And the next U.K. Prime Minister will be?

[Angra Mainyu]

Here is a "U.K. current affairs" argument.

P1 - Jeremy Corbyn is not Boris Johnson;
P2 - Boris Johnson is not Jeremy Hunt;
P3 - Jeremy Hunt is not Jeremy Corbyn;
P4 - The next U.K. Prime Minister will be either Boris Johnson or Jeremy Hunt;
P5 - The next U.K. Prime Minister will be Jeremy Corbyn;
C - Therefore, the next U.K. Prime Minister will be Boris Johnson.

Thank you to say whether you consider this argument valid or not.

Invalid. The five premises cannot all be true at the same time.

If the question were not whether the argument is valid, but whether the conclusion follows from the premises, would you not say that it does follow?

 

[Angra Mainyu]

Invalid. The conclusion doesn't necessarily follow from the premises.

The conclusion follows necessarily from the premises (maybe you misread?): From P3 and P5, it follows that the next U.K. Prime Minister will not be Jeremy Hunt. From "the next U.K. Prime Minister will not be Jeremy Hunt" and P4, it follows that the next UK Prime Minister will be Boris Johnson.

 

[Angra Mainyu]

To everyone:

From

P3 - Jeremy Hunt is not Jeremy Corbyn

and

P5 - The next U.K. Prime Minister will be Jeremy Corbyn,

we derive the following conclusion:

C1: The next U.K. Prime Minister will not be Jeremy Hunt.

From C1 and P4

P4 - The next U.K. Prime Minister will be either Boris Johnson or Jeremy Hunt

we derive

C: The next U.K. Prime Minister will be Boris Johnson.

That said, there is some lack of clarity in the premises, as one might think: well, what if Jeremy Hunt is not Jeremy Corbyn, but will be Jeremy Corbyn? So, I'm going with some implicit assumptions (which I think are reasonable in this context) about the meaning of the words involved in the statements, to make those derivations.

 

[lpetrich]

Invalid. The five premises cannot all be true at the same time.

If the question were not whether the argument is valid, but whether the conclusion follows from the premises, would you not say that it does follow?

I would say that the conclusion does not follow, since the premises themselves contradict each other.

 

[Jimmy Higgins]

Invalid. The five premises cannot all be true at the same time.

If the question were not whether the argument is valid, but whether the conclusion follows from the premises, would you not say that it does follow?

I would say that the conclusion does not follow, since the premises themselves contradict each other.

Valid =/ sound for this, which I think is the issue at hand. The argument is valid, but it is also stupid, full of it, and redonkulous... but it is still "valid", from a very specific definition of the word 'valid'.

 

[Speakpigeon]

I would say that the conclusion does not follow, since the premises themselves contradict each other.

Valid =/ sound for this, which I think is the issue at hand. The argument is valid, but it is also stupid, full of it, and redonkulous... but it is still "valid", from a very specific definition of the word 'valid'.

The question is explicitly whether you consider the argument valid.

Not whether some self-proclaimed specialist told you it was valid.

I would hope you don't go in life without your own personal opinion on the validity of arguments generally.
EB

 

[Angra Mainyu]

Invalid. The five premises cannot all be true at the same time.

If the question were not whether the argument is valid, but whether the conclusion follows from the premises, would you not say that it does follow?

I would say that the conclusion does not follow, since the premises themselves contradict each other.

How would the fact that the premises contradict each other preclude the conclusion from following?


P1: If A, then B.
P2: A.
Conclusion: B.

That follows:
Now,


P1: If A, then B.
P2: A.
P3: ¬A.

Conclusion: B (from P1 and P2).

 

[Speakpigeon]

Invalid. The five premises cannot all be true at the same time.

If the question were not whether the argument is valid, but whether the conclusion follows from the premises, would you not say that it does follow?

I would say that the conclusion does not follow, since the premises themselves contradict each other.

I understand, as it is rather apparent, that you have a sustained interest and some serious practice in mathematics generally. How come you don't abide by any of the definitions of validity current in mathematical logic? Are you even aware of the fact?
EB

 

[fast]

I would say that the conclusion does not follow, since the premises themselves contradict each other.

Valid =/ sound for this, which I think is the issue at hand. The argument is valid, but it is also stupid, full of it, and redonkulous... but it is still "valid", from a very specific definition of the word 'valid'.

The question is explicitly whether you consider the argument valid.

Not whether some self-proclaimed specialist told you it was valid.

I would hope you don't go in life without your own personal opinion on the validity of arguments generally.
EB

Wait, you actually thinks it’s a function of opinion?

I might consider the following argument sound:
P1: If a whole number is even, then the whole number is divisible by two.
P2: A whole number is even
P3: no dogs bark
Therefore, a whole number is divisible by two

And my reasoning might be that the truth remains despite the irrelevant third premise, but an arguments soundness is an objective matter that can be tested for accuracy.

Is validity so different from soundness that while an arguments soundness is an objective matter, validity is not, or do you also hold soundness to also being a function of subjective opinion?

How much money you have in your bank accounts, how old you are, and whether it’s indeed true you prefer vanilla over chocolate are all objective matters. Not validity, I now see, but what say you on soundness?

 

[DBT]

Invalid. The conclusion doesn't necessarily follow from the premises.

The conclusion follows necessarily from the premises (maybe you misread?): From P3 and P5, it follows that the next U.K. Prime Minister will not be Jeremy Hunt. From "the next U.K. Prime Minister will not be Jeremy Hunt" and P4, it follows that the next UK Prime Minister will be Boris Johnson.

Maybe I am misreading it, but I cannot see where it either says or implies that "the next U.K. Prime Minister will not be Jeremy Hunt"

It would be clearer if it included ''...not be Jeremy Hunt''


P1 - Jeremy Corbyn is not Boris Johnson;
P2 - Boris Johnson is not Jeremy Hunt;
P3 - Jeremy Hunt is not Jeremy Corbyn;
P4 - The next U.K. Prime Minister will be either Boris Johnson or Jeremy Hunt;
P5 - The next U.K. Prime Minister will be Jeremy Corbyn;
C - Therefore, the next U.K. Prime Minister will be Boris Johnson

 

[Angra Mainyu]

Invalid. The conclusion doesn't necessarily follow from the premises.

The conclusion follows necessarily from the premises (maybe you misread?): From P3 and P5, it follows that the next U.K. Prime Minister will not be Jeremy Hunt. From "the next U.K. Prime Minister will not be Jeremy Hunt" and P4, it follows that the next UK Prime Minister will be Boris Johnson.

Maybe I am misreading it, but I cannot see where it either says or implies that "the next U.K. Prime Minister will not be Jeremy Hunt"

It would be clearer if it included ''...not be Jeremy Hunt''


P1 - Jeremy Corbyn is not Boris Johnson;
P2 - Boris Johnson is not Jeremy Hunt;
P3 - Jeremy Hunt is not Jeremy Corbyn;
P4 - The next U.K. Prime Minister will be either Boris Johnson or Jeremy Hunt;
P5 - The next U.K. Prime Minister will be Jeremy Corbyn;
C - Therefore, the next U.K. Prime Minister will be Boris Johnson

I am deriving that the next U.K. Prime Minister will not be Jeremy Hunt from P5 "The next U.K. Prime Minister will be Jeremy Corbyn" and P3 " Jeremy Hunt is not Jeremy Corbyn". But you're right it's somewhat unclear as I mentioned in this post, because one needs the premise that Jeremy Corbyn will not be Jeremy Hunt, while one only has that Jeremy Corbyn is not Jeremy Hunt (by P3). But what if Jeremy Corbyn were to become Jeremy Hunt? I think some reasonable assumptions about language (including proper names) and identity preclude that, but they are needed, so this muddies the waters.

 

[DBT]

Maybe I am misreading it, but I cannot see where it either says or implies that "the next U.K. Prime Minister will not be Jeremy Hunt"

It would be clearer if it included ''...not be Jeremy Hunt''


P1 - Jeremy Corbyn is not Boris Johnson;
P2 - Boris Johnson is not Jeremy Hunt;
P3 - Jeremy Hunt is not Jeremy Corbyn;
P4 - The next U.K. Prime Minister will be either Boris Johnson or Jeremy Hunt;
P5 - The next U.K. Prime Minister will be Jeremy Corbyn;
C - Therefore, the next U.K. Prime Minister will be Boris Johnson

I am deriving that the next U.K. Prime Minister will not be Jeremy Hunt from P5 "The next U.K. Prime Minister will be Jeremy Corbyn" and P3 " Jeremy Hunt is not Jeremy Corbyn". But you're right it's somewhat unclear as I mentioned in this post, because one needs the premise that Jeremy Corbyn will not be Jeremy Hunt, while one only has that Jeremy Corbyn is not Jeremy Hunt (by P3). But what if Jeremy Corbyn were to become Jeremy Hunt? I think some reasonable assumptions about language (including proper names) and identity preclude that, but they are needed, so this muddies the waters.

It appears rather convoluted, yet it may possibly work when you put like that.

Plus it appears to depend on information and assumptions that are extraneous to the premises.

 

[Learner]

I got it wrong again

 

[Angra Mainyu]

Maybe I am misreading it, but I cannot see where it either says or implies that "the next U.K. Prime Minister will not be Jeremy Hunt"

It would be clearer if it included ''...not be Jeremy Hunt''


P1 - Jeremy Corbyn is not Boris Johnson;
P2 - Boris Johnson is not Jeremy Hunt;
P3 - Jeremy Hunt is not Jeremy Corbyn;
P4 - The next U.K. Prime Minister will be either Boris Johnson or Jeremy Hunt;
P5 - The next U.K. Prime Minister will be Jeremy Corbyn;
C - Therefore, the next U.K. Prime Minister will be Boris Johnson

I am deriving that the next U.K. Prime Minister will not be Jeremy Hunt from P5 "The next U.K. Prime Minister will be Jeremy Corbyn" and P3 " Jeremy Hunt is not Jeremy Corbyn". But you're right it's somewhat unclear as I mentioned in this post, because one needs the premise that Jeremy Corbyn will not be Jeremy Hunt, while one only has that Jeremy Corbyn is not Jeremy Hunt (by P3). But what if Jeremy Corbyn were to become Jeremy Hunt? I think some reasonable assumptions about language (including proper names) and identity preclude that, but they are needed, so this muddies the waters.

It appears rather convoluted, yet it may possibly work when you put like that.

Plus it appears to depend on information and assumptions that are extraneous to the premises.

It depends on how one interprets the premises. Natural languages, like English, are ambiguous, and the use of the identity relation in the premises has different interpretations. In short, I think it wasn't a good example to begin with - not that this belongs in the "Political Discussions" forum.

 

[Speakpigeon]

Maybe I am misreading it, but I cannot see where it either says or implies that "the next U.K. Prime Minister will not be Jeremy Hunt"

It would be clearer if it included ''...not be Jeremy Hunt''

P1 - Jeremy Corbyn is not Boris Johnson;
P2 - Boris Johnson is not Jeremy Hunt;
P3 - Jeremy Hunt is not Jeremy Corbyn;
P4 - The next U.K. Prime Minister will be either Boris Johnson or Jeremy Hunt;
P5 - The next U.K. Prime Minister will be Jeremy Corbyn;
C - Therefore, the next U.K. Prime Minister will be Boris Johnson

The premises certainly don't imply that the next Prime Minister will be Boris Johnson. This is enough to decide it is obviously invalid, contrary to what mathematical logic says since 1853.


I guess I didn't have to use the future "will be". The argument reads just as well with "The next ... is" and without the ambiguity:

P1 - Jeremy Corbyn is not Boris Johnson;
P2 - Boris Johnson is not Jeremy Hunt;
P3 - Jeremy Hunt is not Jeremy Corbyn;
P4 - The next U.K. Prime Minister is either Boris Johnson or Jeremy Hunt;
P5 - The next U.K. Prime Minister is Jeremy Corbyn;
C - Therefore, the next U.K. Prime Minister is Boris Johnson

But, that's not necessary because it doesn't change the result.
EB

 

[Speakpigeon]

I got it wrong again

Well, you're not the only one and you at least you seem to have realised your mistake! Think of the millions of mathematicians who would insist the argument is valid and never budge from that, somewhat like AM here.
EB

 

[Speakpigeon]

So, for now it's really only two votes for "Valid". Against at least five for either "Not valid" or "Doesn't make sense".

Same as elsewhere.
EB

 

[Angra Mainyu]

So, for now it's really only two votes for "Valid". Against at least five for either "Not valid" or "Doesn't make sense".

Same as elsewhere.
EB

Three for "valid", two for "invalid". Two vs. two if you don't count Learner, who is not saying it's invalid (he said he got it wrong again). But this case is particularly obscure because of the future thing, since the negation of identity in the premises has a temporal as well as an non-temporal interpretation.

 

[Speakpigeon]

So, for now it's really only two votes for "Valid". Against at least five for either "Not valid" or "Doesn't make sense".

Same as elsewhere.
EB

Three for "valid", two for "invalid". Two vs. two if you don't count Learner, who is not saying it's invalid (he said he got it wrong again).

LOL. You do sound desperate.

But this case is particularly obscure because of the future thing, since the negation of identity in the premises has a temporal as well as an non-temporal interpretation.

Particularly obscure?! Whoa. You sure sound desperate.

No. The argument is perfectly understandable. No one took into account the completely fictional notion that Jeremy Corbyn could become Boris Johnson.

And it's only two "Valid" against the three "Not valid" and the three "Doesn't make sense"..

And it's the same elsewhere.

And your own vote for "Valid" is irrelevant because biased by your training at mathematical logic

And Fast doesn't really feel the argument is valid.

Case closed.
EB

 

[Speakpigeon]

And we only have 9 votes casts!

29 visitors didn't vote:

barbos,
BH,
Eldarion Lathria,
Enigma,
fxfriy
Hickdive,
hurtinbuckaroo,
J842P,
jab,
Jarhyn,
Jason Harvestdancer,
Jayjay,
Jimmy Higgins,
Jolly_Penguin,
jonatha,
Keith&Co.,
loose cannon,
Matthewskipt,
Morgan,
Patooka,
Sarpedon,
The AntiChris,
The Colourful Jester,
Tigers!,
Tom Sawyer,
Trausti,
WAB,
ZiprHead,

Come on, people, this is a serious empirical investigation for the public good. There is no correct or incorrect answer. Only votes and all votes count!
EB