Blind Reasoning

[Capitalism Forever]

what the formal thing "->" expresses is causation

http://en.wikipedia.org/wiki/Table_of_logic_symbols

Causation isn't even a relationship between two propositions. Propositions don't cause things; entities do! (And I don't know of any logical symbol assigned to causation, or even a serious treatment of causation in formal logic--which reflects on the sad rationalistic state of the science.)

[aleph_0]

Then what does he think P --> Q means?

He thinks it means that whenever you have P you have Q, just as we all agree. We could change it to perhaps the most epistemically obvious representation, ~(P & ~Q). Whenever you have P you have Q. You can never have a situation where you get P and ~Q. So he agrees to P and he agrees to ~(P & ~Q), and he agrees that whenever we have these two we have Q. But we haven't gotten to Q. All we have is ~((P & ~(P & ~Q)) & ~Q).

Then he is convinced! Although I know that he is not convinced, since A is not A, he is also convinced.

I actually thought of this too, but I don't think it works here because the only reason accepting a contradiction gets you to prove every possible statement (both the true and the false) is by MPP or some equivalent derivation rule. Here, the derivation rule isn't (yet) working the way we want it to.

May I ask why you are interested in this issue? Are you yourself unsure of the validity of the use of implication in reasoning? Or do you hope to derive some benefit to your life from this? I just don't see why anyone would want to spend any of his time on such a question.

I hope to formally, rigorously, fundamentally kill any possible suspicion that inference, reasoning, and induction are subjective or cultural--and to rather prove that they are grounded in objectivity. I give other people an impossibly hard time about arguing these points because, even if we permit some slack in talking to each other about points upon which we agree, the subjectivist will not.

[aleph_0]

To give a particular example of the kind of battle that is at stake here, theologian Bahnsen has been called "every atheist's worst nightmare" because he argues--with appeal so strong that atheists he has argued against have admitted to being unprepared for his argument and have failed to admit that they have in effect not risen to the challenge--that inference is unjustifiable without god. Inference cannot be without justification for the reasons I have laid out either here or in the other topic of this same title, or both. So we must understand what that justification is. If that justification is faith, the atheist is indeed in a poor position for objectivism (and Objectivism) will require a theology.

It is precisely because it is so basic that it is so difficult to bring to the forefront of one's mind, but it is a project that must be completed entirely and without compromise if the subjectivist is to be left no quarter.

[y_feldblum]

Correlation, under a proper epistemology, means nothing. Causality is everything that correlation isn't. Things are a certain way and act a certain way, and it is with observations of these two facts that logic must deal. A system of logic which severs the connection between abstraction and fact is wrong, even if it is rigorously formalized with highly condensed mathematical notation. In other words, logic must deal with reality - with entities, and with their attributes and actions - and a system of logic which does not deal with reality is incorrect. If formalized logic deals with propositions and correlations independent of any tie to entities, attributes, and actions, then it is in need of fixing. If a statement such as P, or a statement such as P --> Q cannot be reduced to the facts of reality, then formal logic is indeed in a sad rationalistic state.

[aleph_0]

Does being a human cause one to be a mammal? If so, that's a terribly obscure notion of causality.

[DavidOdden]

http://en.wikipedia.org/wiki/Table_of_logic_symbols

Causation isn't even a relationship between two propositions. Propositions don't cause things; entities do! (And I don't know of any logical symbol assigned to causation, or even a serious treatment of causation in formal logic--which reflects on the sad rationalistic state of the science.)

You know, all you're doing is adding further evidence to support my claim that the connective "->" is not valid: that it is purely syntactic sugar. The connective refers to an arbitrary one of 64 tables that express the mapping of two values to one. You're right to point out my error in sugesting that "->" expresses something -- I often slip, in dealing with guys who reify symbolic logic, by assimilating to their word usage too much. Let me restate:

There is a valid concept of causation; in actual usage in formal logic, logician most often attempt to express that concept in a formula employing "->".

[y_feldblum]

The relationship "Socrates is a man --> Socrates is an animal" means is, essentially, the hierarchical relationship between the concepts "man" and "animal". This hierarchical relationship between two concepts can, of course, be further reduced to actual men, to the properties which they hold in similarity to and in difference with other animals.

[DavidOdden]

Does being a human cause one to be a mammal?

No, that was a weak moment on my part. If you try to get domain restriction via the notion of causation, it just messes up the concept of causation. As Y Feldblum said, that class of uses of "->" refers to proper inclusion in a hierarchy, e.g.

ANIMAL{{Fish} {Insects} {Reptiles} {Amphibians} {Birds} {Mammals}...}

MAMMAL{{Monotremes} {Marsupials} {Rodents} {Lagomorphs} {Artiodactyls} {Carnivores} {Primates}...}

PRIMATE{{Prosimians} {Anthropoidea}}

etc. down to Socrates.

[intellectualammo]

Some blind reasoning indeed.

Our recalcitrant friend in your example closes his eyes to the very fact that if he were to accept p and p-->q, as you say that he does, then he totally blanks out the part of how you get from p(which is a premise) to the conclusion of a conditional statement like p-->q. He blanks out a premise, that of q. You HAVE to have that other premise here. There is no way around this truth table:

p___________q________________p-->q

T-----------------T-----------------------------T

Our friend can slam his fist down on this truth table and shout at us that he accepts p and p-->q, but denies q all he wants too, but that will not change the truth table. He will only hurt his fist, ruin his voice, and end our discussion by trying. There is absolutely no way you can deny q and get away with it, when you have already accepted p and p-->q.

If he attempts to blank out, or denies, does not accept, does not see, ignores, evades the premise q, then all he has is a p.

If all he has are (p)eas, then he doesn't have a (q)lue. We will know what the real name of our friend is a then....modus moron.

You would have to accept the simple truth table above in all its entirety before you could even reach the modus ponens argument form, specifically the one which has nothing but beautiful "T's" holding up the table, right?

As an aside, I have only had a few weeks of logic in college...(I'm a four or five time college dropout)...aren't these thingy's "-->" really horseshoe shaped symbols? I've seen "If...Then..." statements using them before and also the p's and q's weren't capitalized either.

*edited to try to fix my crappy looking truth table

Edited November 21, 2006 by intellectualammo

[DavidOdden]

...aren't these thingy's "-->" really horseshoe shaped symbols?

The "-->" thing really is a "-->" thingy. It corresponds, via symbol substitution, to ⇒, →, ⊃ in printed logic textbooks. Similarly, the universal quantifier is conventionally symbolized as ∀ and the existential quantifier as ∃. Because computer symbol encoding hasn't been standardized long enough and user interfaces are still primitive, it's conventional to eschew special symbols and use similar expressions such as "Ax" or "P->Q" in online discussions of logic. It can be inconvenient if you have not seen a particular usage before.

There is no way around this truth table:

I don't understand what you mean "there is no way around". Here is a different truth table:

P Q (P*Q)

T T T

T F T

F T F

F F T

You can shout and slam your fist on the table (truth table or coffee table), throw things at me, and pull out a gun and shoot me (or, simply silently hate me), but that won't change the table. The thing you have to ask is, what aspect of reality does one of these tables represent? Why would you not accept my above table as the truth table for "->"? How is a truth table justified in the first place: and especially (this is where formal logic goes entirely haywire) how do you justify a given truth table without reference to human cognition? Answer: 'It's totally arbitrary: you can define "->" this way if you want'. But that gives our recalcitrant friend the keys to the kingdom.

PS, d'oh. 16, not 64.

[intellectualammo]

I don't understand what you mean "there is no way around".

There's no way around the table I had set, so to speak. If you have accepted both p and p-->q,as modus moron has, then there is no way q can be false, regardless if he wants to accept that fact or not.

[DavidOdden]

There's no way around the table I had set, so to speak.

So you mean, if you accept the particular propositions, and you accept the truth table usually associated with "->", and you are obligated to enter or accept any line in a derivation that .... something. I don't think that explicitly spelling out that "something" is child's play.

If you have accepted both p and p-->q,as modus moron has, then there is no way q can be false, regardless if he wants to accept that fact or not

Yikes, did you really say that?? Let me try to apply that principle.

"If it's raining, the cat must be dead"

"It's raining"

And therefore, by the act of accepting these antecedent propositions, the poor cat must be dead, regardless of whether or not it really is dead. Nah, I don't think you really meant that.

[intellectualammo]

Nah, I don't think you really meant that.

When I used q alone, I am specifically referring to the premise q.

Edited November 21, 2006 by intellectualammo

[DavidOdden]

When I used q alone, I am specifically referring to the premise q.

Okay: I was specifically referring to your statement which implies that acceptance of a set of propositions actually has an effect on reality. Thus if you accept those premises, then q must be a fact.

[intellectualammo]

Okay: I was specifically referring to your statement which implies that acceptance of a set of propositions actually has an effect on reality. Thus if you accept those premises, then q must be a fact.

The way that I used it, I was definately referring to something else. The fact I'm talking about is that whatever q may be, when the premise p and the conclusion are accepted, then q is also going to be true every time, according to the truth table. Refusing to recognize as such, would be an act of evasion.

Edited November 21, 2006 by intellectualammo

[Cogito]

The way that I used it, I was definately referring to something else. The fact I'm talking about is that whatever q may be, when the premise p and the conclusion are accepted, then q is also going to be true every time, according to the truth table. Refusing to recognize as such, would be an act of evasion.

I'm not sure, but I think (or rather, hope) what you mean to say is that whatever q may be, whenever the premise p and the conclusion are true, then q is also going to be true every time, according to the truth table. [edit: and also, according to reality]

Edited November 21, 2006 by Cogito

[intellectualammo]

I'm not sure, but I think (or rather, hope) what you mean to say is that whatever q may be, whenever the premise p and the conclusion are true, then q is also going to be true every time, according to the truth table. [edit: and also, according to reality]

Exactly! That's what I've been repeating. To accept, is to accept as being true, that's how I've at least understood it to mean in this topic.

Edited November 21, 2006 by intellectualammo

[aleph_0]

The relationship "Socrates is a man --> Socrates is an animal" means is, essentially, the hierarchical relationship between the concepts "man" and "animal". This hierarchical relationship between two concepts can, of course, be further reduced to actual men, to the properties which they hold in similarity to and in difference with other animals.

Fine. But it's a non-causal relationship in which, whenever (if) Socrates is a man, then Socrates is an animal. Otherwise written, P --> Q, assigning appropriate meanings to P and Q.

No, that was a weak moment on my part. If you try to get domain restriction via the notion of causation, it just messes up the concept of causation. As Y Feldblum said, that class of uses of "->" refers to proper inclusion in a hierarchy, e.g.

ANIMAL{{Fish} {Insects} {Reptiles} {Amphibians} {Birds} {Mammals}...}

MAMMAL{{Monotremes} {Marsupials} {Rodents} {Lagomorphs} {Artiodactyls} {Carnivores} {Primates}...}

PRIMATE{{Prosimians} {Anthropoidea}}

etc. down to Socrates.

Exactamundo.

it's conventional to eschew special symbols and use similar expressions such as "Ax" or "P->Q" in online discussions of logic.

Where is this convention for 'Ax'? I've never seen anybody but people online use this--most of the time, logicians in the absence of special symbols (or sometimes not even in the absence of special symbols) use '(x)' for "for all x".

As for the rest of the conversation, I believe I've sufficiently addressed it in my last post to the other topic of the same name.

[DavidOdden]

Where is this convention for 'Ax'? I've never seen anybody but people online use this

That's exactly where. Would you have an easier time understanding if I used ∀? I suppose nobody has any problems with funny symbols anymore.

[aleph_0]

Just anything that didn't look like a predicate would be fine.

[Capitalism Forever]

I hope to formally, rigorously, fundamentally kill any possible suspicion that inference, reasoning, and induction are subjective or cultural--and to rather prove that they are grounded in objectivity.

So what you're trying to do is prove the validity of logic using the rules of logic to a person who doesn't accept the rules of logic. That's impossible--it's like trying to send an e-mail explaining how to set up an e-mail address to a person who doesn't have an e-mail address.

There is no way to communicate with people who reject logic. No matter how meticulously and rigorously you prove something to them, they'll simply reject your conclusion. You cannot force a person's mind, and therefore you cannot force them to accept Q. You can only make them accept a proof if they are willing to think, and the willingness to think includes a willingness to abide by the rules of logic.

[Capitalism Forever]

Correlation, under a proper epistemology, means nothing. Causality is everything that correlation isn't. Things are a certain way and act a certain way, and it is with observations of these two facts that logic must deal. A system of logic which severs the connection between abstraction and fact is wrong, even if it is rigorously formalized with highly condensed mathematical notation. In other words, logic must deal with reality - with entities, and with their attributes and actions - and a system of logic which does not deal with reality is incorrect. If formalized logic deals with propositions and correlations independent of any tie to entities, attributes, and actions, then it is in need of fixing. If a statement such as P, or a statement such as P --> Q cannot be reduced to the facts of reality, then formal logic is indeed in a sad rationalistic state.

Whom is this addressed to?

[Capitalism Forever]

The connective refers to an arbitrary one of 64 tables that express the mapping of two values to one. You're right to point out my error in sugesting that "->" expresses something

Do you think concepts like "or" and "and" are also meaningless? After all, they also refer to "arbitrary" mappings of two values to one.

BTW, the number of possible mappings is 16, not 64. Two to the power of four is sixteen.

There is a valid concept of causation; in actual usage in formal logic, logician most often attempt to express that concept in a formula employing "->".

Could you give an example?

[y_feldblum]

To the idea that P --> Q means a correlation between two arbitrary propositions.

[aleph_0]

So what you're trying to do is prove the validity of logic using the rules of logic to a person who doesn't accept the rules of logic. That's impossible--it's like trying to send an e-mail explaining how to set up an e-mail address to a person who doesn't have an e-mail address.

There is no way to communicate with people who reject logic. No matter how meticulously and rigorously you prove something to them, they'll simply reject your conclusion. You cannot force a person's mind, and therefore you cannot force them to accept Q. You can only make them accept a proof if they are willing to think, and the willingness to think includes a willingness to abide by the rules of logic.

The task should not be termed "prove the validity of logic", though I might have slipped up and called it that anyway, so if it was my fault then I apologize. The task is to prove the warrant-transfer of any given valid inference and to define a valid inference (note, this last is clear enough in the case of MPP but until it is demonstrated that only MPP or any equivalent is a valid inference then we need to be concerned with valid inferences as such). That is, assuming we have warrant to believe P and P --> Q, then the warrant from these transfers to a warrant of asserting Q. This is different from proving the validity of logic--i.e. proving that the system moves from logical truth to logical truths as defined in the system--which you are quite right, is circular.

For imagine this: Someone asks you what is the justification that Q if you have P, P --> Q and MPP? You could either go with no justification, in which case you have not made a justified inference, or there is a justification. What kind of a justification, if you go that route? Is that justification inferred by a yet more fundamental inference, and if so what is the justification for that new inference? (Hence a Carrollian regress like we began with.) Well then, suppose the justification is not inferential. It's a kind of rational insight. If so, how does this then allow that logic is not just in the mind but actually objective?

The project is to answer these questions and any others about what justifies an inference.