Okay. Three quick questions. First, I'm curious if you think your statement put into correct categorical form ("Some monsters are not things that are in my closet") still seems to be true.

Second, does this mean that you think that your earlier example ("Some humans are not females") doesn't imply that any humans exist?

Third, how would you deal with negative particular statements that do imply existence?

First, you are missing the quantifier here. When I add it (as I do above), your four cases don't seem nearly so obvious to me. For instance, now "Some S are not P" doesn't seem to say that the concepts S and P are not united in existence, since it is compatible with "Some S are not P" that "Some S are P." Rather it seems to assert something more definite, that some S-things are not P-things. But for that assertion to be true there must in fact be some S-things.

In other words, you seem to be reading "Some S are not P" as saying there is no SP combo, i.e. you are reading "Some monsters are not things in my closet" as claiming that there are no "monster/thing-in-my-closet" combos. But that is just clearly false. That is the correct interpretation of an E-statement (which we all agree doesn't imply existence), but not of an O-statement.

Second, there is already an interpretation of what S and P are--they are categories (think of a category as being something like a set). Thus, to say that "Some S are not P" is to say that there exists at least one thing that is in the S-category (monster category) that is not also in the P-category (things in the closet category) (at least this is what it means on standard interpretations).

I'm confused...is there a typo here? The first premise looks false any way I read it...

Much of this seems to center on a perceived difference between "not P" and "not-P" (or "non-P"). To elaborate, as in the example from the quoted logic textbook earlier in the thread, some people may perceive a difference between

A = "Every dog is not vicious.", and
B = "Every dog is non-vicious."

One might read A, and understand the word "not" as having the effect of negating the entire sentence. Then

A = "It is not the case that every dog is vicious."
= "There exists a dog which is non-vicious."

Written this way, it is clearly different from B.

Similarly, we could compare

A' = "Some monsters are not things that are in my closet."
B' = "Some monsters are things that are not in my closet."

As above, one might read A' as saying

A' = "It is not the case that some monsters are things that are in my closet."
= "Every monster is a thing that is not in my closet."

In English, the word "not" is generally understood to negate a sentence, so this interpretation seems reasonable to me. With this interpretation, A and B' assert existence, whereas A' and B do not.

From: http://www.logicmuseum.com/cantor/Eximport.htm

Traditional Logic never reads the I proposition as existential and Symbolic Logic must read it as existential in order to have an I proposition. Thus, in Traditional Logic some men are white means that the quality white modifies some cases of man; it does not mean, nor even imply, that there are also some who are not white. Nor does it mean that some white men exist [my emphasis]. To get this said requires an existential proposition, e.g. some white men are, where there is no strict logical predicate. The point of the I proposition is not the existence of some men but the whiteness of some men. (Wade 1955)

Now the above citation doesn’t mention the (E) proposition, but I think it goes far enough that we can infer that if (I) doesn’t mean ‘some -> exist’ then neither would (E).

edit:

Also from the article:

Brentano argued that every categorical proposition can be translated into an existential one without change in meaning and that the "exists" and "does not exist" of the existential proposition take the place of the copula. He showed this by the following examples:

The categorical proposition "Some man is sick", has the same meaning as the existential proposition "A sick man exists" or "There is a sick man".

The categorical proposition "No stone is living" has the same meaning as the existential proposition "A living stone does not exist" or "there is no living stone".

The categorical proposition "All men are mortal" has the same meaning as the existential proposition "An immortal man does not exist" or "there is no immortal man".

The categorical proposition "Some man is not learned" has the same meaning as the existential proposition "A non-learned man exists" or "there is a non-learned man".

Modern logic depends on precisely this idea...

As a follow-up to my recent post, we can now see clearly the flaw in McCall's reasoning. From the above quote, according to McCall,

"Every dog is not vicious."
= it is FALSE that "Every dog is vicious."
= "Some dog is not vicious."

But by that same reasoning,

"Some dog is not vicious."
= it is FALSE that "Some dog is vicious."
= "No dog is vicious."

But I am sure that even McCall does not believe this, since it directly violates the classical square of opposition.

In the end, then, only by interpreting "not vicious" as "non-vicious" can we be consistent with the classical assumption that "Some S are not P" and "All S are P" are negations of one another. Then, if we are consistent, we must interpret "Every S is not P" as "Every S in non-P", which is the same as "No S is P".

There’s a difference between:

(p): No object can exceed the speed of light.
(q): Every object cannot exceed the speed of light.

(p) is a universal proposition.
(q) is an enumerative totality, i.e. a particular proposition.

Einstein didn’t run around clocking the speed of all the objects in the universe to arrive at his conclusion (p). It’s a universal postulate that applies to any particular object in the universe and/or every object in the universe.

What’s getting lost in all this, IMO, is why universal propositions are separated from particular propositions. When I say,
(r) all swan is white.
I don’t mean,
(s) all swanS are white.

In this instance (r) is designating the proposition as universal. That is, I’m saying there is something in the nature of swan that only allows swan to be susceptible to the color white. With (s), I’m just describing an enumerative totality and the proposition is particular. What I mean with (s) is that I’ve taken tally of all the swans and they’re all white.

So what’s getting lost is that when I say, “x is swan, therefore x is white,” if I’m working off of (s) there’s really no advance in knowledge, because that x is part of the totality I used to conclude (s). On the other hand, if I’m using (r) then there is an advance in knowledge because I didn’t know beforehand that that swan is white, but instead arrived at the conclusion deductively.

Another way to look at it is if I'm the only human alive, then it is true that ‘every human is not female’, but that isn't a universal claim as to the nature of human, it's just a particular enumerative assessment. That seems to me why we shouldn't equivocate 'no S is P' with 'every S is not P'.

A google search for "enumerative totality" gives 7 results, the top two being books on Vedic religious terminology. Can you explain using more standard language what you mean by this?

Edit - I realize the Einstein comment is connected, but a definition would be helpful I think.

I am doubtful that this reference is accurate. IEP, SEP, and my logic textbooks all say differently. It could be correct, or it could just be that traditional logic wasn't consistent on this issue, but I would have to look at the full references to check.

If that means, “some monster IS NOT a thing that is in my closet,” that seems okay. But if it means, “some monster is not a thing that IS in my closet,” that seems ambiguous.

It could, if I’m asserting something but it may not be if I’m just denying what the (A) proposition is asserting. So if (A) is ‘all humans are female’, I can just use the definition of human as male and female and assert ‘some human is not female’, without really asserting the existence of any particular human. It just depends on the context, I guess.

If you mean something like ‘McCain is not President’, I’d contradict with ‘McCain is President’. I could probably say, “no president is that man, McCain,” if I need to. I’m just not sure what you’re asking for, though.

If I say, “some moon is not in orbit around Venus,” I don’t take that as implying there is some moon in existence that is not in orbit around Venus. To me, it just means there’s not a moon in orbit around Venus, i.e. there's not some Venus-moon.

Well, if there are roses and no roses are red, said roses are non-red, i.e. no rose is red.

Just a countable sum. It’s basically the difference between a universal like, ‘Freshmen Class’ which isn’t indicative of individual students and the particular ‘freshmen class’ taken as the sum of students in the class.

I found this on google docs:

(A): ∀x (Sx → Px) ∧ ∃x Sx
(E): ∀x (Sx → ¬Px)
(I): ∃x (Sx ∧ Px)
(O): ∃x (Sx ∧ ¬Px) ∨ ¬∃x Sx

(O): Either some monster is not in my closet OR there is not some monster. That seems to work with (A) and (O), no?

Ok. Again, this distinction looks easy to make by a careful choice of predicates. Can you explain why not?

In any case, jason1990's posts #103 and #105 seem to settle that we must give existential import to the "Some S is Not P" construction. Barring a substantiative counter-argument, I think we should take that as the correct position.

That's how I would read it.

I started by addressing each point individually, but found myself saying things that have already been said many times. So instead here's some general advice--stop trying to do logic straight from the English language.

Don't treat the A, E, I, and O statements as if they were statements in the English language. They are not. They are formulas in a logical system with specific rules about how they should be formed and what inferences involving them are valid. You keep on appealing to the meaning of sentences in English to figure out what inferences are valid in this logic. But that is backwards. We first fully interpret our logical system and then see if we can translate a sentence in English into that logical system.

So when I ask you what implications an O-statement has, I'm not asking you to figure out the meaning or implications of an O-statement in English, rather I am asking about what kind of logical system you are using. That is, are you using a modern version of the Square of Opposition, where O-statements are understood as implying existence? Or do you prefer the traditional versions where the A-statement also implies existence?

If you want to reject both of these versions, i.e if you understand the categorial statements in a non-standard way, then you are developing your own logical system. That is fine, but then I just don't know what inferences are valid in that system and so I can't judge whether the inferences you are making are correct.

I don't know why not. How do you distinguish between a universal and a particular?
Except…
… it doesn’t follow that if (O) is true then (I) is false. Consequently, it doesn’t follow that (E) is true, either.

I’m not trying to invent a new system. All I’ve been doing lately is giving examples as to why I reject the notion of an existential import. I reason:

If ‘no thing is in my closet’ is true, then ‘some monster is not in my closet’ is true.
Therefore, an existing subject is neither implied nor required to affirm (O) is true.
Therefore, “a modern version of the Square of Opposition, where O-statements are understood as implying existence,” seems unfounded, false or limited in scope.
So, I reject that version and stick with the traditional version.

Exactly, that's the entire point! This is why we must give existential import to [O]. If we don't, we are either inconsistent or violate the classical square of opposition a la McCall. (Put another way: giving existential import to [O] simply amounts to enforcing the intuition you stated in the quote above.)

Perhaps I'm missing something, but this seems settled to me without new arguments.

But this is my point. Your examples are all based on your intuitive understanding of the meaning of certain phrases in English. Now, I disagree with some of your claims there, but ultimately this is not a discussion about the meaning of statements in English. Rather, it is about providing a semantics for Aristotelian categorial logic.

You've stated a preference for a semantics where both the I and O statements can be true even when there is no S. Fine. So just tell me the truth-conditions for the statements: "Some S are P" and "Some S are not P." More specifically, when there is no S, but I is true, how can I tell that it is true? Or is it always true in the empty case?

For example, "Some unicorns are mammals." Presumably, there are no unicorns. So is this claim true or false? How do we tell?

The bolded is not the right question. You should be asking yourself, if "No unicorns are mammals" is true, then is it possible for "Some unicorns are not mammals" to be false. And here there isn't a single answer. Rather, we just have an ambiguous statement.

By "Some unicorns are not mammals" you could mean something like "Some unicorns exist and they are not mammals." This is the standard interpretation and would lead to the standard conclusions about the Square of Opposition.

Alternatively, you could mean something like, "Not every unicorn is a mammal" where this is not meant to assert that a unicorn exists. Of course, to do this we would have to also change our understanding of the A statement to something more like the strict conditional. This would mean that the A statement could be false even if all existing unicorns are mammals if there are possible worlds where there are unicorns that are not mammals. Similarly, even if there are no unicorns, if there are possible unicorns that are not mammals, then the A claim would be false. So the negation of A (on this interpretation) would not imply that a unicorn actually exists. Instead, it would be something like, "Possibly there exists a unicorn that is not a mammal." Correspondingly, the I statement would be understood as something like, "Possibly there exists a unicorn that is a mammal."

So ultimately I don't think we can settle this issue by just looking at our intuitions about the English language. Instead, we have to settle it in terms of what logical systems we are working in. But this is primarily a matter of choice. I don't have to say that my version is right and yours is wrong. I can prefer my version as richer and as more accurately preserving the inferences of natural language, but that doesn't mean that your logic is unsound. So I think that inventing a new system is exactly what you are doing, but that is fine--I'll work with it as long as you can tell me what it is.

Not to ignore your other points, but this is kind of the heart of the matter, IMO. I think of what I’m doing as explaining an old system (according to my understanding of said system) rather than inventing a new logic, but for all intents, that’s not a big deal. However, it doesn’t appear I’m making any sort of progress in doing so, anyway. I think there’s just some fundamental difference between how we conceive of the Division of Categoricals that’s preventing any sort of agreement. Primarily, I think our interpretation of ‘some’ differs. So, as a sort of last-ditch attempt:

In Aristotelian logic, the universal (A) proposition is saying that included in the comprehension of the concept ‘unicorn’ is ‘mammal’, i.e. mammal is a note of unicorn or unicorn is denoted as mammal.

The (I) proposition is the particular extension of that universal comprehension of unicorn. Meaning that what is true of the subject universally (as denoted in the comprehension of the subject) is likewise true of the subject in particular. In other words that which is universally affirmed of a subject is affirmed of every particular that falls under that subject.

My impression is you, et al, are treating (A) as an empirical or inductive conclusion, like we’d say, “all swans are white,” but that’s not the kind of quantity (A) represents in Aristotelian logic. “All swans are white,” if we arrive at that proposition empirically, is actually an (I) proposition. In other words, it’s just a collective of particulars, not a universal proposition. So, when I’m saying ‘some’ I’m not implying that it’s a numerical quantity of ‘every’ or ‘all’, but instead ‘some’ is an extension of the universal into particularity, that is, an extension from a universal nature that cannot accept numerical quantity into a particular nature than can accept numerical quantity, particulars and/or singulars.

The above holds for the negative propositions as well. So, that which is universally denied of a subject is denied of any particular under that subject. In other words, the predicate does not extend over the subject, nor does it become part of the comprehension of the subject either in the universal or when that universal is extended to the particular. Then, like (I) is an extension into particularity of the universal (A); (O) is the same with (E). As a derivative of (E), what (O) means is: no [particular] man is a rational being. Not ‘some man’ as a part of the empirically collective ‘every man’.

So, while I realize such a meaning of ‘some’ is somewhat counter-intuitive, or maybe highly counter-intuitive for someone with a mathematical reasoning background, it doesn’t seem to me incomprehensible.

Beyond all that, though, I think another area of confusion is that aside from the logical inferences found in the square of opposition, the above is pretty much where Aristotelian logic ends. Formal deductive logic, or what they used to call ‘prior analytics’, deals only with the correct methodology, validity and the logical reasoning process, not the empirical aspect of whether things exist which we generally need for soundness. That’s inductive reasoning or what they used to call ‘major logic’ or ‘posterior analytics’. Now, I’m not familiar enough with the inner workings of modern logic, but the impression I’m getting from you and others itt is that the deductive and inductive processes are merged, intertwined or integral with the formation of propositions in modern logic. And so, ‘∃’ which has existential import, really has no place in the formation of my propositions, even though it sounds like we’re saying the same thing. As I said above, to me, ‘some’ designates a proposition as the particular extension of the universal, not an empirical quantity. It could be the case that, “some… are” or “some… are not,” but Aristotelian logic isn’t saying some are or are not, in that existential sense, but more as a relation. So, if your logic cannot remove the existential notations and mine can’t accept them…

Here's the issue from my perspective. While I think your translation of these statements is incorrect, I'm mainly interested in you putting whatever it is you want to say into some kind of familiar logical form so that I can see what inferences you mean to be using to infer your conclusion. Simply putting it into the familiar categorial form isn't helpful as that doesn't disambiguate your intended meaning from at least three other interpretations of these forms that have been proposed in this thread, all of which have different inferences.

I've proposed the strict conditional as the logical form of the universal statements that you're interested in here. Is that acceptable to you?

I also wanted to add that while I am certainly no scholar of Aristotle, as far as I can tell from a casual perusal your interpretation of his logic (or of the logic that becomes known as "Aristotelian logic") is at best controversial.

The first thing to say is that the standard view is as I originally reported--that in medieval and Aristotelian logic it is claimed of all categorical statements that in order for them to be true the subject term must refer. We see this in IEP, in wiki, in standard intro logic textbooks like Copi/Cohen and A Logic Book. Other texts also seem to say this, such as the Blackwell Companion to Philosophical Logic in its article on "History of Logic: Medieval" where it asserts that the I statements carries existential import in Aristotelian logic.

However, SEP is an outlier here, as the author of the article on the Square of Opposition argues that only the positive statements (A and I) should be regarded as having existential import (you can see Parsons full argument here).

The fullest discussion I can find online of this topic is from this article by Scott Carson. Here he argues that statements such as "Socrates is sick" should be understood as implying that Socrates exists. Here the strongest textual evidence he uses is this passage from the Categories:

While this refers to a sentence with a singular subject, Carson argues that this applies as well to general terms. Anyway, since we seem to have moved on from the original topic to this more general discussion of medieval logic, I thought I'd make the case for my view more explicitly.

Also, I think the main lesson here should be that trying to do logic using Aristotle instead of modern propositional logic is to do logic with both hands tied behind your back. The disagreement that bunny and I had with your original argument is so clear in modern logic that the issue could have been resolved immediately.

I’m not sure. What started all this was my proposition, “no thing is possibly in existence,” or “some thing cannot possibly exist.” So, what exactly am I saying, or can I even say what I’m saying below?

1. ⟡(Big Bang’s singularity → necessarily, no thing is in existence.)
2. ⟡(Big Bang’s singularity → necessarily, some thing is not in existence.)
3. ⟡(Big Bang’s singularity → possibly, no thing is in existence.)
4. ⟡(Big Bang’s singularity → possibly, some thing is not in existence.)

As an aside, I’ve been reading a bit on the tense operators (F, P, G & H) and I think they’ll better serve what I’m trying to accomplish. (Once I figure out how to properly form propositions in modern logic, that is.)

All I know is what I was taught from a Jesuit teacher I had in high school. I’m pretty sure he learned it through seminary and I recall him being fairly adamant about how modern (secular) teachings deviated from the Aristotle-Aquinas tradition. So, I’m not really sure what’s correct. I’m just a little surprised that traditional logic is considered antiquated or outmoded, since I didn’t learn it all that long ago.

Anyway, if you’re interested, I found a download version of one of my old logic textbooks:

An Introduction to Logic by Jacques Maritain
http://www.archive.org/details/AnInt...ionToLogic_880

(It’s a scanned, but readable copy. However, you need to download the pdf file in order to rotate the pages.)

Ok, I'm sorry, but are you now willing to cede that this post was pure revisionist history? E.g....

1. If you really understood even the first thing about Bohmian QM, you would be steeped in mathematical reasoning.
2. Unless your "atheist-looking-for-answers" phase was in your pre-teens, it obviously did not precede notable exposure to the Gospels.

...I mean, seriously. Seriously. That post did not describe a real-life timeline. Just admit it.