Barry Arrington and StephenB at Uncommon Descent have frequently invoked “the rules of right reason” in their arguments.
Today, Barry posts them thus:
The Rules of Thought.
The rules of thought are the first principles of right reason. Those rules are:
- The Law of Identity: An object is the same as itself.
- The Law of Non-contradiction: Contradictory statements cannot both at the same time be true.
- The Law of the Excluded Middle: For any proposition, either that proposition is true or its negation is true.
And claims:
Note that the three laws of thought cannot be proven. They are either accepted as self-evident axioms – or not. The fundamental principles of right reason must be accepted as axioms for the simple reason that they cannot be demonstrated. There is no way to “argue for argument” and it is foolish to try to do so. If one’s goal in arguing is to arrive at the truth of a matter, arguing with a person who rejects the law of idenity is counterproductive, because he has rejected the very concept of “truth” as a meaningful category.
This seems to me fallacious. (heh.)
They are indeed axiomatic – in other words, they are axioms on which a certain form of logic is based. Now I’m no logician, but I am capable of seeing that if we assume those axioms are true, we can construct a logical language in which useful conclusions can be drawn, and useful computations performed.
But there are some propositions that simply are not possible in that language, because those axioms themselves are based on more fundamental assumption: that we know what an “object” is; that we know what “time” is – in other words, that we know what “is” is.
As one of your presidents once said.
And we often don’t. Often the reality (the truth, if you like) that we want to uncover relates to those referents signified in those very assumptions: what is an object? what is time?
And a classic (or perhaps non-classical) example, it seems to me (and I’m more at home here than with quantum physics) is: what is a person? Am I an object? Is it sensible to say that I am myself, if, by the time I have said it, I have become something different – an object with different properties – to the self I was when began to utter the sentence?
And if I am an object, what are the properties of that object? Does it exist in both time and space, or just space at a given time? Does it make any sense to say that a person exists at all in an instantaneous moment, or is being a person a process?
In other words, it seems to me that “The Rules of Right Reason” simply do not cover all the truths there are to investigate, and cannot cover them. To assert this is not to reject, as Barry suggests, “the very concept of truth as a meaningful category”. It is to assert that there are true statements that can be made that nonetheless cannot be made if we rigorously adhere to the rules of right reason, and “objects” that we cannot consider.
And that these include mind, person, consciousness, designer, intelligence, and, ironically, God.
Sigh! Such confusion.
Darwinism, as a statement, uses words that refer to reality.
LNC does not use words that refer to reality.
We apply logic to descriptions of reality, not to reality itself. Reality comes to us without descriptions, and without a language in which to form descriptions. In order to communicate about reality, humans came up with language, and with ways of forming descriptions. If those descriptions happen to be usable within logic, it is because humans made usefulness in logic one of their requirements for how to describe.
If we find descriptions of reality that violate the LNC, that would only be a conflict between our use of language and LNC. Reality itself would not be in any violation of LNC.
Neil,
Nicely explained.
If Maus still doesn’t get it, I am going to give up on him.
If you think my argument was ad Gutenberg then you missed most of it.
Fantastic, it saves me making the same analogy. Now pick which layer reality is on, your nerve endings are on, and your brain is on.
“It is impossible for the same thing to belong and not to belong at the same time to the same thing and in the same respect” — Dead Dude
This, of course, is the original formulation of it. To get to the full monty on propositions you need to slog through the discussion about propositions, predication, and negation.
This may be the source of confusion. Reality is what reality is. If reality violates the LNC it is that the LNC is in error, not reality.
A couple things need stressed here as some may not understand the difference. When we say ‘classical logic’ we are speaking of the modern logic created and popularized for the logicist program in mathematics.
But a generic syntactic and deduction system of a rough 100 years vintage does not remotely cover the breadth and depth of the topic. The most unfortunate thing about classic logic being that it is consumed uncritically as if it sprung fully formed from Hilbert’s forehead. And yet it is, in the sentential portion, crucially and critically based on the hash the Scholastics made of Aristotle’s logic — and you cannot derive first-order sentences without traveling all the same ground as Aristotle. Otherwise you end up doing and claiming abusive symbolic nonsense such as Horse + Ford = Footstool. Where all the plain meaning are implied. It’s the same nonsense abuse of syntactic fiddling that underlies all x*0 = x proofs you’ll find wandering around.
But it is this context free context that is taught in collegiate philosophist courses as the One True Logic.
At this point, I can’t even tell what we’re agreeing and disagreeing about! I suspect that we may actually be in agreement without realizing it, but I’m not sure!
If you think that changes anything, then you are still confused.
Maus,
Get kairosfocus to explain the concept of layering to you.
Once you can grasp that, we can proceed from there.
To Carl dated at 10:49 pm is excellent – says very well what I was struggling to explain to Stephen B.
is very succinct, so is
is also.
Thanks
Intuitionistic logic does question the law of the excluded middle. Quantum logic does question the distributivity of conjunction and disjunction.
Then google it.
Logic is not based on any particular metaphysics, Aristotlean or not.
I have no idea what this is supposed to mean. If the LNC it analytically true, then it is true no matter what sentences we’re talking about.
This is not true, the Many Worlds Interpretation is quite popular among physicists.
And, of course, the Copenhagen version is taught (a) because textbooks are conservative, (b) because most people probably use the Copenhagen interpretation because most people were taught the Copenhagen interpretation because most textbooks use the Copenhagen interpretation. But it’s simply not true that other interpretations are some sort of philosophers’ fancy.
You mean Frege’s, surely?
Is it? I don’t remember Frege mentioning the Scholastics at all in the Begriffsschrift. Did Hilbert do so? Where? How?
I’m not sure what that was supposed to mean, but Frege’s achievement is precisely his invention of quantifiers, which allowed logic to advance beyond Aristotlean logic. Aristotlean logic is essentially monadic first-order logic, which is much less expressive than full first-order logic.
Yes, slight correction here, though: logic tells you what you shouldn’t do rather than what you should do. Logic cannot force you to assert anything, it can only tell you what you shouldn’t assert.
The Rules of Right Reason, as conceived at UD and elsewhere, are synthetic truths. That is, “A & ~A = false” obtains as a statement about nature, our extramental reality. This is StephenB’s explicit position, for example, and the basis for Barry’s banning of many, for not declaring without qualification the primacy of the LNC as a synthetic truth, a universal synthetic truth (true and applicable in all real-world contexts).
This conflation of LNC as a trivial truth, a logical axiom, with a synthetic truth, a synthetic meta-principle, is where the train jumps the rails. Classical logic is so successful and useful that it gives rise to the suspicion that it’s a metaphysical imperative, and not just an axiom from logic. But then, in some areas of existence, classical logic doesn’t work, and its status as “synthetic law”, a metaphysical principle about how intelligible reality is for humans, and how we must render it sensible, is discredited.
Oh. Did you actually want me to address the errors as if they were a serious argument?
For starters you did list a couple different interpretations and noted the problems. You also didn’t list others that don’t have the same defect; notably and including one of the two versions of Copenhagen. And that’s really rather interesting in its own right as the three largest iceboxes Von Neumann sold to the Eskimos all got mention today.
Von Neumann was a great man and mathetician, and his skill in math was only exceeded by his skill in selling vacuous nonsense to philosophers. Just a couple threads up from here we have a discussion about ‘Shannon entropy’; a term given us by Von Neumann as part of a sales pitch for Shannon. And of course, above in this thread transfinite cardinals were mentioned. Those becoming fait accompli once Von Neumann built V with the as a hereditary operator. Such that there was finally a valid use of them, and the general continuum hypothesis, even if it was only as a structural device disguising a type system.
Which brings us to the vapid Jonestown nonsense in Copenhagen. It didn’t start out that way and the one version doesn’t contain that nonsense. And then there’s the version that does. Who do you think was responsible for selling the philosophers on quantum unicorns? Give you three guesses, and the first two don’t count.
He was a legend. All the more so for his ability to get philosophers — men of broad dreams and shallow minds — to do his pimping and publishing for him. And for all three we’re still having to routinely deal with the boggled nonsense that issues from it. cf Dembski, Copenhagen.
So yes, I failed to note you mentioning that about one version of Copenhagen. I also failed to note where you mentioned that incompleteness and difficulty are of no concern for you in theories. What with QM getting it’s start with flagrant violations of various laws itself.
But if you want to suck the snake oil Von Neumann created for the purpose of duping the rubes in the Philosophy department? Knock yourself out. Just ask Elizabeth to change the site name to ‘thegulliblezone.com’.
Yes, that’s a better way of putting it! I’d forgotten a nice phrasing from Brandom, which I’ll paraphrase as, “modus tollens only tells you that you should not assent to all of P, ~Q, and P –> Q. It doesn’t tell you what you should do!”
Although, writing that out in this context makes me wonder . . . surely we should say that modus ponens also says that we should not assent to all of P, ~Q, and P –> Q. So both inference rules amount to the same claim: that those three statements form an inconsistent set. Is there a difference between them? Why I am getting myself so confused about this?
At least now I better understand the old slogan, “one person’s modus ponens is another person’s modus tollens!”
Carl
I didn’t know we were in disagreement! Shall we be gentlemen and disagree to agree?
Your air tight rebuttal has sealed all rejoinders, good sir.
In other words, you’re out of your depth. No worries, it happens.
Frege for the sentential portion, yes. Hlibert for the common deduction system. Frege spoke to Aristotle (second source, I don’t do German) but then when anyone speaks to Aristotle they usually mean the Scholastics. The tells are with existential import, ex falso, and some other Schoolmen nonsense. I can’t recall anything from Hilbert on the subject specifically however.
Extending them to quantify over variables and, of course, the nesting of them. I’ve absolutely no beef with Frege and he did great work. But you have to travel the same path from the bottom up as Aristotle to get the deed done. Hilbert was interesting. His work is excellent so long as you postulate the same sort of machine that Hilbert wanted to run on. Absent that it’s a bit pants from where I sit.
Only in the direction you read the implication for the inference.
But there’s nothing in the rules of inference themselves which specifies which way to read the implication, is there?
Maus,
One day you will start making sense. Today’s not that day. Too bad. 🙂
This post (the whole post, not just the bit I quoted), was very funny. But, somehow, I have a suspicion that it was intended to be serious.
Carl Sachs,
You’re right — both modus ponens and modus tollens are based on the same underlying logic. I think of modus tollens as modus ponens with a twist.
In modus ponens, we start with P->Q, we assert P, and we conclude Q.
In modus tollens, we start with P->Q and (here’s the twist) implicitly convert that to the equivalent ~Q->~P. We then assert ~Q and use modus ponens to conclude ~P.
Sadly ironic, really. But just as well you enjoyed it.
The day you admit to understanding me is the day when hell sends out for gelato. Good to see you’re still doing well.
…and I thought I was just tired enough to see word salad where there was really cunningly hidden rodent wisdom…
but then, even cunningly hidden wisdom usually has some actual pieces of information, or at the very least actual references to actual pieces of information in it….
Well, one involves negation, while the other doesn’t, so modus ponens can be used by people who only understand conditionals, whereas to use modus tollens, you must understand both conditionals and negation. Whether there is a difference in their strength depends on how one construes negation. What modus ponens says is that you shouldn’t assert P, P–>Q while denying Q. What modus tollens says is that you shouldn’t assert ~Q, P–>Q while denying ~P. If you identify the assertion (denial) of ~P with the denial (assertion) of P -in other words, if you have a Boolean negation – there is no difference. If you do not, for whatever reason, then there is. Replacing modus ponens by modus tollens in any of the usual Hilbert calculi for propositional intuitionistic logic, for example, will yield a strictly weaker system, as any non-axiomatic theorem will be of the form ~P. (I conjecture that it would be complete with respect to that class of sentences, in the sense that any sentence of the form ~P is provable in the modified calculus iff it is provable in the original calculus.)
Okay, that’s not how I’d put it myself, but I guess I roughly agree.
Over at UD, StephenB asked me the big question:
I told him I agreed about ending the madness, and told him I’d see him later.
The discussion here has helped me understand this situation better, so here’s what I might say to Stephen if it wasn’t sheer madness to try to keep talking with him:
The question is very much of the “Have you quit beating your wife” type: No matter what you answer, if you answer at all you implicitly assent to the premises which frame the question in the first place.
Without repeating all the discussion on this, the two main premises embedded in Stephen’s question might be summarized thusly:
1. That the word “pertains” in the question, to Stephen, implies that there is some type of causal relationship between logic and reality, as opposed to a practical one of using logic as a tool to help us think about the world, and
2. That the universe is fundamentally made up of “things”, which are clearly distinguished from all other things; and more generally, that all properties are dichotomous: either A or not A, with nothing in between. This is a property of logic, but it is not a property of the real world.
So answering his question either yes or no implicitly assents to broader principles which I don’t agree with. Therefore, I won’t answer his question.
aleta,
Hi aleta,
Invite StephenB to come over. That would be fun. (Hi Stephen!)
“Pertains” doesn’t imply causation, only correlation.
A thing cannot exist without being whatever it is; whatever “it” is necessarily connotes what “It” is not.
“the moon simultaneously exists and does not exist”
Obviously, I’m neither StephenB or Barry, and what some say that they would say may indeed be correct. But I say . . .
The quote above is not unintelligible, or nonsense in the same way as not making sense at all. It is known what is meant, very, very clearly, by the statement.
The moon exists. (no problems so far, right?)
The moon does not exist. (still no problems, right?)
If both of those sentences are intelligible, then, clearly, so is the sentence “the moon simultaneously exists and does not exist”. To say otherwise is to have selective amnesia.
Brent, I don’t think anyone said the sentence was unintelligible.
Brent,
Even Kariosfocus calculated a non-zero probability for the superposition of the moon, and yet he was not banned. He said pretty much what the people who were banned said, and was not banned.
He answered the question using more than the one word, “no’,” and was not banned.
So what is the meaning of this statement?
Brent:
Hi, Brent! Welcome to TSZ!
I don’t have any problem with using classical logic to help solve problems for which classical logic is an appropriate tool.
It’s just that there are problems (including quantum physics problems, but also other ontological problems) for which classical logic doesn’t work very well. I think that’s why some people were reluctant to give a straight “no” to Barry’s challenge. I wouldn’t have done.
the law of non contradiction is inviolable in math an logic where x is x and only x. unless is it specified to equal a different value. Most words and especially nouns, are not as easy to fit into nice easy boxes.
Not only the nouns but their referents too.
Maus,
The day anyone starts understanding you is the day you start making statements that are understandable.
As per my suggestion that you should talk to kairosfocus, if you don’t think he understands why software is layered, there are other people who can help over at UD.
Gil Dodgen could explain it well and he is actually posting here.
I think that sort of insight could help you see why the LNC is not a physical layer property.
Brent,
If they had stopped there, everything would have been okay, but they didn’t.
They brought the “LNC” into the argument.
The LNC is no more a part of the real world than a meter is.
If our measurement and processing tools actually impacted on the world, I could make a case that circles don’t really exist since the value of pi, according to our limited mathematical abilities, is infinite.
A meter doesn’t enforce a “length” upon anything and the LNC doesn’t enforce “relationships” in the physical world.
A meter is a property of measurement and the LNC is a property of logic.
Brent,
To give a better example, imagine looking up into sky and seeing three stars close together.
We can see “visually” what their positions are in relation to each other, but we cannot be sure of their “actual” positions relative to each other.
The reason is that gravitational lensing bends light and so we cannot trust our visual senses.
On Earth this doesn’t come into play and so we can ignore it, but at large distances, what we see isn’t necessarily what we get.
Logic, like any other tool helps us understand the physical world, but at very small scales involved in quantum physics and very large scale physics such as star systems, these tools need to be extended.
Since we made these tools, why would we allow them to mandate to us a reality that wasn’t envisioned when they were initially developed?
Maus,
How does “your” lack of understanding, leave “me” out of my depth?
This is nice: over at UD, Stephen has, more clearly than ever, made exactly the point that I, and others here, disagree with. For the record:
Stephen states well what I reject: the ontological aspect of the Law of non-contradiction – the necessary link between logic and reality. Although, of course, I don’t think I have abandoned rationality in doing so.
Aleta,
What I don’t understand is why kairosfocus agrees with StephenB.
Take for instance, 5V TTL logic.
An input below 0.8V is false while a signal above 2.2V is true.
What if it’s in that grey window between true and false?
The output will take a value of true or false but we don’t know which.
Is this a violation of the LNC?
If you put a second chip in parallel, would it disagree with the first chip or not?
If we had a disagreement between devices, clearly that should be a violation of the LNC, only if StephenB is right about the LNC’s tie to reality.
Also however, if StephenB is right, it would be an example of our ability to manufacture a physical device which violates the LNC and thus physics in our real world.
The actual answer is that we have misused a device whose role it is to provide us with a logical assertion by providing us an interface to the physical world.
Communication protocol stacks work the same way, in that there is a separate layer that deals with physical devices.
Upper levels deal with the processed data received from the physical devices and trust that the data is valid.
If you make an assertion at the physical layer that says, “Jupiter exists”, that’s what the logic has to work with.
Lawyers know legal details need to be addressed very specifically, but I don’t understand why they believe scientific details don’t need to be addressed with the same care.
So you have proof of this then? Of course you don’t, anymore than you have reading comprehension as I’ve never claimed it was a mandatory ontological feature. You will note that I’ve discussed the manners in which to empirically demonstrate the invalidity the principle. Right there, that’s a little thing called science.
No. And if you don’t know the difference between contradictories, negation, and contraries then you are quite obviously out of the depth of your knowledge.
Once again, no. Two chips in each in one state simultaneously are not one chip in two states simultaneously. Seriously, this is kindergarten material that everyone save pathological schizophrenics have sorted out by the time they’re into learning the alphabet.
All you need to do is pick up an apple and look at it. Is it red, to you? It doesn’t matter if you state the question out loud, type it, think it, or just simply gaze vacantly at fruit. It will be red, or not, but never the both. You are a participant to personally testing the LNC as a valid law simply by having your eyes open and seing that the world isn’t in every instant what it is and is not. That’s called ‘observation’ and it’s a critical part of science.
In truth you have a visual acuity, on average, for 60hz before it gets sketchy. But lets cut that in half to 30 frames per second. Each frame being one frame, one observation, no matter how many objects are in that visual frame. And let’s say that you are in permanent adolescence, 16 hours awake on average, for every day of your life. Then in each your you will visually test the LNC at the insanely lowballed estimate of 631,152,000 times. This year, the human population will collectively visually test this theory 4,418,064,000,000,000,000 times. And if we take the estimated human population since the time Plato and Aristotle were banging about, all the way up to the present, this theory has been tested 504,471,091,905,599,920,000 times.
How many seconds did it take you to digest that number? Two, three? Or did you skip past before your eyes glazed at numeral overdose?
That’s a stupidly large number. If we took one US penny as representing one test and stacked them all up it would create a stack 82.65 lightyears tall. If we simply ran pennies from here to the next nearest star each in turn we would reach: Sol, Alpha Centauri, Barnard’s Star, Wolf 359, Lalande 21185, Sirius, Luyten 726-8, WISE 1541-2250, Ross 154, Ross 248, and get halfway to Epsilon Eridani.
If, to put it into a human scale, we considered each test the inspection of one base pair of DNA singly. Then that magnitude would represent fully sequencing the genome of every human currently alive on the planet.
Twenty four times.
And for all that there has yet to be one, single, replicable demonstration of the failure of this principle.
So I’m curious: What are your standards of science? And just for the religious giggles over what underpinned this entire topic in the first place: Design or Darwin, what religion do you hold to?
Is this guy a philosopher or something?
Human perception is not exactly a foolproof device. Take a yellow apple and look at it through a red glass with your left eye and through a green glass with your right eye. You will perceive it to be both red and green. 60 frames a second or whatever that is in light years.
Maus,
Redness is a pretty good example of a quality that is linguistically ambiguous. Redness is a perception rather than a property of objects. There are many ways to induce the perception other than having an object emit or reflect a specific wavelength of light.
Much of our descriptive language fails when we attempt to correlate it with properties measured with instruments. The question isn’t about the principles of logic, It is about what we mean by objects existing, and what we mean when we assign properties and attributes.
Through each eye, already mentioned by Aristotle and that was mentioned already in this thread. Nice red herring.
That’s one tally for the Darwinist column.
“Red, to you”. And yet our instruments have yet to show one, single, replicable failure. Also mentioned already in this thread, but another nice red herring.
That’s two tallies for the Darwinists.
But I’m most curious as to what camp Toronto is in.
Are you perhaps referring to this:
It is nonsense.
Firstly, Church-Turing is usually called a thesis, not an hypothesis. That’s because it is not the kind of thing that you could prove or disprove. Secondly, intuitionistic mathematics has been around for 100 years or so, and rejects LEM. The intuitionists have not disproved Church-Turing, and I am not even aware that they have any objections to Church-Turing.
Over at UD, Stephen makes a point worth responding to. However, I’m going to respond here, not there, because the environment here is, shall we say, more conducive to constructive discussion, with more and different people able to join in.
Stephen wrote,
I think this distinction between valid and sound is useful. It’s the nature of that distinction that I’m am trying to make: the truth of the premises are not given to us by logic itself, but are investigated, in the broadest sense, scientifically in respect to the empirical evidence to see if they “accurately reflect the real world.” Sound arguments are therefore contingent, always, at least theoretically, tentative, and subject to revision.
So of course there is a link between logic and reality, but it is provisional, revealing itself in the soundness of the assertions that we develop about reality. There is no direct “logic to reality” link, which is what I think Stephen meant when he wrote, “the LINK between LOGIC and REALITY is INHERENT in Law of non-Contradiction, which includes the logical, the psychological, and the ONTOLOGICAL.”
Another way of looking at this: Stephen’s last sentence is, “Clearly, if logic was not linked to the real world, there would be no such thing as a true premise and, therefore, no such thing as a sound argument”
A “true premise” is a hybrid of sorts – it’s a statement in some type of language (often mathematical) which “accurately reflects the real world” in terms of the empirical evidence and which fits into a logical structure with other premises: it is what provides the link between logic and reality. We reason about the world – as someone said earlier, logic is about how assertions relate to other assertions, but logic is only one component of that process of developing true assertions. There is no direct link from logic to reality without the intermediary process of us developing and testing our assertions.
If I may say so, it is a rather silly point.
Humans temporarily link their logic to the world when making arguments about the world. That does not require any metaphysical linkage.
Part of the powerfulness of logic is in the fact that we can make these temporary linkages as needed. We can conclude that 2+3=5 abstractly without a link to the world. And then we can use it to conclude that 2 apples + 3 apples = 5 apples, or that 2 oranges + 3 oranges = 5 oranges. If logic were metaphysically linked to the world, then the statements about apples and oranges would require separate independent proofs.
What you (or Stephen?) seem to be saying here isn’t that the LNC is logically sound or unsound, but rather that descriptions of the real world embedded in our premises might be inherently incapable of being validated, or even decidable.
How would we even go about validating a premise like “God is good”? Or how about the premise “evolution is not plausible”? This latter premise seems to be the very core and soul of ID, but it certainly can be true and not true at the same time. And how can any premise making a claim about a hypothetical but in principle speculative agency, even be decidable?
I’d suppose that any non-trivial real-world system would be rife with undecidable premises. Which means logic is too often in the position of producing garbage out, due to the garbage in.
Maus,
No, only my vision will be tested that many times, not the LNC.
In order to test the LNC, I need to actually perform logic at the same rate, not simply see objects.
Your attempt at an analogy has failed at our point of contention.
Logic is performed on assertions, not sensory inputs.
Here’s an analogy that I hope is going to turn out better than yours.
I have three apples in front of me and I intend to select a red one.
I choose number two.
That was great so I decide to choose another.
I choose number one.
Whoa!!!! What happened??
An apple that was not a choice the last round has been selected in this one.
The problem for your side is that my logic did not change at all.
What changed is my assertion of the attribute “red”.
Apple three is green, while apple two was a light shade of red and apple three was a deep ruby red.
After processing my sensory visual interface, I asserted one apple out of all the offers to be “red”, and any remainders were “NOT red”.
My logical decision which followed, in all cases was:
IF (CurrentApple == Red)
{
EatApple();
}
ELSE
{
DontEatApple();
}
The logic itself did not change for either apple, nor did the actual physical colours, only my assertions about the apples did.
Please show me what is wrong with my logic program itself.
In both cases, it successfully provided me with the apple that was red and the logic never changed.
If I am right, and logic is not tied to physical reality, anyone reading this should be able to imagine an assortment of apples , and using my logic as stated above, choose an imaginary “red” apple as if it actually existed.
Here’s the interesting thing.
If you make all the apples in your imagination the same colour, you can assert they are all “red” or you can assert they are all “NOT red”, but you cannot say they are all both “red” and “NOT red” at the same time.
That would be a violation of the LNC.
What links thought to the world is our embodied perception and action. Thought does not have mystical powers to attach itself to the real all by itself.
To respond to StephenB’s comment:
This is quite right, as far as it goes, but it doesn’t work in StephenB’s favor. The LNC is a test, all right, but it is a test for validity, not for soundness. An unsound argument (one with false premises) can avoid contradiction just as much as a sound argument can.
We test for soundness — for truth in our premises — in a variety of ways. In some cases, yes, I’m willing to admit that there are a priori truths. But the law of non-contradiction does not, and cannot, reveal them to us. And in most cases — in both science and common-sense — the truth of the premises is confirmed by observation.
In any event, one need not be an Aristotelian in order to be a rational animal and to know that one is!
Best,
Carl
Reject the LEM as a valid rule of inference in a Hilbert deduction system. And of course Church-Turing cannot be disproven with the math we *have* as the may we have supports it. Reread the post about it.
This is a vast improvement over your previous. Kudos, seriously.
If you try to treat it as the logical positivsts did then: Absolutely. Affirming the consequent is an ancient fallacy and the philosophists should have known better.
To Carl: I agree, Stephen seems to be making a point which supports my position, not his, and I agree with all the rest that you wrote.
to Flint: I wrote, “So of course there is a link between logic and reality, but it is provisional, revealing itself in the soundness of the assertions that we develop about reality. There is no direct “logic to reality” link. It is Stephen who wants to claim a direct “logic to reality” link.
I don’t think I quite understand what you are saying with some of the rest of your post. However, you have pointed out the elephant in the room: an important aspect of Stephen’s beliefs about logic is that he wants to be able to use logic, starting with “self-evidently” true logical premises (in his eyes) to prove things about the nature and existence of God, absolute morals, and so on. The view that logic without empirically validated assertions is just content-free manipulations of invented symbols directly challenges that view.
No, you only need to be witness to it. “I’m blind” would have been an awesome sophist troll for a response. Claiming that your neurons are unresponsive, and that you are therefore brain dead, is not.
“Red, to you”. Not even remotely a good red herring. Take up with either of the other two for lessons. olegt is good, Petrushka is absolutely thorough.
Might be a lost cause though as you’ve absolutely no ability to read English. This point has been addressed several times and is entirely valid for what you’re responding to.
I note that none of the contestants have enough courage to discuss what the standard of science are for them. And I note that you don’t have enough courage to let us know which team gets your score.