Christian Objectivist

[Michael Stuart Kelly]

How about this?

Limes are the size of houses and square.

Limes are tiny, round and flat like a penny.

Both statements contradict each other, but both are false.

What am I missing?

Michael

[Mike82ARP]

Compatibility in this case is independent of factual truth.

How so? I would think one would need to know if something were true before attempting to compare it to another thing (which should also be true) before evaluating their compatibility. For example, if I were going to compare apples and oranges and mistakenly used a lemon instead of an orange, would the resulting compatibility determination be correct?

Maybe there’s some O’ist philosophical gymnastics that can be proposed to support your point, but being relatively new here, I can’t think of any.

I'm not an Objectivist, nor am I arguing from an Objectivist point of view here.

As for the 'truth' issue, I doubt this will get us very far in this debate because before long we will reach the realm of pure belief, with no empirical facts to back it up.

But I have the feeling that this issue is still very important to you, so I'll give it a try; I suggest a step by step approach

"A statement is true if it corresponds to fact". Could we agree on this as a common ground for the discussion?

I'll await your reply before continuing.

“Could we agree”? Yes. Can a “fact” be false? I’d be more likely to go along with a practical certainty as a definition of truth, that which we feel comfortable to act upon.

But I still can’t see how you can state that compatibility is independent of fact.

[We Erred Rand]

>>>@ Michael:

Limes are the size of houses and square.

Limes are tiny, round and flat like a penny.

>>>Both statements contradict each other,

No. They do not contradict each other.

>>>... both are false.

Correct. Both are false. That's the clue that they are not *formal* contradictories.

>>>What am I missing?

You might be confusing "contradiction" with "contrary" (or "contrariety"). In casual conversation, we might substitute one term for the other, but in formal logic, they are utterly different.

The textbook examples are usually the following:

1) All swans are white.

2) No swan is white.

These two statements are "logical contraries" (not "contradictions"). They are both false. Therefore, they leave open the possibility of some 3rd alternative that hasn't been considered. In logical jargon, these two statements are "strongly opposed to each other" but not "perfectly opposed to one another."

In order to be "perfectly opposed," two statements must leave no possibility of a 3rd alternative; they must present you with a choice of "either / or." In the above textbook example, two perfectly opposed statements would be:

1) All swans are white.

2) Some swans are not white.

The two assertions present an either/or alternative, with no 3rd alternative possible: in other words, if 1 is true, 2 is false; if 2 is true, 1 is false. They cannot both be true, and they cannot both be false.

The formal name for this sort of "perfect" opposition is: CONTRADICTION.

In your example, the contradiction of "(All) Limes are the size of houses and square" would be "(Some) Limes are not the size of houses and square." They cannot both be true and they cannot both be false. It's "either / or."

[Michael Stuart Kelly]

We Erred Rand,

It's math?

OK.

How about this one (in addition to your all and none thing):

All limes are the size of houses and square.
All limes are tiny, round and flat like a penny.

If one is all, the other can't be any.

A direct contradiction.

In other words, the problem no longer concerns limes and is only about math.

Yet the limes live on in the statements. They are essential to it because we are talking about limes.

Do logicians usually use math to muddy the limes?

Michael

[We Erred Rand]

>>>All limes are the size of houses and square.
>>>All limes are tiny, round and flat like a penny.

>>>If one is all, the other can't be any.

>>>A direct contradiction.

No. It's merely materially false, and not a formal contradiction.

To contradict a statement in formal logic, you have to put the proposition in the correct form. For example, suppose a fellow named Smith shows up at a social event and is introduced by the host with the assertion, "This is Smith," if someone then says "You're Jones!", he's not formally contradicting anything, he's merely uttering a falsehood. It becomes both a falsehood and a formal contradiction if he says "You are NOT Smith!"

The contradiction of "All limes are the size of houses and square" is "Some limes are not the size of houses and square."

As a matter of material fact, it might be true that the reasons "some limes are not the size of houses and square" is because all of them happen to be tiny, round and flat like penny. It might be materially true, but it is formally irrelevant. Logic only needs to know that some limes are not the size of houses and square to establish a contradiction.

The contrary of "All limes are the size of houses and square" is "No lime is the size of a house and square."

You might be trying to conflate the notions of "factual untruth" and "logical contradiction." They're very different.

>>>In other words, the problem no longer concerns limes and is only about math.

　

I don't see any math, but you're right that the problem here is not about any sort of factual truth about limes; it's about the logical relation between propositions qua propositions.

>>>Yet the limes live on in the statements. They are essential to it because we are talking about limes.

No. We're merely talking about the word "limes", not real material limes.

Formal logic only pertains to statements about limes; not real limes, or the practical science of cultivating them.

That is only relevant to the practical science of lime-growing; it is irrelevant to logical statements about limes.

[Michael Stuart Kelly]

I don't see any math...

All is a quantity of units. Each unit is represented by the number one. We can call "all" a boundary of a mathematical set, just like "none."

That seems kind of obvious to me. But then again, I never studied formal logic to unlearn it.

We're merely talking about the word "limes", not real material limes.

In other words, all these logic rules pertain to nothing connected to reality outside the human skull?

(Ahem... we already know we're covering old ground in O-Land discussions, don't we? )

Michael

[We Erred Rand]

>>>All is a quantity of units.

No it isn't. Where did you get that idea?

If "all" were a quantity of units, then we could replace the word "all" in the assertion "All men are mortal" with an actual number representing the quantity of units, e.g., "6 billion men are mortal." It's perfectly true that "6 billion men are mortal" but the point is that it doesn't mean the same thing as "ALL men are mortal" which is most definitely not a quantity, or enumeration, of units. The two sentences mean different things.

>>>Each unit is represented by the number one. We can call "all" a boundary of a mathematical set, just like "none."

You could if you were a nominalist. But I'm not a nominalist. You could also do it if you believe that syllogistic reasoning from premises to conclusion is nothing but a tautology; i.e., in order to construct the syllogism, "All men are mortal / Socrates is a man / therefore, Socrates is mortal" you would not only have to enumerate the "units" of men (e.g., "6 billion" units in total) but since your enumeration of "all" would obviously have to include "Socrates" as one of the units you've counted, it would be superfluous to state the conclusion that "Socrates is mortal", because that fact was already known to you when you included him in your enumeration of "All."

"All men [the enumeration of which includes Socrates, of course] are mortal"

"Socrates is a man" [already known by you in the major premise]

"Therefore, Socrates is mortal" [already known by you in the major premise"]

To assume a mathematical/set-theory/nominalist approach to logic makes the very study of it superfluous.

>>>That seems kind of obvious to me.

To those who never studied basic physics, it might seem obvious that heavy objects fall faster than light ones. Educated people believed it for centuries. That it happens not to be so is actually a bit counter-intuitive.

>>>But then again, I never studied formal logic to unlearn it.

That seems kind of obvious to me. You should take a course in it. I think you'd like it.

>>>In other words, all these logic rules pertain to nothing connected to reality outside the human skull?

Formal logic is the study of propositions and how they relate to one another, irrespective of how — or even if — they relate to physical reality.

"All skidoodles are kerfluffled"

"Jupiquarlin is a skidoodle"

"Therefore, Jupiquarlin is kerfluffled"

Formally, a perfectly valid argument in logic, even if the terms are nonsensical.

In any case, don't fret. Leonid has already admitted that many of the things we make statements about during ordinary discourse — e.g., color, sound, scent, texture — are phenomena that occur only inside the human skull, and which usually (though not necessarily) correlate to some extra-skull entity or process. They are percepts requiring a perceiver. When we make statements about "the color blue", "the sound of ocean waves", "the scent of lavender", and "the feel of velvet", we are not making statements about electromagnetic wavelength, air vibration, pheromone molecules, and electro-chemical impulses transmitted from the skin to the brain. Those are merely correlate to our percepts. We are making statements about our percepts (our subjective percepts), which occur only inside our human skull. Yet that in no way invalidates or weakens our ability make logical propositions out of them, and to draw logical conclusions from them.

[Michael Stuart Kelly]

Formal logic is the study of propositions and how they relate to one another, irrespective of how — or even if — they relate to physical reality.

If that is true, then propositions are no more useful--or valid for living--than daydreams.

If that's your view, then why bother discussing it? It's not important.

Well, maybe if you like games as the only way to use reason. I suppose a case could be made that the meaning of life is to spend it playing sudoku or doing crossword puzzles or things like that--and that logic is nothing more than a type of that.

Obviously, I am more Randian in my epistemology than boilerplate academia. In other words, according to the standard I use, there is a reality connection to abstractions. Oh... there's also imaginary stuff, but there is real correspondence, too.

In fact, I will, go one further, which takes me out of Rand's epistemology. I contend that human consciousness is made of the same basic stuff as the rest of the universe and that the reason an abstraction can correspond to, say, an external form with validity in the first place is because both are made of the same stuff, therefore both obey the same laws of nature.

By stuff, I mean form things like holons on the top-down side, and the quantum particle level on down on the bottom-up side. These things are perfectly reflected in the way abstractions are organized in the mind. Reality organizes that way and so do abstractions. Same stuff.

(And "all" is a math expression. It's more in the ordinal camp than cardinal, but it's still math. You don't have to agree.)

Michael

[BaalChatzaf]

Formal logic is the study of propositions and how they relate to one another, irrespective of how — or even if — they relate to physical reality.

If that is true, then propositions are no more useful--or valid for living--than daydreams.

If that's your view, then why bother discussing it? It's not important.

Well, maybe if you like games as the only way to use reason. I suppose a case could be made that the meaning of life is to spend it playing sudoku or doing crossword puzzles or things like that--and that logic is nothing more than a type of that.

Obviously, I am more Randian in my epistemology than boilerplate academia. In other words, according to the standard I use, there is a reality connection to abstractions. Oh... there's also imaginary stuff, but there is real correspondence, too.

In fact, I will, go one further, which takes me out of Rand's epistemology. I contend that human consciousness is made of the same basic stuff as the rest of the universe and that the reason an abstraction can correspond to, say, an external form with validity in the first place is because both are made of the same stuff, therefore both obey the same laws of nature.

By stuff, I mean form things like holons on the top-down side, and the quantum particle level on down on the bottom-up side. These things are perfectly reflected in the way abstractions are organized in the mind. Reality organizes that way and so do abstractions. Same stuff.

(And "all" is a math expression. It's more in the ordinal camp than cardinal, but it's still math. You don't have to agree.)

Michael

I think you might have missed the point.

Logic is the study/discipline/science of the valid -forms- of inference. Logic, qua logic does not concern itself with the truth of premisses. It concerns itself only with the validity of the inference of the conclusion from the premisses.

For a logical argument to be convincing -two- conditions must hold.

1. the conclusions were inferred from the premisses in a valid manner.

2. the premises are true.

If both of these hold then the conclusion -must- be true. Not probably true, not possibly true but necessarily true.

Clear?

Ba'al Chatzaf

[We Erred Rand]

>>>If that is true, then propositions are no more useful--or valid for living--than daydreams.

Daydreams are extremely useful and valid for living.

Logic might not be "valid for living" (whatever that means), but it is both useful and valid for confirming or disconfirming the validity of arguments.

>>>if that's your view, then why bother discussing it? It's not important.

Because the ability to discriminate between "valid" and "invalid" in the realm of arguments is a useful skill.

>>>Well, maybe if you like games as the only way to use reason. I suppose a case could be made that the meaning of life is to spend it playing sudoku or doing crossword puzzles or things like that--and that logic is nothing more than a type of that.

How does playing sudoku or doing crossword puzzles help one discriminate between the categories of "valid" and "invalid" among different kinds of arguments?

>>>Obviously, I am more Randian in my epistemology than boilerplate academia.

One might say you're a boilerplate Randian. On the other hand, you've also admitted that you've never studied logic, so on what do you base this opinion?

>>>In other words, according to the standard I use, there is a reality connection to abstractions.

All abstractions? Or only some abstractions?

>>>Oh... there's also imaginary stuff, but there is real correspondence, too.

And logic is a tool capable of working with both the imaginary stuff and the stuff with real correspondence.

>>>In fact, I will, go one further, which takes me out of Rand's epistemology. I contend that human consciousness is made of the same basic stuff as the rest of the universe and that the reason an abstraction can correspond to, say, an external form with validity in the first place is because both are made of the same stuff, therefore both obey the same laws of nature.

Interesting. That, of course, was not Ayn Rand's view, but you're entitled to your own speculations even if they are 100 years out of date. Material reductionism went out a long time ago, at least as a plausible philosophical model. If consciousness is simply a very finely attenuated form of matter, and follows the same laws of matter (including, of course, the 2nd law of thermodynamics, which all matter obeys), and since matter cannot contradict its own nature, you'll have to explain how it happens that when it becomes very rarefied and "mind-like" it becomes capable of holding the statement "All X is Y" in one person's mind, yet the same kind of matter, with the same identity, and therefore obeying the same laws of physical nature, becomes capable of holding the statement "Some X is not Y" in someone else's mind!? A logical contradiction. The two statements cannot both be true, and neither can they both be false. Just like the Act Heading in Atlas Shrugged: it's Either-Or. Yet according to you, it's matter comprising these two statements: matter that apparently has no problem contradicting itself.

And if you were to reply, "There are simply many different kinds of particles that become mind-like and comprise ideas: one kind of particle comprises the statement 'All X is Y' in Joe's skull, and another kind of particle comprises the statement 'Some X is not Y' in Mary's skull. Problem solved!"

My response would be: Not exactly. Because in that case, we cannot say that the particles in Joe's skull are objectively true (or false), nor can we say that about the particles in Mary's skull: In this kind of universe, there are simply two sets of particles, functioning as material agents, causing two kinds of effects. We cannot validly claim that the material effect in Joe's skull is worthier of our consideration than the material effect in Mary's. The concept of "Objective Truth" is now gone!

>>>(And "all" is a math expression.

Interesting. What's the symbol for it?

>>>It's more in the ordinal camp than cardinal,

Ordinal camp: First, Second, Third, Fourth, . . . these show the order of something within a series. How does "all" show the order of something within a series?

>>>but it's still math. You don't have to agree.)

You're both kind and generous to me. Thanks. I don't agree.

[Michael Stuart Kelly]

Formal logic is the study of propositions and how they relate to one another, irrespective of how — or even if — they relate to physical reality

WER,

Let's put it this way.

Rather than try to untangle the mess and speculations about what I really mean in your last post, this statement from above hits the core of the issue.

What is the mechanism to you about how propositions can relate to reality?

How does that work in a non-propositional way, since the rules governing valid/invalid propositions--to you--are not bound by reality?

What's the conceptual connection between in here and out there?

(I would appreciate talking in plain English rather than all those snooty isms, but you have your own style, I guess.)

Michael

[We Erred Rand]

>>>What is the mechanism to you about how propositions can relate to reality?

It's irrelevant to logic, which studies the relation of propositions to one another. You're confusing logic with epistemology.

>>>How does that work in a non-propositional way, since the rules governing valid/invalid propositions--to you--are not bound by reality?

I wrote that they are not bound by physical reality, not simply reality. Big difference to those of us who don't reduce all of reality to the merely physical/material part of it.

[Michael Stuart Kelly]

WER,

I'm fine if you don't want to answer my questions.

Michael

[Xray]

Daydreams are extremely useful and valid for living.

Decoding anagrams can be quite useful too. Just sayin'.

'Xyra'

[Xray]

“Could we agree”? Yes. Can a “fact” be false? I’d be more likely to go along with a practical certainty as a definition of truth, that which we feel comfortable to act upon.

I would put it this way: What is regarded as fact can turn out to be false. But in that case, the alleged fact was never a fact.

Example: suppose in a criminal case, the police regarded it as fact for quite some time that a certain 'person of interest' had an airtight alibi.

But later it turned out that a good friend had given this person a false alibi. The alleged 'fact' had never been a fact.

[BaalChatzaf]

“Could we agree”? Yes. Can a “fact” be false? I’d be more likely to go along with a practical certainty as a definition of truth, that which we feel comfortable to act upon.

I would put it this way: What is regarded as fact can turn out to be false. But in that case, the alleged fact was never a fact.

Example: suppose in a criminal case, the police regarded it as fact for quite some time that a certain 'person of interest' had an airtight alibi.

But later it turned out that a good friend had given this person a false alibi. The alleged 'fact' had never been a fact.

To establish that, the alibi must be cracked. Not always easy to do.

[Mike82ARP]

“Could we agree”? Yes. Can a “fact” be false? I’d be more likely to go along with a practical certainty as a definition of truth, that which we feel comfortable to act upon.

I would put it this way: What is regarded as fact can turn out to be false. But in that case, the alleged fact was never a fact.

Example: suppose in a criminal case, the police regarded it as fact for quite some time that a certain 'person of interest' had an airtight alibi.

But later it turned out that a good friend had given this person a false alibi. The alleged 'fact' had never been a fact.

I understand that people sometimes misuse the word “fact”, but what does this have to do with your statement that, "Compatibility in this case is independent of factual truth.”?

[Xray]

We're merely talking about the word "limes", not real material limes.

The word "limes" refers to what exactly then?

[Xray]

[quoting MSK] >>>What is the mechanism to you about how propositions can relate to reality?

It's irrelevant to logic, which studies the relation of propositions to one another. You're confusing logic with epistemology.

"We Erred Rand": Do you think of logic as irrelevant to epistemology?

[We Erred Rand]

WER,

I'm fine if you don't want to answer my questions.

Michael

And I'm fine if you want to meander aimlessly into topics that have little or nothing to do with formal logic.

[We Erred Rand]

[quoting MSK] >>>What is the mechanism to you about how propositions can relate to reality?

It's irrelevant to logic, which studies the relation of propositions to one another. You're confusing logic with epistemology.

"We Erred Rand": Do you think of logic as irrelevant to epistemology?

Good God, no. But I do think of epistemology as irrelevant to logic. And the discussion thus far has been about logic, not epistemology.

[Michael Stuart Kelly]

WER,

Are you the crazy lady's sidekick, Darren?

What do you want here?

Michael

[We Erred Rand]

We're merely talking about the word "limes", not real material limes.

The word "limes" refers to what exactly then?

You can assign any meaning you want to it. The logical relation among the premises and the conclusion won't change.

Did you think it would?

[Xray]

We're merely talking about the word "limes", not real material limes.

The word "limes" refers to what exactly then?

You can assign any meaning you want to it.

Of course I can personally assign 'any meaning' to any term, but in using language you would get a complete communication breakdown if (random example) you'd decide to assign the meaning 'umbrella' to the term 'lime'.

"It's going to rain. I'll need a lime."

The arbitriness in assigning is therefore quite limited.

The logical relation among the premises and the conclusion won't change. Did you think it would?

The debate has not been about formal logic. Instead it was about the incompatibility of a faith in a supernatural power with Rand's stance on this issue. That's what it was about.

Terms like "contradiction" and "incompatibility" are not exclusively used in formal logic, but in countless other situations as well.

[Xray]

[quoting MSK] >>>What is the mechanism to you about how propositions can relate to reality?

It's irrelevant to logic, which studies the relation of propositions to one another. You're confusing logic with epistemology.

"We Erred Rand": Do you think of logic as irrelevant to epistemology?

Good God, no. But I do think of epistemology as irrelevant to logic. And the discussion thus far has been about logic, not epistemology.

Actually the opposite had been the case before you jumped in with formal logic in an issue where it was is not needed. As I wrote in my prior post, terms like "contradiction" and "incompatibility" are not exclusively reserved for formal logic; they are also used in countless other contexts without causing any misunderstanding in communication.

In criminal cases for example, evidentiary findings can contradict a suspect's version of events.

Defense laywers would have field day day in court if the prosecution could only build a case against their clients if they formally conradicted themselves.

Example for demonstration purposes:

Let's say defendant D has stolen a motorbike; an eyewitness has even seen him with the vehicle.

D says he had been at a different location at the time. But then additional evidence is discovered: his DNA is found on the mororbike. This evidence contradicts D's version even further.

Do you really believe that the defense counsel is going to be successful in court if he tells the prosecution: "But you don't have a case agaist my client because he never formally contradicted himsellf!"