are based on fallacies or a violation of basic logic, truth or knowledge.

Remember only that Zeno was a sophist and as such he --as other sophists too-- were paid teachers of philosophy and rhetoric in Ancient Greece, associated with scepticism and specious reasoning. Even today, the term "sophist" means a person who reasons with clever but false arguments.

One can race a man against a turtle and see that men and turtles traverse finite distances over time. — Nils Loc

This is exactly the point: There are no finite distances or tile periods. It is we who arbitrarily define them as such for the purposes of description or physical phenomena, geometric problems, etc., based on measuring units, which we have arbitrarily created, such as meter, yard, day, hour, etc.
And we have to use devices like clocks to measure these "finite" distances or periods. But even so, devices can never be perfect, i.e. so precise as to consider a measurement as something absolute.

This is the dream of some mathematician, who introduces infinity as a problem to a real world scenario. If a finite distance is infinitely divisible in the realm of maths, so be it, but it doesn't apply in a way that makes motion in time impossible — Nils Loc

Exactly, it's just a dream. :smile:

I already answered your question 5 years ago: https://thephilosophyforum.com/discussion/comment/181078

A lot of you are missing the point when they start applying Zeno's paradox to real world circumstances. It was an allegory for a mathematical argument he was having with other Greek philosophers. It isn't intended as a theory of motion but as argument against the then prevailing idea that a mathematical line is build up of points (atoms) and a finite number could not be divided infinitely (again, atoms!). It's an argument against there existing an indivisible mathematical quanta that they thought existed at the time.

As a mathematical argument it's quite good and easily imagined but the allegory is just an aid for understanding the mathematical argument not intended as to say anything sensible about the real world. So once you realise it isn't about physical reality, the paradox disappears. — Benkei

Lazy with the search function, eh? :wink:

I already answered your question 5 years ago: — Benkei

I undestand that you mean this in a figurative way. But still, you have not answered any question. I have mentioned Zeno's Achilles and the Tortoise paradox as a challenge for "spotting the falacy" which is the motto of this topic. Your message has nothing to do with that. It's just out of place and time.

In your 5-year old message, you say:

"A lot of you are missing the point when they start applying Zeno's paradox to real world circumstances. It was an allegory for a mathematical argument he was having with other Greek philosophers."

I guess "all of us, not just a lot of us" :smile:
What "paradox"? There are more than one know Zeno's paradoxes.
Where have you read about this "allegory" stuff? Is it your own idea? Are you confusing maybe some of Zeno's paradoxes with Plato's Allegory of the Cave? Because I have read somewhere that these two were correlated.

Whatever you think, it is well known that Zeno's paradoxes are basically a set of philosophical problems.

Anyway, all this does not explain Zeno's Achilles and the Tortoise paradox as such, which is what I set as a chellenge and which is based on a fallacy and it still puzzles --alas!-- a lot of people ... even philosophers, from what I have read ...

You can read the thread I replied to yes? It's a simple straw man fallacy by representing the mathematical argument as a paradox of actual motion.

I'm good. Thank you.

Zeno assumes falsely --but I believe for us only, not for himself-- that time and space are finite and have a discrete (discontinuous) form, and so they are divisible. But this is a fallacy. They are not; they are infinite and continuous, so they are indivisible. — Alkis Piskas

Why is it right to conclude that time and space are really infinite and continuous rather than discrete and discontinuous? Either of these abstract properties are just mathematical inventions/conventions which prove to be useful. Time and space can obviously be divided (measured in units), or treated as infinite and continuous.

If time is infinite, it's still divisible by seconds in relation the diurnal or lunar cycle.
If space is infinite, it's still divisible by length of feet in relation to how much horse food, water or minutes it takes to get to town.

Through ordinary material/spatial divisions,we see that are practical/natural limits to the notion of infinity.

So what am I missing?