Logic/causality puzzle

[aleph_0]

Uh, no, the statement "All men are mortals" is a recognition of an aspect of man's identity. You do recall, I presume, that "identity" doesn't mean "equivalence".

An aspect of man's identity is a predicate of man. Two things share the same identity if the truth-value of every statement about each is exactly the same--so in this unique sense, identity is equivalence, though entities are usually not to said to be equivalent but rather statements about entities.

Hey, are you familiar with Katz & Fodor's paper on this from the 60's? If so, then you know why that's a lousy example.

Is that the one that takes issue over the uncertainty of what constitutes "being a man" and "being unmarried"? If so, I'm just assuming we all take those phrases to be meaningful and definable and, once done, the statement "All bachelors are unmarried males," becomes a meaningful, definable, and by definition true statement.

Well, since there aren't any analytic truths, there's no reason to distinguish mindless tautologies such as "All married men are married men" from synthetic truths like "All men are mortal". We have to decide what this little chat is about. Onar seems to be interested in symbolism and reasoning, so your examples are off topic (you may supply your intended formal statement, to get yourself on topic).

This is relevant to symbolism since we are talking about what can be symbolized with what meaning. If you argue that the symbolism '~(P & ~Q)' is invalid symbolism, or likewise going down to quantified symbolism (x)~(P(x) & ~Q(x)), then it's relevant. Here, for B(x), M(x), and U(x) with their obvious meanings, I make the claim that you need not investigate anything--that it is true simply by what you mean to express--that (x)~(B(x) & ~(M(x) & U(x))). (Otherwise written, '(x)(B(x) --> (M(x) & U(x)))'.). So likewise, it is relevant that I assert there are analytic truths.

Yes, yes, we all know what these primacy of consciousness jerks have done to modern philosophy and logic. We're talking about actual reasoning and cognition, not the made-up nonsense of POC philosophers. This forum presumes Objectivism, so I can only conclude that you forgot that we're not assuming the nonsense assumed over at the Eye Heart Kant club.

I don't believe the majority of modern philosophers believe in the primacy of consciousness, though nearly all of them, if not all of them, believe in the existence of analytic truths. The claim is that this part of reasoning is actual reasoning and is applied to experience to produce synthetic truths. I know we're not assuming Kant--but I also thought this was a forum for conversation and investigation, not dogmatism and quarantined ideas.

To show that "=>" is valid, you have to prove that it has real referents. And since you know very well that "=>" is just syntactic sugar, I don't know why you're bothering to try to defend it.

Are you arguing that, for some statement to be true, each term must have a referent? So for the statement "Every action has an equal and opposite reaction," to be true, the word "an" must have a referent? '=>' is not independently valid or invalid, but is only intelligible in application to referents—namely, statements and statement clauses.

[DavidOdden]

An aspect of man's identity is a predicate of man.

But we don't need any talk of "predicates". You still seem to be confused about the term "identity". I'm not talking about whether two things are identical, I'm talking about the identity (properties) of a man or men in general.

Is that the one that takes issue over the uncertainty of what constitutes "being a man" and "being unmarried"?

Okay, the point is that "bachelor" sentences are true only given a specific reading of the word, viz. "unmarried male", and not "person with a bachelor's degree", "non-mating male animal esp. fur seal" and "young knight in the service of another knight". Hence these are not definitionally-true sentences.

If you argue that the symbolism '~(P & ~Q)' is invalid symbolism

Symbolism is valid only if it refers to something in reality. The nots and ands are fine, since they do refer to something. I'm gonna ignore the rest of your comment since I can't see that it refers to anything that I'm talking about.

I know we're not assuming Kant--but I also thought this was a forum for conversation and investigation, not dogmatism and quarantined ideas.

This is a forum for conversation and investigation of Objectivism, so if you want a generic chat room, well, sorry, I can't actually help there but I think somebody here might be able to provide you a link. Apart from the point about not using OO as a forum to spew anti-Objectivist philosophy, which I assume you would not do, it is also assumed that you have basic understanding of Objectivism or are willing to acquire same. And above all, I think you should know that the argument "But millions of flies, uh, I mean, modern philosophers can't be wrong" is just plain wrong. And finally, the really central point is that analytic sentences have nothing to do with this thread, which is (apparently) about the connective "=>" and the concept "causation".

Are you arguing that, for some statement to be true, each term must have a referent?

Excellent! Progress is being made.

So for the statement "Every action has an equal and opposite reaction," to be true, the word "an" must have a referent? '=>' is not independently valid or invalid, but is only intelligible in application to referents—namely, statements and statement clauses.

Are you equivocating on "term"? We were talking logic, not natural language. So are you asking about the formal semantics of indefinite articles?

[RationalBiker]

but I also thought this was a forum for conversation and investigation, not dogmatism and quarantined ideas.

Ahh, let's pull out the D word, that's always good for intimidation (ironically being used in a discussion about logic). The logical implication of your statement is that if one accepts Objectivism to be true and prefers to limit discussion to that on this forum, then one must have abandoned logic in favor of Dogmatism. Even a novice can recognize that to be a fallacious argument.

If I give you the benfit of the doubt, I would assume that you simply don't understand the purpose of this forum, this Objectivist forum. This forum that has a specific focus. Review the forum rules for that purpose.

So sorry, you can't buy shovels in this shoe store. If you want shovels, go to a shovel store.

[Onar Åm]

Onar, you are right that if A causes B we can say that A logically implies B, but we CANNOT necessarily say that if A logically implies B, then A CAUSES B. You can't always reverse it.

True, but I never claimed this. What I was asking about was: if A CAUSES B, then clearly A IMPLIES B, (and by this I mean that you cannot have A without also having and from this it is also clear that ~B IMPLIES ~A. But this latter logical implication derives its truth from the causal relationship A causes B, yet it seems unreasonable to say that ~B *causes* ~A. What then is the causal nature of this latter logical implication?

[hunterrose]

Things you always wanted to know but were afraid to ask: birds don't urinate.

Onar Åm:

If a platypus has a duckbill and lays eggs, then clearly a platypus is a bird, (and by this I mean that a platypus has some of the characteristics of a bird) and from this it is also clear that platypi don't urinate (a characteristic of birds). But this latter logical implication derives its truth from the fact that a platypus has a duckbill and lays eggs, yet it seems unreasonable to say that platypi don't urinate. What then is the causal nature of this latter logical implication?

[DavidOdden]

Hunterrose, some birds do urinate, for example the bat. And not all birds have duck-type bills (for example flies and sparrows). You've made a common misidentification: fish don't urinate, and they do swim; platypi are fish, because they share with fish the characteristic of swimming and not urinating.

[Onar Åm]

No, I'm saying that there is no single way to abstract out a pattern from all forms of valid reasoning, especially if you're going to use FOP logic. If you take reasoning to be primary and extract symbolic logic from that, there's no problem. You will get the connective "&", come hell or high water. But you will not get the connective "=>" used the way it is in typical logic 101 class fashion; instead, you'll get something like generalized quantifier theory. You will also get a separate concept of "causation", although this is as much a part of logic as the concepts "individual", "number", "identity", "existent", "consciousness" and "comparison" (inter alios). The error arises in accepting the modern logicians' package deal, when it comes to the nature of logic (as being completely separate from man's cognition), and assuming that there is -- a priori -- such a thing as "=>". What is the proof that "=>" is a valid expression of something in logic? Why should I grant that "=>" is valid? What is it valid for?

I'm very interested in this line of reasoning although I don't understand it. I fully understand the analytic/synthetic dichotomy and agree that there is no such thing as an analytic truth or a synthetic truth, only truth. Truth means that the statement has a referent in reality. I also understand the notion of floating abstraction, meaning a concept without a referent in reality. But what I don't understand is the claim that "=>" is a floating abstraction. I use the term "imply" in my daily language to mean that if A is true then B is necessarily also true. You could say that "A=>B" is a short hand for "~(A^~" but I don't see the crime in that short hand.

(edited for typos)

Edited December 23, 2006 by Onar Åm

[hunterrose]

You've made a common misidentification

In the same sense as Onar Åm?

I use the term "imply" in my daily language to mean that if A is true then B is necessarily also true.

You could say that "A=>B" is a short hand for "~(A^~B )" but I don't see the crime in that short hand.

You don't?

You have an operation (causation) that in one respect but not in others is (or is similar to) an implication.

Then, you are applying a wholly different property of implications to causation. Because if one property of implications is shared with causal relations, then surely other properties of implications are shared with causal relations, right?

And since sharing one property of implications means it ought to share the other properties of implications, whenever this obvious truth seems false, then there is a contradiction that requires a really, really, really easy straight answer. Which you haven't received in 33 posts. Obviously.

Edit: removed dastardly emoticon that interrupted logical flow

Edited December 23, 2006 by hunterrose

[DavidOdden]

But what I don't understand is the claim that "=>" is a floating abstraction. I use the term "imply" in my daily language to mean that if A is true then B is necessarily also true. You could say that "A=>B" is a short hand for "~(A^~B )" but I don't see the crime in that short hand.

You are now anchoring the abstraction, which is good. I don't object to the shape "=>" or to something concrete, so from now on in this thread I will simply assume this specific definition "if A is true then B is necessarily also true". That makes things much simpler for me. It means that there are a lot of uses of "=>" that I don't have to think about, namely things that are not about causal relations.

(Now let me find something else to pick on). Although I believe in using ordinary language when possible, there is an important distinction that ought to be cleared up, namely implicature vs. entailment, the former (in some semantic theories) being a broader category that includes the latter i.e. the truth of A requires the truth of B. Ordinarily, we can say "John was implying that you shouldn't drink so much" without John having said that literally, or anything that logically entails that statement. To be explicit, then, I construe your interest as being about the stronger thing, entailment.

One such entailment, of the type that we are talking about, is "If it's Christmas in Tromsø, the sun will remain below the horizon". Proposition A does not cause proposition B to be true: instead, facts about the angle of Earth's rotational axis, the latitude of Tromsø, the time-referent of Christmas, Earth's orbit plus other fancy physical stuff are what cause B to be true: the facts that give rise to A also give rise to B. Facts cause facts. The negation of a proposition doesn't (automatically) refer to a fact, it refers to the absence of a particular fact. I think the main concept that needs exploration here is "cause".

[Onar Åm]

One such entailment, of the type that we are talking about, is "If it's Christmas in Tromsø, the sun will remain below the horizon". Proposition A does not cause proposition B to be true: instead, facts about the angle of Earth's rotational axis, the latitude of Tromsø, the time-referent of Christmas, Earth's orbit plus other fancy physical stuff are what cause B to be true: the facts that give rise to A also give rise to B. Facts cause facts. The negation of a proposition doesn't (automatically) refer to a fact, it refers to the absence of a particular fact. I think the main concept that needs exploration here is "cause".

Indeed, now we are getting somewhere. This proposition is an example of logical implication, i.e. necessary truth. From the equivalence (A=><=>(~B=>~A) it follows that "if the sun does NOT remain below the horizon, it is NOT Christmas in Tromsø." Both derive from the same facts. Obviously identity (one of which is causality) plays a role in this argument, but the the relationship is far from obvious, even in instances when there is a direct causal relationship between A and B. E.g. "if the car crashes at high speed into a concrete wall, the car will deform." Here we can say that A *causes* B. Yet, (A=><=>(~B=>~A) implies that "if the car does NOT deform, the car did NOT crash at high speed into a concrete wall." And in this case it does not make sense to say that ~B *causes* ~A. So even in such a simple case as this the relationship between causality and logic is not trivial. What's going on?

[aleph_0]

But we don't need any talk of "predicates". You still seem to be confused about the term "identity". I'm not talking about whether two things are identical, I'm talking about the identity (properties) of a man or men in general.

But you are talking about predicates. The collection of predicates of a man or men. Unless there is a specified non-standard logic you are assuming (and since this conversation began in the context of discussing formal logic), "identity" is taken to be unique to members of the domain.

Okay, the point is that "bachelor" sentences are true only given a specific reading of the word, viz. "unmarried male", and not "person with a bachelor's degree", "non-mating male animal esp. fur seal" and "young knight in the service of another knight". Hence these are not definitionally-true sentences.

Well, to use my phrasing (which you have also chaffed against), it is still true by what you mean to say. And the sentence "All bachelors, where 'bachelor' does not refer to persons with a bachelor's degree, non-mating males, or servant knights, are unmarried males," would be true by definition of the terms therein. Obviously, it would be easy enough to produce other sentences which contain words with only one definition which are exhaustively defined in terms of the other words.

Symbolism is valid only if it refers to something in reality. The nots and ands are fine, since they do refer to something.

To what?

This is a forum for conversation and investigation of Objectivism, so if you want a generic chat room, well, sorry, I can't actually help there but I think somebody here might be able to provide you a link. Apart from the point about not using OO as a forum to spew anti-Objectivist philosophy, which I assume you would not do, it is also assumed that you have basic understanding of Objectivism or are willing to acquire same. And above all, I think you should know that the argument "But millions of flies, uh, I mean, modern philosophers can't be wrong" is just plain wrong. And finally, the really central point is that analytic sentences have nothing to do with this thread, which is (apparently) about the connective "=>" and the concept "causation".

I don't want a generic chat room--I don't see why you would draw that conclusion. I was discussing logic (forgive me for discussing, I thought that was the point of the forum), which is a topic in metaphysics about which Objectivism has made claims. Part of that discussion involves the analytic/synthetic distinction. If you wish to forbid this subject, well, I'll need to see the rule in the Forum Rules. I see nobody "spewing" anti-Objectivist philosophy (though a bit of spewing its contrary, and I'm guessing that's not the point of the forum either).

Are you equivocating on "term"?

Are you? You posit: All the terms of a statement must refer to something in reality. I ask: Even the indefinite articles? To what could they refer? What about the division sign (÷) in mathematical equations? To what does it refer? In what ways are these valid but the implication sign (-->) invalid, when it merely "refers" to any propositions in which, when the antecedent is true, the consequent is also true. Moreover, if you accept '~' and '&', one is perfectly able to reconstruct standard propositional logic. So I don't really care if you reject '-->'. I can do all the same lifting with '~' and '&'.

Ahh, let's pull out the D word, that's always good for intimidation (ironically being used in a discussion about logic).

What of the intimidation, "Such things are not to be discussed in an Objectivist forum. You don't want to be non-Objective, do you?" If we are not to be dogmatic, we should... not entertain a dogma like, "the analytic/synthetic distinction is a false dichotomy", but rather argue it.

The logical implication of your statement is that if one accepts Objectivism to be true and prefers to limit discussion to that on this forum, then one must have abandoned logic in favor of Dogmatism. Even a novice can recognize that to be a fallacious argument.

But apparently it takes an expert to pull it out of thin air.

If I give you the benfit of the doubt, I would assume that you simply don't understand the purpose of this forum, this Objectivist forum. This forum that has a specific focus. Review the forum rules for that purpose.

I'll give you the benefit of the doubt and assume you didn't understand a word I posted.

[DavidOdden]

But you are talking about predicates.

The concept "predicate" is silly; I said that there is no need to talk about predicates, so your reply is incomprehensible to me. I am not talking about predicates, since predicate is a non-referring expression. In fact, that is my last word on the topic of predicates, so find a new way to say what you want to say. It won't be difficult.

Well, to use my phrasing (which you have also chaffed against), it is still true by what you mean to say. And the sentence "All bachelors, where 'bachelor' does not refer to persons with a bachelor's degree, non-mating males, or servant knights, are unmarried males," would be true by definition of the terms therein.

This is not relevant to the topic of the thread, which is not about the AS distinction. You're wrong, but I will only pursue that point in a thread on the AS distinction, so as to not confuse the issue at hand. Post appropriately: one topic in a thread, and read the initial post to see what the topic is.

I see nobody "spewing" anti-Objectivist philosophy (though a bit of spewing its contrary, and I'm guessing that's not the point of the forum either).

Kantian philosophy (and its brethren and spawn such as logical positivism) is dimetrically opposed to Objectivism, and you are spewing Kantology. The debate forum is the appropriate forum for that.

Let me mention, if you don't know this, that there is an alternative forum, namely HPO, which doesn't have any real principles of conduct or expectations of behavior, and oblique insults are perfectly acceptable, indeed virtually mandatory. If you want to chat about pure logic, that's a great place -- Kolker, Sollars, Dance and Elam will be happy to engage you.

[miseleigh]

Logic and causality are intimately related. If we know that A causes B then we can also say that A logically implies B. Thus, A=>B. However, consider the following logical equivalence:

(A=><=>(~B=>~A)

If A causes B then A=>B, but this is equivalent to saying ~B=>~A. Is this then the same as saying ~B causes ~A?

What makes this so tricky is that in order for A to cause B, A must be an event that precedes B in time, but is it meaningful to say that ~B precedes ~A in time? If not, is it still valid to say that ~B *causes* ~A since A causes B?

E.g. "if the car crashes at high speed into a concrete wall, the car will deform." Here we can say that A *causes* B. Yet, (A=><=>(~B=>~A) implies that "if the car does NOT deform, the car did NOT crash at high speed into a concrete wall." And in this case it does not make sense to say that ~B *causes* ~A. So even in such a simple case as this the relationship between causality and logic is not trivial. What's going on?

What's going on is this: implies is to causes as rectangle is to square. Just as a rectangle can be a square but it isn't always a square, implication can be causal but it doesn't have to be. As has been said, there isn't a logical equivalent of causal relationships. So when you take your ~B=>~A statement and try to convert the => back to 'causes', you're going to have problems.

Assume p= 'A causes B'.

Assume q= 'A=>B'.

So p=>q, and also ~q=>~p.

However, q=>p does not follow.

[softwareNerd]

So even in such a simple case as this the relationship between causality and logic is not trivial. What's going on?

There is no assumption of cause and effect when one says "A implies B"? I hear a sound of thunder and shortly thereafter I see lightning. The one -- correctly identified -- implies the other. Yet, the light does not cause the sound, nor the sound the light. "A implies B" simply means that if you know that "A" is true, then you can also conclude that "B" is true; it says nothing about what's causing A and B to be true.

[aleph_0]

Kantian philosophy (and its brethren and spawn such as logical positivism) is dimetrically opposed to Objectivism, and you are spewing Kantology. The debate forum is the appropriate forum for that.

Questioning an assumption and proposing an idea which is not found in Objectivism is "spewing"? I took "spewing" to be making a series of unfounded claims in an attempt at psychologically barraging somebody into submission... Wait... Hmm... I wonder who most fits that picture here...

In any case, if you're saying that some concepts are "off limits" even if the conversation naturally causes them to arise, then I suppose there's no reasoning with you. So I won't try.

(Note, I brought up necessary truth as an alternative example to "causal implication" for the use of 'if... then...' and had goal of pursuing the concept of necessary truth, but the conversation arose out of your argument against the concept. Nobody randomly threw it into the mix.)

Let me mention, if you don't know this, that there is an alternative forum, namely HPO, which doesn't have any real principles of conduct or expectations of behavior, and oblique insults are perfectly acceptable, indeed virtually mandatory.

I only respond in kind.

[DavidOdden]

In any case, if you're saying that some concepts are "off limits" even if the conversation naturally causes them to arise, then I suppose there's no reasoning with you.

You are missing the obvious: off topic is not off limits. (Actually, if you're not a native speaker of English, I wouldn't expect you to have know that). This is the wrong thread to go mucking around in the AS mire, since that is not the topic of this thread, which is about causality. I presume you know how to use the search function to find an existing thread on AS, to see if that resolves all of your problems, and if it doesn't, you know how to pick a new fight, uh, I mean start a new thread.