# All; therefore some?



## Thunal33 (Oct 22, 2018)

Thunal33 said:


> I took logic class and the professor said so.


I think it's because "All A are B" is like an if then statement where if something is A then that thing is B. If there isn't anything in the class A then All A are B is an if then statement with a false hypothesis which is true.


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## Scoobyscoob (Sep 4, 2016)

Speakpigeon said:


> I certainly didn't make any tautological statement because I didn't make any statement. I asked about the validity of the arguments. They are all valid, you say, good. This is what I asked.
> EB


Statement, argument - I was using those two words interchangeably. You made a tautological argument, so you made a non-argument, is the point I was making. In other words, your argument is logically valid because it is tautologous, so no new truth is revealed from such an argument.

Logical arguments hold value on the condition that such an argument reveals a truth of some kind. A redundant argument does no such thing.


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## xwsmithx (Jan 17, 2017)

Gesælige Cristesmæsse said:


> Oh right, in that case then yeah, 100% valid. If all A's have F trait, then if you single out certain members of that group then they'll have that trait too. Otherwise not all A's would have F.
> 
> Edit: Although now that I think about it, I guess it's more an argument of semantics. If you think of "some F's" as singling out members of the group and asking if they have F trait, then rationally they would do. But if "all" =/= "some" then the answer would be no, because with that interpretation _only_ "some" A's would have it, and not "all". But I think of it as "all A's have F, so if you single out a selection of A's then those members will have the trait".


I think this is the best answer. By definition, if all A's have F, then certainly any subset of A's would have F, but if you take the statement on its own, "Some A's have F," the _implication_ is there that _not all_ A's have F, which in your scenario would not be true. So then the statement, "Some A's have F" might not be _false_ but it might well be misleading. All colas have food coloring added to make them brown (I think they're green naturally), but if a soda company said in an advertisement, "SOME colas have food coloring added to make them brown," the implication clearly would be that their colas DON'T have food coloring added, which of course would be false.

More interesting scenario: How many exceptions does it take for "all" to become "some"? It's generally accepted as a trait of mammals to have hair, but some rare exceptions, even among humans, are completely hairless. So when does it become not true that all mammals have hair as a general rule?


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## Speakpigeon (Jul 31, 2019)

Euclid said:


> Asking if some of them will have a lounge bar would be some kind of misunderstanding, since that would entail an existential commitment.


Yet, like Aristotle, most people would ask if some of the flats in a block being planed will have, for example, three bedrooms.

The Pope could probably say for example that some of the gods people believe in don't exist at all. So, where would be the mistake here exactly?

It seems to me that mathematicians don't just disagree with Aristotle but with just about everybody outside people trained in mathematical logic.
EB


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## Speakpigeon (Jul 31, 2019)

Thunal33 said:


> I took logic class and the professor said so.


I guessed as much.
EB


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## Speakpigeon (Jul 31, 2019)

SantaScoob said:


> Statement, argument - I was using those two words interchangeably. You made a tautological argument, so you made a non-argument, is the point I was making. In other words, your argument is logically valid because it is tautologous, so no new truth is revealed from such an argument.
> 
> Logical arguments hold value on the condition that such an argument reveals a truth of some kind. A redundant argument does no such thing.


Sure, but the question was only about validity.
EB


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## Scoobyscoob (Sep 4, 2016)

Speakpigeon said:


> Sure, but the question was only about validity.
> EB


Well okay, your argument is valid but not a cogent argument.


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## Euclid (Mar 20, 2014)

Speakpigeon said:


> Yet, like Aristotle, most people would ask if some of the flats in a block being planed will have, for example, three bedrooms.
> 
> The Pope could probably say for example that some of the gods people believe in don't exist at all. So, where would be the mistake here exactly?
> 
> ...


I don't think any of them disagree with Aristotle, as in thought any of his syllogisms were erroneous, but rather that they want to be able to reason about things that can't be done with Aristotle's logic alone. Anyways this is the essential problem with Aristotle (from the wikipedia article I linked previously):


> It is claimed Aristotle's logic system does not cover cases where there are no instances. Aristotle's goal was to develop "a companion-logic for science. He relegates fictions, such as mermaids and unicorns, to the realms of poetry and literature. In his mind, they exist outside the ambit of science. This is why he leaves no room for such non-existent entities in his logic. This is a thoughtful choice, not an inadvertent omission. Technically, Aristotelian science is a search for definitions, where a definition is 'a phrase signifying a thing's essence.'... Because non-existent entities cannot be anything, they do not, in Aristotle's mind, possess an essence... This is why he leaves no place for fictional entities like goat-stags (or unicorns).


So "flats in a block being planned" cannot be reasoned about using Aristotle's logic alone. This can be seen in the application of barbari:

All M are P
All S are M
__________
some S are P

which translated into predicate logic:
∀x: Mx⇒Px
∀x: Sx⇒Mx
∃x:Sx
∃x:Mx
∃xx
___________
∃x: Sx⇒Px

If we try to apply this by assigning S= flats in a block being planned, then we immediately run into the problem that the flats don't yet exist, however the existence of at least some is implied: ∃x:Sx. If we drop the premises with existential commitment then the conclusion no longer follows. Essentially mathematical logicians want to be able to make arguments without existential commitments.


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## Speakpigeon (Jul 31, 2019)

Euclid said:


> I don't think any of them disagree with Aristotle, as in thought any of his syllogisms were erroneous, but rather that they want to be able to reason about things that can't be done with Aristotle's logic alone. Anyways this is the essential problem with Aristotle (from the wikipedia article I linked previously):
> 
> So "flats in a block being planned" cannot be reasoned about using Aristotle's logic alone. This can be seen in the application of barbari:
> 
> ...


It is Barbara, not "barbari" as you say.

And the last line is wrong...

All M are P
All S are M
__________
All S are P (and not "some S are P" as you say)

The rest is irrelevant mathematical logic.

If you cannot argue from what Aristotle said, you cannot argue. If all you can do is use mathematicians' wrong interpretation of Aristotle's syllogisms, then you cannot argue.

It would be easy, though. Give me any argument couched in Aristotle's syllogistic and explain in good English why it is absurd.

Here is a possible example:



> All planed flats will be for rent;
> Some planed flats will have three bedrooms;
> Therefore, some rented flats will have three bedrooms.


EB


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## Euclid (Mar 20, 2014)

Speakpigeon said:


> It is Barbara, not "barbari" as you say.


Barbara is a different syllogism (A-A-A) 
Barbari is (A-A-I)
A = Universal affirmative = All P are Q = (∀x: Px⇒Qx) ∧ (∃x: Px) ∧ (∃x: Qx)
I = Particular affirmative = Some P are Q = (∃x: Px⇒Qx) ∧ (∃x: Px) ∧ (∃x: Qx)
Since we have particular affirmative in the conclusion, the syllogism was named bArbArI with the I at the end, like all the syllogisms have the vowels A E I O in their names to make it easy to remember them according to the table of square oppositions:
https://en.wikipedia.org/wiki/Square_of_opposition



Speakpigeon said:


> And the last line is wrong...
> 
> All M are P
> All S are M
> ...


For Barbara yes, but I'm talking about Barbari.



Speakpigeon said:


> The rest is irrelevant mathematical logic.


It's the translations in mathematical logic for comparison and for elucidation why Aristotle's logic cannot express arguments lacking of existential commitments.



Speakpigeon said:


> If you cannot argue from what Aristotle said, you cannot argue. If all you can do is use mathematicians' wrong interpretation of Aristotle's syllogisms, then you cannot argue.


Why is it wrong though? 



Speakpigeon said:


> It would be easy, though. Give me any argument couched in Aristotle's syllogistic and explain in good English why it is absurd.


That's not the dispute though, but rather that mathematical logic is more expressive.


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## tanstaafl28 (Sep 10, 2012)

Everything, therefore nothing.


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## Speakpigeon (Jul 31, 2019)

Euclid said:


> Barbara is a different syllogism (A-A-A)
> Barbari is (A-A-I)
> A = Universal affirmative = All P are Q = (∀x: Px⇒Qx) ∧ (∃x: Px) ∧ (∃x: Qx)
> I = Particular affirmative = Some P are Q = (∃x: Px⇒Qx) ∧ (∃x: Px) ∧ (∃x: Qx)
> ...


Sorry, I don't understand what is your point, if any. If you are unable to explain your point in plain English, then you haven't argued anything.
EB


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