Register to reply

Can someone explain what Bertrand Russell is saying on Aristotle's logic?

by Khichdi lover
Tags: aristotle, syllogisms
Share this thread:
Khichdi lover
#1
Oct8-11, 06:57 AM
P: 11
Bertrand Russell in A History of Western Philosophy :-
Aristotle's Logic
Let us begin with the two statements "Socrates

is a man" and "all Greeks are men." It is necessary to make a sharp
distinction between these two, which is not done in Aristotelian logic.
The statement "all Greeks are men" is commonly interpreted as
implying that there are Greeks, without this implication, some of
Aristotle's syllogisms are not valid. Take for instance-
"All Greeks are men, all Greeks are white, therefore some men
are white." This is valid if there are Greeks, but not otherwise. If
I were to say-:
"All golden mountains are mountains, all golden mountains are
golden, therefore some mountains are golden." my conclusion would
be false, though in some sense my premisses would be true. If we are
to be explicit, we must therefore divide the one statement "all Greeks
are men" into two, one saying "there are Greeks," and the other
saying "if anything is a Greek, it is a man." The latter statement is
purely hypothetical, and does not imply that there are Greeks.
The statement "all Greeks are men" is thus much more complex
in form than the statement "Socrates is a man." "Socrates is a man"
has 'Socrates" for its subject, but "all Greeks are men" does not have
"all Greeks" for its subject, for there is nothing about "all Greeks"
either in the statement "there are Greeks" or in the statement "if any-
thing is a Greek it is a man."
I want to know whether I have understood this right.
We shouldn't be saying , "All Greeks are men,all greeks are white,therefore some men are white".

So we should be saying "there are Greeks, if anything is Greek it is a man. All Greeks are white.Therefore some men are white " ?

Or we should also replace the statement all greeks are white by "if anything is Greek it is white" ?


Further, what kind of statement is the statement "if anything is Greek it is a man" ? Does it fall under subject predicate form or is it different. if it does fall under subject predicate form ,what is the subject of it. Bertrand Russell says that "all Greeks" is not the subject of it.
I could understand that "there are Greeks" doesn't have "all Greeks" as a subject but I am having trouble in understanding what is subject of "if anything is Greek it is a man"
Phys.Org News Partner Science news on Phys.org
'Office life' of bacteria may be their weak spot
Lunar explorers will walk at higher speeds than thought
Philips introduces BlueTouch, PulseRelief control for pain relief
Chuck V
#2
Oct13-11, 02:45 AM
P: n/a
Quote Quote by Khichdi lover View Post
Bertrand Russell in A History of Western Philosophy :-
Aristotle's Logic


I want to know whether I have understood this right.
We shouldn't be saying , "All Greeks are men,all greeks are white,therefore some men are white".

So we should be saying "there are Greeks, if anything is Greek it is a man. All Greeks are white.Therefore some men are white " ?

Or we should also replace the statement all greeks are white by "if anything is Greek it is white" ?


Further, what kind of statement is the statement "if anything is Greek it is a man" ? Does it fall under subject predicate form or is it different. if it does fall under subject predicate form ,what is the subject of it. Bertrand Russell says that "all Greeks" is not the subject of it.
I could understand that "there are Greeks" doesn't have "all Greeks" as a subject but I am having trouble in understanding what is subject of "if anything is Greek it is a man"
You're largely right on both points. Russell is in fact advocating for part of your first point. But while yes, we could replace 'All Greeks are white' with 'if anything is Greek' but we don't have to, and Russell's not saying that we must. What he is saying (and this is why he rewrites it with the 'if anything is Greek') is that we ought to recognize that statements involving the words 'All, Some, No' have quantifiers in them, represented by those words. And a statement involving universal quantification e.g. 'All F' does not imply existential quantification, which is present in sentences like 'There are Fs.' Here's a little thought I just had about this, and I hope I'm not wrong about it, but I think it's a decent illustration of Russell's idea. "All unicorns have horns." To my eyes, that sentence is very much true. But just as true is that "There are no unicorns." I think these truths are wholly compatible, and the fact that they are, gives us reason to believe that Russell's points about statements involving quantification are pretty good.

In response to your second question, I think that most philosophers today do not believe that " 'If,then' statements," or "conditionals" as they're called, are of the subject-predicate form. I don't think the sentence we've been discussing about Greeks does what a subject-predicate statement does, I don't think it really attributes a property to a subject. But consider the following:

"If anything is Greek, then it is a man' is of course a compound statement made up of 'Anything is Greek' and 'it is a man' with the conditional connective sitting between them. Both of the components might be interpreted as subject-predicate propositions. We might say that both the first and second components have the same subject "Anything ('it.')" So I imagine that if we were to interpret this conditional as one which expresses a subject-predicate proposition, we'd say that what's really been said is that "Anything is a man in virtue of the fact that it is Greek." In this case, by attributing the 'property of being a man in virtue of the fact that it is Greek' to 'Anything,' we seem (I think) to have captured all the information represented by the conditional sentence 'if anything is a Greek it is a man.' Whether or not the statement expressed by said conditional sentence really is of the subject-predicate form, I think that we can use sentences to express it which suggest that it is of s-p form. (Somebody correct me if I'm mistaken about anything I've said here?)
Khichdi lover
#3
Oct13-11, 04:20 PM
P: 11
Quote Quote by Chuck V View Post

In response to your second question, I think that most philosophers today do not believe that " 'If,then' statements," or "conditionals" as they're called, are of the subject-predicate form. I don't think the sentence we've been discussing about Greeks does what a subject-predicate statement does, I don't think it really attributes a property to a subject.
This seems a good point to me.Could you provide some good references to the above. I would really like to learn more on this point of view.

Quote Quote by Chuck V View Post
"If anything is Greek, then it is a man' is of course a compound statement made up of 'Anything is Greek' and 'it is a man' with the conditional connective sitting between them. Both of the components might be interpreted as subject-predicate propositions. We might say that both the first and second components have the same subject "Anything ('it.')" So I imagine that if we were to interpret this conditional as one which expresses a subject-predicate proposition, we'd say that what's really been said is that "Anything is a man in virtue of the fact that it is Greek." In this case, by attributing the 'property of being a man in virtue of the fact that it is Greek' to 'Anything,' we seem (I think) to have captured all the information represented by the conditional sentence 'if anything is a Greek it is a man.' Whether or not the statement expressed by said conditional sentence really is of the subject-predicate form, I think that we can use sentences to express it which suggest that it is of s-p form.
I am not sure if we can use "anything" as "it" . The statement "Anything is Greek" can't be taken in isolation. It seems meaningless.(although, "It is a man" is a meaningful statement)
Furthermore , the statement "Anything is a man in virtue of the fact that it is Greek" also doesn't seem to be a substitute for the if-then statement.
"Anything is a man in virtue of the fact that it is Greek" seems to commonly imply that to be a man it is necessary condition to be a Greek not just a sufficient one.
"If anything is a Greek , it is a man " is an if-then statement , but "Anything is a man in virtue of the fact that it is Greek" seems to me to be an if-and-only-if/iff statement. The if-then statement states unambiguously what is intended.


Hence, I think what you said earlier about if-then statements not being of s-p form makes sense. I would really like to study this from a good source which doesn't assume much background.

Chuck V
#4
Oct13-11, 05:18 PM
P: n/a
Can someone explain what Bertrand Russell is saying on Aristotle's logic?

Quote Quote by Khichdi lover View Post
This seems a good point to me.Could you provide some good references to the above. I would really like to learn more on this point of view.



I am not sure if we can use "anything" as "it" . The statement "Anything is Greek" can't be taken in isolation. It seems meaningless.(although, "It is a man" is a meaningful statement)
Furthermore , the statement "Anything is a man in virtue of the fact that it is Greek" also doesn't seem to be a substitute for the if-then statement.
"Anything is a man in virtue of the fact that it is Greek" seems to commonly imply that to be a man it is necessary condition to be a Greek not just a sufficient one.
"If anything is a Greek , it is a man " is an if-then statement , but "Anything is a man in virtue of the fact that it is Greek" seems to me to be an if-and-only-if/iff statement. The if-then statement states unambiguously what is intended.


Hence, I think what you said earlier about if-then statements not being of s-p form makes sense. I would really like to study this from a good source which doesn't assume much background.
You are absolutely right in criticizing me, I don't know what I was thinking. Here's what I take to be a superior paraphrase, tell me what you think:

"For any x, if x is a Greek, then x is a man."
=
"Any thing that is a Greek, is a man in virtue of being a Greek."

In the subject position of the subject-predicate paraphrase, I have the description "Any thing that is a Greek" which I take to refer to any thing at all that is a Greek. Because 'a man' is the kind of thing a Greek is (rather than a dog or a pogo-stick) It's a sufficient condition for being a man (what Aristotle mean by men) for being Greek.

Here's a more contemporary example: "Any thing that is a Playstation 3, is a video game console in virtue of being a Playstation 3." This works because an object's being a Playstation 3 is a sufficient condition for it's being a video game console. It's a token of the type 'video game console.'

The general form of my paraphrase is this:

"For any x, if x is an F, then x is a G." = "Any thing that is an F, is a G in virtue of being an F"

Any more criticisms? There must be!

To get to the important part, I'd recommend Russell's "Logical Atomism"

http://www.amazon.com/Philosophy-Log...8544594&sr=8-3

It's a series of lectures about his earlier metaphysics and philosophy of language. It's a delightful book, short and easy to read! Very stimulating though! He talks all about truth conditions, quantification, etc. I think he mentions the fact that not all propositions are of the subject-predicate form, but I'm not sure where. It's all over his work though, he believed that the fundamental problem with philosophy prior to his time was that they falsely believed every proposition was of the subject-predicate sort! For instance, if I'm not mistaken, he thought that this was what led Hegel to think that there was really just one subject under of all our propositions, 'the Absolute' (i.e. reality/The World), and given that, anything we say about any allegedly particular item is just an attribution of some property to it.

Happy reading, Enjoy!
Khichdi lover
#5
Oct13-11, 05:39 PM
P: 11
Quote Quote by Chuck V View Post
You are absolutely right in criticizing me, I don't know what I was thinking. Here's what I take to be a superior paraphrase, tell me what you think:

"For any x, if x is a Greek, then x is a man."
=
"Any thing that is a Greek, is a man in virtue of being a Greek."

In the subject position of the subject-predicate paraphrase, I have the description "Any thing that is a Greek" which I take to refer to any thing at all that is a Greek.

"Any thing that is a Greek, is a man in virtue of being a Greek."
Now I am confused , doesn't this imply something about existence of Greeks.

However ,
"For any x, if x is a Greek, then x is a man." , this one seems better. But this is just writing the if-then statement in a more formal way. Maybe we shouldn't think in terms of S-P.
I recall Russell saying somewhere that "For any x, if x is a Greek, then x is a man." is a propositional function. And perhaps as you say S-P form doesn't apply to such functions.

I will read the book you say. Is any background needed to read the book. I know elementary set theory. The minimum that is taught in undergrad maths courses. Also is any philosophical prerequisiteneeded? I have only read "problems in philosophy" by Russell and his "Human Knowledge". But both books didn't have much details on Symbolic logic.

Furthermore, I would like to know a modern philosopher who has written on these topics.(And hopefully one who doesn't assume much technical background in philosophy). Would love to know recent happenings in this field.
Chuck V
#6
Oct13-11, 06:00 PM
P: n/a
Quote Quote by Khichdi lover View Post
"Any thing that is a Greek, is a man in virtue of being a Greek."
Now I am confused , doesn't this imply something about existence of Greeks.

However ,
"For any x, if x is a Greek, then x is a man." , this one seems better. But this is just writing the if-then statement in a more formal way. Maybe we shouldn't think in terms of S-P.
I recall Russell saying somewhere that "For any x, if x is a Greek, then x is a man." is a propositional function. And perhaps as you say S-P form doesn't apply to such functions.

I will read the book you say. Is any background needed to read the book. I know elementary set theory. The minimum that is taught in undergrad maths courses. Also is any philosophical prerequisite is needed? I have only read "problems in philosophy" by Russell and his "Human Knowledge". But both books didn't have much details on Symbolic logic.
Well, yes, I completely meant to write out the "For any x, if..." version with an equals sign. That one is obviously not the the subject-predicate one I know that much, it's purpose was to show where the placeholders are in between the connectives, thus allowing you to take any such conditional with a universal quantifier in front and convert it into my proposed subject-predicate paraphrase...

"Any thing that is a Greek, is a man in virtue of being a Greek."

Does not to my eyes, necessarily entail that there are Greeks. Though I will concede that one would assume that what you're talking about exists if you uttered it. That doesn't mean though, that anything in it explicitly says there are Greeks. Here's a meaningful sentence of the exact same subject predicate form, using a description.

"The man in the blue with the red cape that is superhuman, is flying around the city in virtue of being superhuman."

Now, the referent of the description in the subject-position is Superman. This statement is meaningful, and it does indeed attribute a property to superman, not merely the property of flying around the city, it's more informative than that, it attributes the property of flying around the city in virtue of being superhuman. I'd also point out that "in virtue of" represents the conditional connective that is in Russell's conditional, but here it is doing a different job playing a more descriptive role in the predicate.

But does this sentence entail that Superman exists? Not necessarily. I can't say more than that. I might ask thought, what exactly is it, that's telling you that it does have an existential quantifier in it?

Btw, I think that what make subject-predicate sentences tricky is that we don't evaluate them the way we do truth-functions. This is because the form they all shared in common has just one 'connective' (if you could even call it that) the "is of predication." These are what Russell called, "Atomic" and all truth-functions are compounds of these. I the Philosophy of Log. Atomism he argues that what makes such sentences true or false is whether or not they correspond to the fact they represent. Thus, they aren't like truth-functions, which have their truth value in virtue not only of their constituent atomic sentences, but also in virtue of their form.

If you know elementary set-theory, and have read the 'problems of phil.' you should be more than ready to take it on. It's a highly accessible book, no background needed.
Khichdi lover
#7
Oct13-11, 06:27 PM
P: 11
"Any thing that is a Greek, is a man in virtue of being a Greek."

I think I will have to read some literature before I can understand whether this statement has existential quantifier or not. I am simply unable to decide and hence I am confused about it.

The if-then statement I am somewhat able to digest better. Thanks for that. I will return to the thread after I read some literature.
Chuck V
#8
Oct13-11, 06:30 PM
P: n/a
Quote Quote by Khichdi lover View Post
"Any thing that is a Greek, is a man in virtue of being a Greek."

I think I will have to read some literature before I can understand whether this statement has existential quantifier or not. I am simply unable to decide and hence I am confused about it.

The if-then statement I am somewhat able to digest better. Thanks for that. I will return to the thread after I read some literature.
Alright take care. Enjoy the book, it's great. Also, be sure to check out his paper 'On Denoting,' a classic.


Register to reply

Related Discussions
Can someone explain the following logic used to define the meter? General Physics 4
Bertrand's Theorem Astronomy & Astrophysics 0
Quote by Bertrand Russell on Probability Set Theory, Logic, Probability, Statistics 1
Wave Race 2: Explain the logic behind this formulary? Introductory Physics Homework 3
Aristotle's Logic General Discussion 17