## View Poll Results: Is the argument valid?

Voters
9. You may not vote on this poll
• Yes, the argument is valid.

3 33.33%
• No, the argument is not valid.

3 33.33%
• I don't know

0 0%
• The argument doesn't make sense

3 33.33%

# Thread: And the next U.K. Prime Minister will be?

1. Originally Posted by fast
There’s an old saying about getting out of a situation the same way you got into it, but life’s not always that easy. The difficulties of doing things one way is not always equivalent to doing things inversely. Jumping off a diving board and into the water is one thing, but jumping out the water and onto the diving board is quite another.

Taking the premises of an argument and propeling our way to a conclusion seems substantively more difficult than safely standing upon a conclusion and gazing out in observance of premises.

If I start with the conclusion “I have salt OR I have pepper,” I can leisurely browse at the available premises:

P1: I have salt
C: I have salt or I have pepper

From that vantage point, I can also start with the conclusion “The Earth is flat OR the moon is made of cheese.”
P1: the earth is flat
C: the earth is flat or the moon is made of cheese

It’s from this perspective where things seem easy—like falling into a hole

But, stand it on its end with no gun powder to power the cannon and I find complexity building.

From a premise of “I have salt” to rolling out a conclusion with another wording seems like something is required. If I program a computer to display only the premises given, then never shall it display something not programmed.

I can go from
C: I have salt or I have pepper
And know that one of two different possible premises are lurking

But flip it and all hell breaks loose
P: I have salt
C: I have salt or Elvis is playing the guitar on the moon made of purple cheese

Who saw that coming?
There's another way to flip this around. Suppose you start at some conclusions and you want a computer to come up with premises from which to derive them. Mathematicians like to do this when they axiomatize a mathematical field down to simple principles. But scientists do it too. For instance, Newton might start with Kepler's laws for planetary motion, and wish to derive the simplest principle that can produce those laws.

So we're doing something like:

C: Planets move according to Kepler's laws.

and now we go looking for premises. And behold! I've found two:

P1: Planets move according to Kepler's laws.
P2: Elvis is playing the guitar on the moon made of purple cheese

Again. WTF?

2. Originally Posted by Speakpigeon
Originally Posted by Angra Mainyu
No, no one "decides" what they are. Rather, one assesses what they are.
So mathematicians waste their time assessing rules without deciding which are correct. I gets better an better.
You grossly misrepresent what I said.
People assess whether rules are correct. They do not decide it. Either they are correct, or not.

Originally Posted by Speakpigeon
So who is going to decide who is good at it?

Ah, yes, I see, nobody ever does. Instead, mathematicians just assess. Assess is the new ultimate reality.
No, everyone assesses questions they think about. Some people think about logic rules. Most don't. Some people are good at logic. Others aren't.

Originally Posted by Speakpigeon
Sure, if, but how do you prove my brain is malfunctioning? Do you just "assess"?
I do not prove it - proofs are for mathematics -, but I have shown it conclusively to any reader being rational and paying attention - for example, by showing that some of your beliefs on these matter contradict others.
Of course, you will never realize that. But similarly, if someone claims the Moon Landing was a hoax, and insists on a conspiracy theory after they have been shown the relevant evidence, I reckon their brain is malfunctioning, as they are making improper epistemic probabilistic assessments. Others will insist that Jesus walked on water. And nearly all of those will insist that I'm the one in error. Well, such is life. They're still wrong. As are you.

Originally Posted by Speakpigeon
Proper? What do that even mean in this context?
I'm using the word "proper" in the usual sense of the word, in English.

Originally Posted by Speakpigeon
Rules are conventions decided by people. Proper just means these dudes agree among themselves. Who cares?
Some rules are conventions decided by people. But usually they decide them for some reason. Other rules are not conventions, but the rules of properly functioning English-speaking humans, which are the same for at least pretty much all present-day languages (I'm not sure whether there are exceptions in humans having language; it seems improbable).

And before you misrepresent my position again (I can see your error coming), no, I did not claim that there is not a single proper human logic for all colloquial languages. I think there probably is, and if there isn't, at least there is one for each language (and it is common to many if not all of them). In formal languages, one can restrict logic in different ways (as one does in mathematics), though one uses our intuitive logic in the metalanguage (my reply that we do not know whether humans have a natural capacity, etc., is explained in that thread, in which I showed why that was so on the basis on your own parameters for assessing what is part of human nature, what is an
"inherent capacity", etc.). In other words, you bungled that thread too.

Now, you talked in other threads about mathematicians using their intuitive logic, rather than what you call "mathematical logic". Well, of course, mathematicians do not use logic formalizations most of the times, in most of the proofs - other than those working on mathematical logic -, but then, what you defined as "mathematical logic" is not tied to any formal system, and it is in fact in line with the logic intuitions that most mathematicians have.

Well, guess what?
Mathematicians are generally way above average at doing logic intuitively - no formalization, no nothing. In part, that is just talent - some of us were well above average at math in primary and high school, before we learned anything about formal logic - and in part, training - most of which, again, happens without formalization of logic.

Originally Posted by Speakpigeon
Interestingly, most people I have tested with contradictory premises disagree with mathematicians. Obviously, they fail to be biased.
No, they fail at logic, in those particularly unusual cases. People's logic intuitions tend to work well enough in most contexts of their daily lives. But the most distant one is from those contexts, human intuitions are generally less reliable. But some people are just better than average. Just as some people are (much) better at running, punching, or at picking up what others are feeling than the average, some are (much) better at logic. And they can get better (anyone can, even though to different degrees) by training, like - say - learning math (whether or not they study mathematical logic).

Originally Posted by Speakpigeon
And most logicians before Boole didn't accept the principle of explosion, so even your claim here is junk.
There is such things as progress. There is a reason people come to accept something: someone provides good reasons for it. It's not as if Aristotle actually had the ideas you believe he had, or that he explicitly rejected arguments for the principle of explosion.

3. Originally Posted by fast
But flip it and all hell breaks loose
P: I have salt
C: I have salt or Elvis is playing the guitar on the moon made of purple cheese

Who saw that coming?
2 + 3 = 5;
Therefore, 2 + 3 = 5 or it is not true that 2 + 3 = 5.

x = 10 or x = 112;
Therefore, x = 13 or x = 112 or x = 11 or x = 114 or x = 15 or x = 117 or x = 17 or x = 118;

x is even;
Therefore, x is even or x is not even.

The premise of this argument is true;
Therefore, the premise of this argument is true or the conclusion of this argument doesn't follow.

The accused is guilty;
Therefore, the accused is guilty or the accused has been framed by the police.

All these are valid but it seems you feel somewhat doubtful about that kind of implication... Maybe it is because in ordinary conversations we sometime use "or" to introduce a contradictory supposition.
EB

4. Originally Posted by Angra Mainyu
Originally Posted by steve_bank
Originally Posted by Angra Mainyu

The conclusion follows from P1 and P2, as explained. It does not follow from P1 alone. There is no sophistry in my argument. In formal logic, it is very easy.

P1: P
P2: ¬P.
C1: P or Q. [this follows from P]
C2: Q. [this follows from C1 and P2].

I am being serious and blunt. In the environments I worked in if you put forth the kind of reasoning you used to declare the moon is made of chees on a real problem you would be labeled incompetent. You do not seem to understand logic.
I am being serious and blunt. In the environments I work in, if you imply that I ever suggested that the kind of reasoning I put forth would provide any good reason to even suspect that the Moon is made of cheese, you would be corrected immediately because you do not even understand the arguments you are replying to. But my logic is correct.
You are apparently using a form of a boo trapping argument.
Again the wording of your syllogism. Therefore the moon IS made of cheese. There is no logical connection to the premises.

The second conclusion is bootstrapped. You draw the first conclusion then you bootstrap the second by selecting one of two contradictory statements p1 p2.

In court bootstrapping is forbidden, it is seen as sophistry to draw a conclusion without any evidence circumstantial or otherwise. Your syllogism works around the lack of evidence in the premise regarding the second conclusion.

If this were a Perry Mason episode and I the judge I would say 'Counselor reword your argument or move on'.

5. fast

Taking the premises of an argument and propeling our way to a conclusion seems substantively more difficult than safely standing upon a conclusion and gazing out in observance of premises.
That is the crux of applying logic. I look at it as top down vs bottom up. Induction vs deduction.

I want to build a bridge. I can start with a known form of bridge design and work backwards to define how it gets built.

I can look at the conditions of the site and the requirements and work towards selecting a design.

In reality it is rarely one or the other. One goes back and forth with some trial and error between conclusion and premises. Start with a design and work backwards finding it will not work. Start with the original derived premises and work toward a different design. It can take multiple cycles.

There are rules of logic but there is no mechanistic set of rules on how to apply logic to achieve a goal.

There is electrical circuit theory but there are no rules on how to put together a circuit to do a task.

Staring out we study theory and simple applications. Then from experience and observation we learn how to apply theory. Two engineers may not come up with the same circuit solution to a problem, while both may work fine.

It is experience and theory distilled to reasoning is how I see it. A function of the brain.

6. I’m paraphrasing and adding, but I was asked why I would follow the rules of logic even when questions linger about justification. It’s an established convention that leaves no one confused when everyone is on the same page. I figure I’m doing well just to know some basics. I’m not out to expose what might be genuine flaws. If I’m going to vote on whether or not I think an argument is valid, I think I’m doing better service to those I speak with to align my vote with what accords with accepted convention.

Sure, I might argue a point here or there (and get my feet wet, so to speak), but as I come to terms with how things are taught, I adjust my positions accordingly.

His logic is taught is my benchmark. I can consider what others are saying, but I think I’m doing good to keep an eye on what extent one deviates from convention.

7. Originally Posted by fast
If I’m going to vote on whether or not I think an argument is valid, I think I’m doing better service to those I speak with to align my vote with what accords with accepted convention.
???

What "convention"?!

Mathematicians don't even agree among themselves on any one "convention", so there is no convention, even less an "accepted convention".

And even if they did, it would remain a convention among mathematicians not necessarily accepted by non-mathematicians.

Why don't you speak French? You know, it's a convention. Along French people, sure, but at least it is really a convention.

In other words, you choose to accept the convention as if you couldn't decide for yourself whether an argument is valid or not.

I wonder how you can go through life without harm since you are clearly not very well versed in the details of this convention. How did you survived until now without it?
EB

8. Originally Posted by Speakpigeon
Originally Posted by fast
If I’m going to vote on whether or not I think an argument is valid, I think I’m doing better service to those I speak with to align my vote with what accords with accepted convention.
???

What "convention"?!

Mathematicians don't even agree among themselves on any one "convention", so there is no convention, even less an "accepted convention".

And even if they did, it would remain a convention among mathematicians not necessarily accepted by non-mathematicians.

Why don't you speak French? You know, it's a convention. Along French people, sure, but at least it is really a convention.

In other words, you choose to accept the convention as if you couldn't decide for yourself whether an argument is valid or not.

I wonder how you can go through life without harm since you are clearly not very well versed in the details of this convention. How did you survived until now without it?
EB
I tried damn it!

True story. Funny story too. I took an English class, a Spanish class, and a French class all in the same quarter (they later switched to the semester system). One day in Spanish class, the teacher would read something in Spanish and a student would stand, translate to Spanish, and speak it aloud.

When it came around to my turn, I did my part, except afterwards (right after speaking), the teacher laughs and says “that came out 1/3 Spanish, 1/3 English, and (in an inquisitive tone said) 1/3 French. The class smiled and I explained I was taking all three. They were rolling that day!

9. Originally Posted by steve_bank
You are apparently using a form of a boo trapping argument.
Again the wording of your syllogism. Therefore the moon IS made of cheese. There is no logical connection to the premises.
Yes, there is. The connection is that applying the logic rules I used in the argument, the conclusion follows from the premises.

Originally Posted by steve_bank
The second conclusion is bootstrapped. You draw the first conclusion then you bootstrap the second by selecting one of two contradictory statements p1 p2.

In court bootstrapping is forbidden, it is seen as sophistry to draw a conclusion without any evidence circumstantial or otherwise. Your syllogism works around the lack of evidence in the premise regarding the second conclusion.
I don't know what you mean by "bootstrapped", but no serious court would forbid the deduction of (P or Q) from P or the deduction of Q from (P or Q) and ¬P. Of course, in a serious court, any argument with contradictory premises intended to provide support for the conclusion would be rejected, and with good reason. However, as I have already said (and it should be clear from my posts), I am not remotely suggesting that such argument would provide evidence for the conclusion. For that matter, the following argument is also valid (i.e., the conclusion follows from the premises).

P1: Either the Moon is made of cheese, or the Earth is flat and the Moon is made of cheese.
C: The Moon is made of cheese.

Originally Posted by steve_bank
If this were a Perry Mason episode and I the judge I would say 'Counselor reword your argument or move on'.
It would be difficult to deal with a judge who does not understand what I'm saying, despite repeated clarifications. But fortunately, I'm not in that situation.

10. Originally Posted by fast
I’m paraphrasing and adding, but I was asked why I would follow the rules of logic even when questions linger about justification. It’s an established convention that leaves no one confused when everyone is on the same page. I figure I’m doing well just to know some basics. I’m not out to expose what might be genuine flaws. If I’m going to vote on whether or not I think an argument is valid, I think I’m doing better service to those I speak with to align my vote with what accords with accepted convention.

Sure, I might argue a point here or there (and get my feet wet, so to speak), but as I come to terms with how things are taught, I adjust my positions accordingly.

His logic is taught is my benchmark. I can consider what others are saying, but I think I’m doing good to keep an eye on what extent one deviates from convention.
Here's another reason to support the rules in question: they are truth-preserving. Whenever the premises are true, the conclusion is guaranteed to be true.

For example, consider the following rule:

From (P or Q) and ¬P, you deduce Q.

Now, if it turns out that (P or Q) is true and ¬P is true, then P is false, right? But (P or Q) is true, so Q is true. Hence, the rule above preserves truth.

Imagine now that you reason by combining two rules, each of which preserves truth. Well, guess what? The use of the two also preserves truth, because assuming your premises are true, the conclusion after the first step (applying one of the rules that preserve truth) will be true, and then the same happens when you use the second rule. Similarly, if you combine several rules that preserve truth, the result preserves truth.

There are of course different systems that are truth-preserving. But there is one that is the strongest, in the sense that any conclusions that follow from a premise by means of a truth-preserving method also follows from this, strongest method. It's classical logic (there are arguments against is usage in mathematics, for example based on the idea that not all mathematical statements are either true or false; that could lead to a much more interesting discussion if people were interested).

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