Logic & Science

[Speakpigeon]

So you think I overstated.

Let me disabuse yourself of that thought. Systems built on test and experiment are the basis for more systems. Some of those system make use of deductions made possible by the inductive empire being built.

Oh, shit, he said deductive.

Point is whether one is better served by induction or deduction. As far as fundamentals of reality are concerned inductive approaches have had a continuous positive record while deductive approaches all lay by the wayside. So given a choice I always prefer inductive approach.

You missed the point of my post which is logic is essentially establishing validity and that inductive approaches are much richer in that respect.

It baffles me that anyone sensible should feel that inductive and deductive logics have to be opposed somehow.

Anyway, you're clearly unable to articulate any scientific perspective on deductive logic. Your mumbo-jumbo puffed-up rhetoric opposing inductive and deductive suggests you don't really know what deductive logic is and how much scientists have to rely on it.
EB

 

[Juma]

So you think I overstated.

Let me disabuse yourself of that thought. Systems built on test and experiment are the basis for more systems. Some of those system make use of deductions made possible by the inductive empire being built.

Oh, shit, he said deductive.

Point is whether one is better served by induction or deduction. As far as fundamentals of reality are concerned inductive approaches have had a continuous positive record while deductive approaches all lay by the wayside. So given a choice I always prefer inductive approach.

You missed the point of my post which is logic is essentially establishing validity and that inductive approaches are much richer in that respect.

It baffles me that anyone sensible should feel that inductive and deductive logics have to be opposed somehow.

Anyway, you're clearly unable to articulate any scientific perspective on deductive logic. Your mumbo-jumbo puffed-up rhetoric opposing inductive and deductive suggests you don't really know what deductive logic is and how much scientists have to rely on it.
EB

deductive logic is a tool for our brain. a binocular for our inner eye. but nothing more than a tool.
inductive logic is the source of knowledge,

 

[braces_for_impact]

The OP seems to be coming to the conclusion that because we don't have 100 percent certainty about anything there are no conclusions to be drawn about the universe we inhabit. To this I say, why should nature itself behave in a way that makes us intellectually comfortable. To me, it would be suspicious if it actually did.

 

[Speakpigeon]

It baffles me that anyone sensible should feel that inductive and deductive logics have to be opposed somehow.

Anyway, you're clearly unable to articulate any scientific perspective on deductive logic. Your mumbo-jumbo puffed-up rhetoric opposing inductive and deductive suggests you don't really know what deductive logic is and how much scientists have to rely on it.
EB

deductive logic is a tool for our brain. a binocular for our inner eye. but nothing more than a tool.
inductive logic is the source of knowledge,

It baffles me that anyone sensible should feel that inductive and deductive logics have to be opposed somehow.

Anyway, you're clearly unable to articulate any scientific perspective on deductive logic. Your mumbo-jumbo puffed-up rhetoric opposing inductive and deductive suggests you don't really know what deductive logic is and how much scientists have to rely on it.
EB

 

[Speakpigeon]

The OP seems to be coming to the conclusion that because we don't have 100 percent certainty about anything there are no conclusions to be drawn about the universe we inhabit. To this I say, why should nature itself behave in a way that makes us intellectually comfortable. To me, it would be suspicious if it actually did.

Dear all,

Happy New Year and good health to you and your pets despite all those dangers looming close by.

Now, I have been thinking a lot about logic recently (I'm hopping it could help save the world) and it occurred to me that its status is somewhat fudgy. On the one hand, scientific theories are dependent on logic so scientists probably wouldn't want to shoot themselves in the foot. On the other hand, I don't see how the principles of logic could be construed as evidence-based and therefore I wonder how scientists could possibly feel justified using logic at all.

One way to solve the problem would be to explain logic as a property of the material world. Personally, I tend to think of logic as a property of the human mind but that would be no good for hardcore materialists, right? It could perhaps be argued, and I could in fact agree, that logic is really a property of the brain, but that would be essentially speculative at this stage. We would really need to know a lot more about the brain than we do today to be able to prove that conclusively.

So, meanwhile, perhaps you could try to articulate properly the view that logic is in fact a property of (or somehow comes out of) the material world? Can you?
EB

EB

 

[Rayschism]

Us Indians had logic long before sciencence came to the new world.

We call it natural law.

That is we make observations that happen in nature, and follow those examples.

Like observing how a wolf pack operates with what you guys now call guerilla tactics.

Funny that.

 

[Speakpigeon]

Us Indians had logic long before sciencence came to the new world.

Greek philosophers first started to discuss logic around 2,300 years ago, well before the scientific revolution started in the 16th century.

We call it natural law.

This suggests that you are talking about science, not logic.

That is we make observations that happen in nature, and follow those examples.

What we call logic is not justified by anything like observation of nature. We can use logic to predict future events on the basis of our observation of a small set of facts but logical laws are not based on our observation of natural facts.

Like observing how a wolf pack operates with what you guys now call guerilla tactics.

More like science.

Funny that.

If Indians really knew anything about logical laws I'd very much like to know that. Could you give specifics?
EB

 

[Rayschism]

Greek philosophers first started to discuss logic around 2,300 years ago, well before the scientific revolution started in the 16th century.

We call it natural law.

This suggests that you are talking about science, not logic.

That is we make observations that happen in nature, and follow those examples.

What we call logic is not justified by anything like observation of nature. We can use logic to predict future events on the basis of our observation of a small set of facts but logical laws are not based on our observation of natural facts.

Like observing how a wolf pack operates with what you guys now call guerilla tactics.

More like science.

Funny that.

If Indians really knew anything about logical laws I'd very much like to know that. Could you give specifics?
EB

According to your science us Indians came around to North America between ten and twelve thousand years ago.

And it very much is logic to observe what happens in nature and follow its rules.

I'll provide more at a later time, but I doubt you'll be receptive to it.

 

[Speakpigeon]

According to your science us Indians came around to North America between ten and twelve thousand years ago.

I will presume that there is no record of those early Indians doing anything like logic at the time.

And it very much is logic to observe what happens in nature and follow its rules.

According to our view of logic, logic has nothing to say about how you can get to know that any specific premise is true or not, save for what we call "logical laws", what modern logic calls "tautologies", things like "either it rains or it does not rain", regarded as necessarily true whether it does rain or not.

Logicians have always seen logic just as good reasoning. Logicians consider that you can reason properly even starting from false premises, even from premises you know to be false, so long as you are able to think of them as being true for the sake of the argument.

So, observation of nature has always been regarded as outside the purview of logic.

That's what we call logic, anyway.

So, you may disagree but then it just means we are talking about different things.

You can try to engage with untermensche, who is very active on this forum, and who seems to have ideas somewhat similar to those of Indians as you report them.

Of course, the bit about "following the rules of nature" does require logic, I would agree with that. Yet, we probably disagree somewhat about what we do exactly when we follow any rule.

I'll provide more at a later time, but I doubt you'll be receptive to it.

I believe I'm exceptionally receptive.

Being receptive doesn't mean you happen to agree with what people say. It means you understand their ideas from what they say and proceed from there, which may well include disagreement.

So, please, don't assume that other people are not receptive just because they happen to disagree with what you say.
EB

 

[ontological_realist]

Speakpigeon, I think that you will agree with me that: A is A and that A is not non A. Now ask yourself that how do you know that.

 

[Speakpigeon]

Speakpigeon, I think that you will agree with me that: A is A and that A is not non A.

Right.

Now ask yourself that how do you know that.

Ok, I just did. So?
EB

 

[Phil Scott]

Speakpigeon, I think that you will agree with me that: A is A and that A is not non A. Now ask yourself that how do you know that.

In the simple theory of types with undefined terms, A is not always A.

Personally, I prefer to work in logics where A = A always holds, but I put that down to taste.

 

[Speakpigeon]

Personally, I prefer to work in logics where A = A always holds, but I put that down to taste.

I think a statement B saying that A is not always A would be repugnant or disgusting.

But then B would not have to always be B.

Something I don't understand.
EB

 

[Phil Scott]

The As in question are undefined terms, like 1/0. So the idea is that 1/0 is not 1/0. However weird this sounds, it's motivated by how mathematicians write equations where each side might be undefined. In other words, the group of most logical folk on the planet apparently think this way.

 

[ontological_realist]

Right.

Now ask yourself that how do you know that.

Ok, I just did. So?
EB

Now please tell me that how do you know that A is A and that A is not non A.

 

[Speakpigeon]

The As in question are undefined terms, like 1/0. So the idea is that 1/0 is not 1/0. However weird this sounds, it's motivated by how mathematicians write equations where each side might be undefined. In other words, the group of most logical folk on the planet apparently think this way.

Yes, well, I'm less than impressed.

To me it's just a sad case of overworked specialists who expediently decide in small self-appointed committees that they can take liberties with the English language.

Me, I can write that a hoblax is a hoblax, or that Atax is Atax, without the least fear of being contradicted even though I know not whatever these things might be if anything.

We should also keep in mind that very few of the words we use describe any object fully, and yet we exchange routinely on the basis that X is X.

What's the problem with these guys?
EB

 

[Speakpigeon]

Right.



Ok, I just did. So?
EB

Now please tell me that how do you know that A is A and that A is not non A.

I will but first I really want to know what's on your mind. Can you explain why you think it may be a problem to do what you just asked?
EB

 

[Phil Scott]

The As in question are undefined terms, like 1/0. So the idea is that 1/0 is not 1/0. However weird this sounds, it's motivated by how mathematicians write equations where each side might be undefined. In other words, the group of most logical folk on the planet apparently think this way.

Yes, well, I'm less than impressed.

To me it's just a sad case of overworked specialists who expediently decide in small self-appointed committees that they can take liberties with the English language.

As such a specialist (and one who is not particularly overworked), the feeling is mutual. I do suspect, however, that I'm one of the few people in the thread who has taken a logic class. Most of what is posted here is just the usual ill-thoughtout high-school meandering.

 

[Speakpigeon]

I do suspect, however, that I'm one of the few people in the thread who has taken a logic class. Most of what is posted here is just the usual ill-thoughtout high-school meandering.

It must be so if you say so.

Still, may I try to probe the depth of your expertise?

I've never been convinced by Modern Logic's use of Truth Tables in the case of the implication. As I see it, the logicians' justification for using them in this case is not convincing at all, to say the least. And it's not just me. Many professional logicians take issue with the official dogma. It's also not new. One guy wrote a book on the subject in 1908 I think, broadly saying that the kind of formal logic proposed in Modern Logic didn't correspond to what humans do intuitively.

So, what do you think on this issue. Is formal logic an apt rendering of our logical intuitions? Is it perhaps even better? Or do you feel it is somehow flawed and if so why is it so difficult to put it right? Unless maybe you know of some system of formal logic which, unlike the official dogma is a perfect interpretation of the human sense of logic?

Let's be specific: The implication (2 = 3) → (10/2 = 5) is true according to standard formal logic.

Do you agree? Do you disagree? And then why?
EB

 

[Phil Scott]

I've never been convinced by Modern Logic's use of Truth Tables in the case of the implication. As I see it, the logicians' justification for using them in this case is not convincing at all, to say the least. And it's not just me. Many professional logicians take issue with the official dogma. It's also not new. One guy wrote a book on the subject in 1908 I think, broadly saying that the kind of formal logic proposed in Modern Logic didn't correspond to what humans do intuitively.

The earliest moanings I read about it were in Quine's Mathematical Logic. It's not new, and it still trips students up, myself included back in 2004.

Whatever complaints you muster, you ultimately want something like the material conditional, whether or not it is the appropriate translation for the English "implies." The conditional, for starters, is that thing which gives you:

P ⊦ Q

therefore:

⊦ P → Q

This is either the deduction theorem, or implication introduction, and it's a big deal.

The truth table for implication is another matter. One basic requirement of implication is that it should be the "exponential" for the lattice of truth values. In the case of Boolean logic, where there are basically only two truth values, you're in this stupidly trivial world where you get the strange equivalence (p → q) ↔ (¬p ∨ q), which makes implication kind of pathetic. It has me suggesting to students that they should simply read classical implication "p → q" as nothing more than "either p is false or q is true."

But in intuitionistic logic, that translation won't fly, and implication feels a lot more "causal." You can start reading the implication arrow as saying that, from p, you can produce q, and I think there's something a lot more intuitive in that reading.

So, what do you think on this issue. Is formal logic an apt rendering of our logical intuitions? Is it perhaps even better? Or do you feel it is somehow flawed and if so why is it so difficult to put it right? Unless maybe you know of some system of formal logic which, unlike the official dogma is a perfect interpretation of the human sense of logic?

I don't think formal logic should strictly adhere to our intuitions, our psychology, or our language. All of modern mathematics starts at something intuitive and then abstracts towards some implied concept that can easily be a long distance from where you started. Logic is the same, IMO. What you end up with as the correct logic is probably not what you instantly thought of, and we shouldn't be trying to justify our informed end state based on how intuitive it is to the beginner.

Just compare how a modern mathematician understands basic geometry compared to a layperson.

Let's be specific: The implication (2 = 3) → (10/2 = 5) is true according to standard formal logic.

Do you agree? Do you disagree? And then why?
EB

I certainly want that implication to be true. It's saying that if you start from an impossible situation, then all bets are off, and you can end wherever you like. No-one will ever be running modus ponens on that implication anyway, because they'll never have evidence that 2 = 3 (unless you're an extreme pessimist, and I am: but then, I live dangerously.)

The first mathematician I've read who got close to this point is Hardy: in a proof by contradiction, you sacrifice the game. Everytime a mathematician entertains a falsehood, all bets are off, and you can play whatever you want. All-bet-are-off (2 = 3) → (10/2 = 5). See the implication arrow as a transition between game states.

As for truth-tables, I'm a card-carrying constructivist, and we don't do truth-tables. If you're doing truth-tables, then you're really just doing arithmetic modulo 2, which is cool. That's much of computing, and not to be sniffed at.