The inference depends on accepting PNC. — Banno

How so? "If the 'true/correct logics' contradict one another, then the PNC has been destroyed."

I have to accept the PNC to accept that claim? I think everyone can see that you are wrong here. Maybe stop dancing and start answering the simple questions being asked?

Edit: Unless you are actually presenting Aristotle's argument in Metaphysics IV, but I doubt it. If that is what you are doing you should be more forthcoming. More transparent. More philosophical.

I'm curious, if you support that position, in virtue of what would true/correct logics be true/correct and false/incorrect ones not be? — Count Timothy von Icarus

I'll just point out what a great question this is, and how it becomes even greater after being dodged. :smile:

Yep, haha. But maybe that's the point.

Great posts of late. Your time away has served you well. :up:

Where you used it to adjudicate over logics — Banno

Do you agree or disagree with that inference? There is no adjudication, just a consequence.

You are not here to addressing the topic of this thread, by your own account. You do not have to be here, and I am not under any obligation to address your posts. — Banno

And yet you are the one who transplanted a different conversation into this thread. You are also the one who abandoned the OP of logical nihilism in favor of logical pluralism when I brought it up.

I will often answer that there is indeed a kind of peer-review and 'quality control' method, if you like, in spiritual cultures, such as Zen Buddhism... — Wayfarer

Yep, and intersubjective validation/confirmation.

The real problem with the idea of higher knowledge is the lack of a vertical axis against which the term 'higher' is meaningful. But that is the very thing that physicalism has undermined. Physicalism has a 'flat ontology', with matter (or nowadays, matter-energy-space-time) being the sole constituent of existence. — Wayfarer

Yes, that's a good point. What's curious is that often higher knowledge is called "wisdom," and I would think that the physicalist would admit that a physicalist possesses wisdom that a non-physicalist does not possess. That is, the ability to know and understand the metaphysical basis of reality constitutes wisdom. Then enters the age-old question of how to account for reason or intellect in terms of the physical.

- Where have I given primacy to the PNC? Are you disagreeing with my argument or not?

That'd be logical nihilism. — Banno

Yep, that's what I said.

Therefore, there are true/correct logics. — Banno

I think Count has addressed this nicely:

I guess a "strong" pluralism would declare that there are multiple equally valid/applicable logics but no morphisms between them? I just find it hard to imagine how this could be the case, since it seems that, by definition, they must have similarities in virtue of the fact that they are equally applicable to the same things. — Count Timothy von Icarus

So we end up with this:

• The "true/correct logics" either contradict one another or they don't.
• If they do, then the PNC has been destroyed.
• If they don't, then we are no longer talking about logical pluralism.

Pick your poison. Your thesis is that there are true/correct logics with nothing in common, such that we cannot call their similarity logic in a singular sense, and we cannot apply a rational aspect under which they are the same. But the natural language itself betrays this, for simply calling them logics indicates that they belong to a singular genus.

As I said:

For example, someone who believes in deductive, inductive, and abductive reasoning is not a logical pluralist. It is in no way controversial that there are different ways of reasoning.*

* Similarly, someone who utilizes different logical languages or formalisms for different arguments is also not a logical pluralist. — Leontiskos

The idea that different formal logics can each yield sound arguments without contradicting one another is not in any way controversial, and I would not call it logical pluralism.

- These topics really can't be addressed in bite-sized forum posts. How do we obtain the simples which logic then manipulates? That is a very large question. I suppose if you search my posts for "intellection" you will find places where I tried to elaborate on it.

-

This is how I want to see a disagreement between Banno and myself:

1. If we have discursive knowledge, then there is a true/correct logic.
L1. We have discursive knowledge.
L2. Therefore, there is a true/correct logic.

1. If we have discursive knowledge, then there is a true/correct logic.
B1. There is no true/correct logic.
B2. Therefore we do not have discursive knowledge.


Then the question is simply whether L1 or B1 is more plausible. The problem with Banno's approach is that, even for any merits it has, it precludes knowledge, and this is much more absurd than the alternative. Of course B1 is not exactly logical nihilism as presented in the OP, but I see no real reason to engage G. Russell's theories on their own terms. I am here because of a tangent that was redirected to this thread, not because of the OP. I would be more likely to address an argument if Banno presented it himself.

Glad we are on a philosophy forum and can adjust to the big picture and zoom in where necessary — schopenhauer1

Yep. At least that's the hope. :grin:

Nice idea. So for your understanding here you are saying that mathematics are basically "arbitrary" forms of logic (that sometimes map to reality)? — schopenhauer1

Metamathematics, not mathematics. Something like "game formalism (SEP). It is something like the study of the logic of symbol manipulation.

I tried to set out my view of logic in my first post here:

Historically logic is the thing by which (discursive) knowledge is produced. When I combine two or more pieces of knowledge to arrive at new knowledge I am by definition utilizing logic. — Leontiskos

On this view the "binding" is part of logic, given that discursive knowledge cannot be produced without it. But there is a distinction between intellection and combination/separation, and we justifiably think of the latter as logic.

To try to get at it in just a few words, we usually think of knowledge of simples as one thing and the manipulation of that knowledge of simples as another thing. That's fine; they are distinct. I call this knowledge of simples "intellection" as opposed to "ratiocination." But even when all the simple pieces on the board are set and ready for manipulation, I would contend that we have still not left intellection behind. Why? Because an inferential move or rule involves intellection. The manner in which we move from premises to conclusions is not endlessly discursive, or not entirely related to ratiocination. We must understand that the inference is valid in order to undertake it, and this understanding is part of intellection. Logic of course tends to calcify or standardize rules of inference, thus forgetting the importance of understanding them. Basically, the closer we move to that "binding" between the formal logical system and reality, the more immersed we are in intellection, and this includes an understanding of inference.

- Good post. :up:

-

As I was saying to Leon, the "foundation" to logic would be a meta-logical theory, not the axioms/logical systems themselves. — schopenhauer1

Sure, if you like. Whether the binding between reality and logic is metalogical is largely dependent on how you conceive of logic. On my view something with no relation to reality (and therefore knowledge) is not logic. Ergo: something without that binding is not logic. It is just the symbol manipulation that Banno mistakes for logic. More precisely, it is metamathematics.

When you want to call the binding metalogical that makes me think that you take logic to be something that is not necessarily bound to reality in any way at all. What I would grant is that it is a somehow different part of logic, but I do not think that these parts are as easily distinguishable as the modern mind supposes.

- I understand, but the same point applies to the edited post. You are prescinding from the translation and focusing entirely on the formalism. In fact you are back-engineering a new English sentence to better fit the formalism. Again, my "parlor trick" includes the translation itself. The levity of the OP derives in large part from the initial plausibility of the translation.

Again, Lionino's thread shows in some detail why there are no obvious English translations for ~(P→A).

Pick up a length of pipe. Look at it from the side and it's rectangular. Look at it straight on, it's circular. Done. "But I didn't mean that." — Srap Tasmaner

A circle does not have a depth dimension. If we were talking about ropes we would have a different case.

I mean, if we define circles as squares, then sure, we can have square circles. But that's not what circles are. Redefining words in an attempt to achieve substantive conclusions does not strike me as good philosophy. We can talk about whether a material "instantiation" is ever a circle or circular, and I of course concede that in a strict sense there are no material instantiations of circles (and that if the great circle is conceived in this way then it is not a circle). But that is a far cry from the conclusion that there are square circles.

At the bottom of this whole thing are important questions about philosophical motivations. When I asked @fdrake about his motivations he said that, "shit-testing is standard mathematical practice." In other words, he has to adopt the persona of an extreme skeptic to see if his ideas hold up. This is a Cartesian mentality through and through, and I submit that it is a bad one. Granted, it is more applicable to mathematics than philosophy generally, but I tend to think it conflates science and mathematics in important ways. Beyond that, when I introduced the term "square circle" into the thread, it was as a metaphor for non-mathematical contexts. In such contexts "shit-testing" really is just Cartesian method, the age-old error of mistaking philosophy for mathematics or indubitable knowledge.

The "parlor trick" is just that the antecedent contains the contradiction "¬(P → A) ∧ ¬P". — Michael

My "parlor trick" includes the translation. The formalism is not very difficult to understand. What's fun is the way that the translation is intuitive. @Hanover's difficulty is this, "Why did we say, 'So I don't pray'?" The explanations I have been giving answer that question and give an account of why the translation is intuitive.

-

I was trying to clear away the enticing parlor trick that made the OP appear plausible so that the error could be revealed. If it can be shown that the use of the logic within the OP will lead to absurd results in other instances, then that is a valid disproof of the logic within the OP. Such is a reductio ad absurdem. — Hanover

You are failing to recognize the non-equivalence of the two. Whenever the "So" premise is justified the argument works. In the OP it is prima facie justified ("So I do not pray"). In your example it is not ("So I do not scream").

The way you are all using it is basically "axiomatic". I take "axiomatic" to mean "don't ask me anything further, this is as far as I'm going", or simply "duh!". It really doesn't mean much except that we need to start "somewhere" and "this seems like a good place to start". — schopenhauer1

Eh. If you take it to mean axiomatic, then it has nothing to do with a good place to start. If you take it to mean a good place to start, then it is not axiomatic. Axioms are not good places to start except in a purely formal or economical sense. This chimera is understandable, given that my use of "foundational" was nothing like "axiomatic." Quite the opposite.

Again, the PNC is a more universal foundation or first principle than modus ponens. It is a foundation in the same sense that the first few feet of the trunk of a Redwood is a foundation. It is stable in a way that the upper branches are not, and folks never directly contravene the PNC. They only do so indirectly when they have climbed out onto limbs and lost track of where they are.

(There's a direction-of-fit thing here: in one case, the center determines the circle; in the other, the circle determines the center.) — Srap Tasmaner

There are different ways to rationally conceive or define (and draw) a circle. Equidistance from a point is one. Aristotle prefers another, "The locus of points formed by taking lines in a given ratio (not 1 : 1) from two given points (KM1 : GM1 = KM2 : GM2 = ...) constitute a circle":



But what a circle is and how a circle is drawn are two different things. Similarly, two different ways of conceiving a circle are immaterial to the question at hand when they are formally equivalent, as is the case here. When I gave some arguments against square circles, I suggested that one could quibble with the arguments, but not oppose them in any way that goes beyond a quibble. I think that has turned out to be right. Aristotle's circle and Euclid's circle are formally equivalent. The definition of a circle is not specifying the manner in which a circle is created; it is specifying what a circle is.

- :up:

-

The two arguments (mine and the OP) are logically equivalent under deductive logic. — Hanover

Except they're not, because your "So..." is entirely different than the OP's "So..." I explained this <here>. — Leontiskos

Teasing this out a bit more, the OP contains an implicit move, "Supposing God does not exist..., I should not pray." The formal translation does not take this route, but the connotation is part of the parlor trick.

The parallel in your own example is, "Supposing I am not a billionaire..., I should not scream."

They are completely different. The implicit connotation in the OP makes perfect sense. Your parallel is perfect nonsense. Not all parlor tricks are created equal. The parlor trick of the OP is a great deal better than your attempt regarding billionaires. Your argument possesses no plausibility because it is so obviously unsound. You are trying to make yourself a billionaire with specious reasoning. The OP is not praying on the supposition that God does not exist.

- :up:

Earlier logicians had drawn up a number of rules of inference, rules for passing from one proposition to another. One of the best known was called modus ponens: ‘From ‘‘p’’ and ‘‘If p then q’’ infer ‘‘q’’ ’. In his system Frege claims to prove all the laws of logic using this as a single rule of inference. The other rules are either axioms of his system or theorems proved from them. — A New History of Western Philosophy, by Anthony Kenney, 155

Contemporary logicians like Enderton and Gensler begin the exact same way. Other starting points are possible, but they are not all on a par if one wants to do actual logic. Of course for metamathematics the starting point is arbitrary. Banno, under the spell of metamathematics, will be at a complete loss before your question about how true reasoning and logic interrelate. As Apokrisis has pointed out numerous times, Banno begins and ends with nothing more than a bit of posturing.

- I am very familiar with Buddhism on its own terms, and I was once a practitioner. It is surely not exactly the same, but the point here is that for the Western mind two-truth theories are either unnecessary or problematic. If the two domains in question do not interact, then it is unnecessary. If the two domains in question do interact, then a two-truth theory is a simplistic bandage on a rather difficult problem. I consider that route a temptation, not a promise. And the concept of methodological naturalism is always flirting with two-truth theories, so this is very relevant.

As to Buddhism, it is strongly influenced by a significantly dualistic ontology in a way that the West is not. I think the Buddhist theory is also wrong, but it is more complicated given the way that it fits more nicely into that organic dualistic ontology. Beyond that, Buddhism grows out of praxis and Western science grows out of theoria, and therefore these are very different animals (even though the West is now becoming preoccupied with a different praxis, namely a Baconian praxis).

- Sure, but Popper's criterion is very strict and seldom followed, given the way that it excludes the soft sciences. Physicalism is metaphysical, and it is also one possible paradigm for scientific inquiry. It is falsifiable in the way that any paradigm is falsifiable, but as you say, not as a theory of the hard sciences. Again, "Metaphysical theories are just a bit harder to falsify insofar as they draw nearer to first principles and presuppositions."

The point here is that the metaphysics involved in physicalism and the metaphysics that I would argue is present in methodological naturalism are adjudicable and non-arbitrary, and therefore they do not succumb to the critiques of metaphysics that many have leveraged. We don't need to be afraid of metaphysics, or believe that it represents some kind of unadjudicable free for all.

- The West rejected the two-truth theory in the Medieval period, and I think it did so for good reason. Simplifying, some theologians at that time posited the idea that there are scientific truths and theological truths, and never the twain shall meet. The two kinds of truth were said to be unable to contradict each other by definition, because they are hermetically separated. I take it that such schizophrenic approaches are very bad, and that it is similar to ask the non-naturalistic scientist to "turn on" a belief in naturalism when he walks into the office and "turn it off" when he leaves. I don't think that sort of bifurcation makes any sense, metaphysically or psychologically.

It appears to me that you miss the point. Physicalism is a metaphysical theory, not a scientific theory. All coherent metaphysical theories are unfalsifiable. It's certainly reasonable to remain agnostic to metaphysical theories, but it's not UNreasonable to treat some metaphysical theory as a working hypothesis to see if it can account for everything we know about the world. Personally, I treat physicalism is the most reasonable default position- my working hypothesis, so I label myself a physicalist. I haven't encountered anything that isn't explainable from this framework... — Relativist

I think you make fair points here, and you are giving my theoretical physicalist rejoinder flesh and blood, which is helpful. But it doesn't sound like you treat physicalism as unfalsifiable. In fact it seems like you believe physicalism would be falsified insofar as you encounter things which are not explainable within the physicalist framework. I think that's as it should be, and what it means is that metaphysical theories are not unfalsifiable. Metaphysical theories are just a bit harder to falsify insofar as they draw nearer to first principles and presuppositions.

- I only meant the foundation of the logical system. Frege's foundation is explicitly modus ponens, and many propositional systems similarly ground themselves in modus ponens. In fact we can think of modus ponens as the basis for the material conditional in propositional logic, where the modus ponens inference is more intentionally foundational to the system than the idiosyncratic behavior of the material conditional (which we are considering elsewhere). I tried to speak a bit to the odd foundationalness of modus ponens <here>.

If you want something more universally foundational, I would point to the principle of non-contradiction, and ultimately its unique character of being simultaneously subjective and objective, which Kimhi alludes to. A lot of the silliness in this thread is either a direct or indirect attack on the PNC.

- I was interpreting you, not Carroll.

yet — Banno

Yet. (!)

I'd vote yes. I think there are plenty of scientists who are to all intents physicalist as far as their work is concerned but agnostic or open-minded with respect to matters that can't be adjuticated by science. — Wayfarer

Well again, the definition of science comes into it.

If methodological naturalism means (temporarily) behaving as if naturalism is true, and if science is bound up with methodological naturalism, then to instruct someone to, "Behave as if you're doing science," amounts to the same thing. Yet the instruction, "Behave as if you're doing science," is useful in showing up the circularity of the argument in question.

And as far as your set of interests are concerned, I would say that methodological naturalism is little more than a stand-in for mechanistic natural philosophy. It asks us to behave as if mechanistic natural philosophy is true. But if mechanistic natural philosophy is false, then why would we behave as if it is true? This is one example of what I meant earlier when I said that for the non-naturalist methodological naturalism is irrational. Then the rejoinder says that science itself presupposes the scientist's behaving as if mechanistic natural philosophy is true. The obvious question is, "Why?" Why accept such a definition of science?

- The closer you get to the foundation, the surer it becomes. For example, modus ponens is arguably the most basic inference or law of propositional logic, and I don't see that it fails.

Circles are straight lines. Squares are circles. Logic is just the manipulation of symbols. And there are no laws of logic. Really a brilliant thread, all around. Everyone here deserves a pat on the back. :wink:

I can't wait until tomorrow, when we show that 2+2=5.

It would appear obtuse to the layman, and maybe it just is. — Leontiskos

- I agree. :up:

"Just the place for a Snark!" the Bellman cried,
As he landed his crew with care;
Supporting each man on the top of the tide
By a finger entwined in his hair. — Banno

And @Hanover, here we see Banno abandoning his Godless ways:

Snark = Jonah
Bellman = God
Crew = Jonah's shipmates

The Biblical allusion is too obvious to ignore. Banno made light of belief in his OP, and now a strange twist of fate has brought it about that his OP led to his belief, not unlike the subject of the OP. :grin:

My question still stands, what’s the use of symbolic logic if the analysts comes before the logic? — schopenhauer1

Well, at the very least it is a useful aid for error-checking, even if it is not infallible. It represents a form of calcified analysis that is useful but limited. And it is useful for conceptualizing extended arguments that are difficult to capture succinctly. There are probably other uses as well. I have fought lots of battles against the folks in these parts who have a tendency to make formal logic an unimpeachable god, so I agree with the sort of objection you are considering.

(There is also a normative use in teaching reasoning skills, for we have some common sense intuitions which are fallacious, and which can be ironed out easily with formal logic. seems to overlook this latter point in his analysis of Aristotle.)

- This OP should not cause you to despair of logic, lol. As I've noted elsewhere, the material conditional is a disproportionately artificial logical construct. A false antecedent makes a material conditional true, and this is something like a bug or at least dross. Much like a bit of imperfect code, as long as you don't exploit the bug the logic is useful. The OP is a fun way of exploiting this bug, among other things. I don't think it is meant to be more than that.

I would give @Banno the credit of levity here, not snark. It is a philosophical joke, aptly placed in the lounge. The justifiable decision to not pray turns out to backfire and prove God's existence, given a logical translation that is initially plausible. Hanover is reading all sorts of strange things into the OP.

Do they need to be counterexamples to Aristotle? — Moliere

They are supposed to be objections to Aristotle, so yes, of course they do. You might as well have objected to Mr. Rogers by telling us that you prefer people who put on shoes. Mr. Rogers puts on shoes in every episode.

(1) is false. (1)

Read that as (1) being the name of the sentence so that the sentence references itself like we can do in plain English. — Moliere

As has been pointed out numerous times, this is just gibberish. What do you mean by (1)? What are the conditions of its truth or falsity? What does it mean to say that it is true or false? All you've done is said, "This is false," without telling us what "this" refers to. If you don't know what it refers to, then you obviously can't say that it is false. You've strung a few words together, but you haven't yet said anything that makes sense.

I guess the silence speaks for itself :meh: — schopenhauer1

Hanover's trying to tell us something?

The two arguments (mine and the OP) are logically equivalent under deductive logic. — Hanover

Except they're not, because your "So..." is entirely different than the OP's "So..." I explained this <here>.

Deductive logic says nothing at all about the world. — Hanover

Sure it does.

(1) All dogs are cats, all cats are rats, therefore all dogs are rats. That is true, except for the fact that dogs aren't cats and cats aren't rats. — Hanover

It is unsound, and that is why it fails to be informative. It is not uninformative because it is deductive.

(1) and (2) are represented the exact same way deductively and are therefore both true deductively. — Hanover

You're flubbing the difference between soundness and validity. A premise being true does not make it inductive.

The crux is that this claim of yours is entirely false:

the speaker has decided to do something to create God — Hanover

- Sure and Lionino's thread delved into this in some detail.

-

- No, I don't think so. The OP is nowhere near as "ridiculous" as your argument about billionaires. The English argument of the OP makes sense in a way that you haven't recognized. I don't see that any of this has to do with deduction vs. induction.

An odd bug.

I go to my post <here>.
I left-click on Lionino's name.
I am taken to the first post of the current thread.

I go to my post <here>.
I right-click on Lionino's name and then select, "Open link in new tab."
I am taken to Lionino's post, which is located in a different thread.

Maybe it has something to do with the hexadecimal symbol in the post reference number?

Same question — schopenhauer1

Same answer: ,

- Then check out 's response.

It seems that Lionino will not sign up ever again, sadly. :sad: — javi2541997

Maybe. He left in frustration but will perhaps change his mind in time. I hope he returns.

I don't see how the conclusion can be derived conditionally from the premises- it is tacked on. — schopenhauer1

Do you agree with this:

~P
∴(P→A) — Leontiskos