This is a helpful OP.

Q1. Why is the number 23 not divisible (evenly) by 3?
Q2. Why are 23 objects not evenly divisible into three collections of whole and unbroken objects? — J

In your other thread we touched on the Scholastic transcendentals or convertibles. Another transcendental besides being and truth is oneness (unum).

For Aristotle mathematics is the study of what belongs to quantity in various different ways. For example, arithmetic is the branch of mathematics that studies discrete quantity.

Now is it a causal fact that reality is bound up with oneness? Not really. Oneness is metaphysically foundational to reality, and is convertible with other foundational rational aspects of reality. Usually when we think of a causal reality we think of something that is limited to some subset of reality or some subset of substances. For example, reproduction via pair mating is a causal reality because it is differentiable from other kinds of reproduction and from other kinds of causes. To call the transcendental of unum "causal" would seem to be mistaken given its extreme ubiquity. Nevertheless, we need not say that it is necessary in some super-metaphysical (mathematical?) sense. So if the only categories are thought to be the category of the causal and the category of the mathematically necessary, then we would be out of luck. A universal metaphysical property of all reality, such as unum, is neither.

This idea is bound up with Platonism: that there are universal forms in which all of reality participates, and in which the human mind participates in a special way through studies like mathematics. In that way I would want to say that mathematics is not prior to reality and reality is not prior to mathematics—which is perhaps an Aristotelian variant of the Platonism. But whether we think of Plato or Aristotle, in either case there must be some tertium quid in which both reality and human knowing participate.

What we really want is an explanatory structure that preserves both of the seemingly ineluctable realities – of logic and of being. Kimhi has his views about how we might get there. A theistic argument might posit a “perfect match” because creation is deliberately thus. Or – using a metaphor from Banno – we find ourselves with a Phillips-head screw and a screwdriver that matches, so let’s leave a designed creation out of it and try to work on the problem in evolutionary terms. (I don’t think such an approach will take us far enough, but it’s certainly respectable.) — J

To say that the alignment between screwdriver and screw is an opaque and brute fact is to have abandoned the search for an overarching explanatory structure. If there is an explanatory structure that preserves both, then that explanation must encompass both the mind that knows reality and reality itself. I don't see how one could arrive at an explanatory structure such as you desire without this overarching aitia.

You forgot that Euclid specifies a circle as a plane figure. — fdrake

No I didn't.

I realise you're not going to accept that a great circle is not a Euclid circle, or that a circle in a plane at an angle isn't a Euclid circle without a repair of his definition — fdrake

See:

Yet perhaps it is not a torus but is nevertheless a set of coplanar points, falling on an implicit plane which possesses a spatial orientation. Is it a circle then? Not strictly speaking, because two-dimensional planes do have not a spatial orientation. — Leontiskos

I've been using the word "verbatim" to try to mean a couple of things:
A ) At face value.
B ) Using only the resources at hand in a symbolic system.

Thus Euclid's definition of a circle, verbatim, would exclude the great circle. — fdrake

But it is here illustrative that I am not familiar with the concept "great circle," especially as to its specific geometrical properties, and I did query you about the picture you posted. You thought there was a verbatim sense of "great circle," but you were mistaken. You would have to explain what you mean by it in order to achieve your contradiction, because "great circle" says very little, verbatim.

And if you want to just talk about your intuitions without recourse to formalism, I don't know if this topic of debate is even something you should concern yourself with. — fdrake

I think you're moving too fast. Formalisms have limits. What are the specific properties of lines, points, circles, great circles, two-dimensional planes, three-dimensional planes, etc.? How do they relate to each other? For example, can points be deleted or not? Is the great circle a torus, and if not is it three-dimensional at all? You're making a bunch of assumptions in all of this and drawing a fast conclusion.

But the deeper issue is that I don't see you driving anywhere. I don't particularly care whether the great circle is a Euclidean circle. If you have some property in your mind, some definition of "great circle" which excludes Euclidean circles, then your definition of a great circle excludes Euclidean circles. Who cares? Where is this getting us?

If you actually want my perspective on things, rather than trying to illustrate points from the paper: I'm very pragmatist toward truth. I prefer correct assertion as a concept over truth (in most circumstances) because different styles of description tend to evaluate claims differently. As a practical example, when I used to work studying people's eye movements, I would look at a pattern of fixation points on an image - places people were recorded to have rested their eyes for some time, and I would think "they saw this", and it would be correctly assertible. But I would also know that some subjects would not have had the focus of their vision on some single fixation points that I'd studied, and instead would have formed a coherent image over multiple ones, in which case they would not have "seen" the area associated with the fixation point principally, they would've seen some synthesis of it and neighbouring (in space and time) areas associated with fixation points (and other eye movements). So did they see it or didn't they?

So I like correctly assertible because it connotes there being norms to truth-telling, rather than truth being something the world just rawdogs into sentences regardless of how they're made. "There are 20kg of dust total in my house's carpet"... the world has apparently decided whether that's true or false already, and I find that odd. Because it's like I'm gambling when I whip that sentence out. — fdrake

Okay, thanks. And I agree with this. I am interested in knowledge—including justification—as opposed to just truth. Very often justified knowledge is precisely that which has been (correctly) logically inferred. I would define logic as that thing that gets you to (discursive) knowledge, or at least to justified assertion.

I would agree that every quantification is into a domain, and I don't think there are context independent utterances. I do not think it follows that there is no metaphysics. I'm rather fond of it in fact, but the perspective I take on it is more like modelling than spelling out the Truth of Being. I think of metaphysics as, roughly, a manner of producing narratives that has the same relation to nonfiction that writing fanfiction has to fiction. You say stuff to get a better understanding of how things work in the abstract. That might be by clarifying how mental states work, how social structures work, or doing weird concept engineering like Deleuze does. It could even include coming up with systems that relate lots of ideas together into coherent wholes! Which it does in practice obv. — fdrake

And this sounds a lot like Srap's approach. I was encouraging him to write a new thread on the topic.

Plato's phrase, "carving nature at it's joints," seems appropriate here. I would say more but in this I would prefer a new or different thread (in the Kimhi thread I proposed resuscitating the QV/Sider thread if we didn't make a new one). I don't find the OP of this thread helpful as a context for these discussions touching on metaphysics.

I would have thought it clear how it relates to logical pluralism. If you model circles in Euclid's geometry, you don't see the great circle. But if you look for models of the statement "a collection of all coplanar points equidistant around a chosen point", you'll see great circles on balls (ie spheres, if you don't limit your entire geometry to the points on the sphere surface). They thus disagree on whether the great circles on balls are circles.

If you agree that both are adequate formalisations of circlehood in different circumstances, this is a clear case of logical pluralism. — fdrake

So:

Let's suppose it is a countermodel. How does the logical pluralism arise? I can only see it arising if we say that a "circle" means both Euclid's definition and the great circle countermodel, and that these two models are incompatible. Is that what you hold? — Leontiskos

For the univocalist the two definitions are incommensurably different. For the analogical thinker there is an analogy between a great circle and a circle. I think both adhere to the definition, "A set of coplanar points equidistant around a single point," but this also involves analogical equivocity between 2D planes and 3D planes.

That also lines up just fine with my view of logic. If logical pluralism means there are incommensurably different logics which are true/correct, then I disagree. If it means there are analogically similar logics which are true/correct, then I agree. But I don't think that all true logics are isomorphic. "Incommensurably" is meant as strong incommensurability, in the sense of excluding analogical equivocity.

The taxicab example is designed as a counterexample to the circle definition "a collection of all coplanar points equidistant around a chosen point", since the points on the edge of the square in Euclidean space are equidistant in the taxicab metric on that Euclidean space. It isn't so much an equivocation as highlighting an inherent ambiguity in a definition. — fdrake

Again, I think there is an equivocation on "distant." Equidistant qua circularity pertains to straight lines. The taxicab circle is premised on an extreme redefinition of "distance" - an equivocation.

The extensional difference between all of these different formalisms are the scope of what counts as a circle. A pluralist could claim that some definitions work for some purposes but not others, a monist could not. — fdrake

Although I don't hold to logical monism, this doesn't seem right. You are claiming that for the logical monist a token such as 'circle' can mean only one thing. I don't think that's right.

The Analytic dispute between logical pluralism and monism strikes me as a superficial dispute. The deeper question is univocal vs. analogical predication. That source abandons the more interesting question as soon as it limits itself to, a "model-theoretic definition." Pluralism looks like a poor man's analogicity, like trying to draw a perfect circle with pixels. My guess is that most versions of soft pluralism and monism are not even differentiable, unless there is some precise concept of "equally correct" logics or arguments (which I highly doubt).

To put it in super blunt terms, Euclid's theory would have as a consequence that the great circle on a ball is not a circle. The equidistant coplanar criterion would prove that the great circle on a ball is a circle. Those are two different theories - consequence sets - of meaningful statements. A pluralist would get to go "wow, cool!" and choose whatever suits their purposes, a monist would not. — fdrake

If they are different theories then they define different things, i.e. different "circles." The monist can have Euclidean circles and non-Euclidean circles. He is in no way forced to say that the token "circle" can be attached to only one concept.

@Count Timothy von Icarus

You might not even be a logical monist in the OP's sense, since the kind of logic it's talking about is formal? — fdrake

Just pulling this for context. The OP is three years old. The recent discussion is not about the OP. After frank bumped the thread Banno brought in an external conversation, and pigeon-holed the discussion into one of those interminable, internecine Analytic disputes (Pluralism vs. Monism).

The external conversation revolves around this post from Srap:

So we have (1) the primary phenomena, everyday language use and reasoning.

Then there's (2) the way logic schematizes these.

And there's the further claim that in carrying out (2), we see (3) the deep structure of everyday language and reasoning, the underlying logical form.

My claim was that we can talk about (2), whether (3) is true or not, and even without considering whether (3) is true or not.

It's the same thing I've been saying all along, that (2) doesn't entail (3). — Srap Tasmaner

This was Srap's attempt to frame it, but we went on to ask whether that framing was neutral or not.

I tried to continue the conversation in that thread, but Banno insisted on bringing it here. If Srap had continued the conversation in that thread I would have simply ignored Banno's transplant, given how insubstantial it was bound to become.

My position has never been logical monism's program of a single true formalization. That's just something Banno falsely pinned on me. For example:

Each time you state the problem in terms of artifice or invention you fail to capture a neutral (2). Do you see this? To call logic an invention of artifice, or a schematization or formalization, is to have begged the question. If that's all logic is then the answer to (3) is foreclosed. — Leontiskos

Fair enough. Part of the issue here is whether pluralism can be set out clearly. As the SEP article sets out, the issue is as relevant to monism as for pluralism. The question is how the various logics relate. It remains that monism must give an account of which logic is correct. — Banno

No, not really. You really ought to read Rombout on the way that Frege and Wittgenstein mean different things by "logic." Your whole frame is mistaken. I am not a "logical monist," and I don't think Timothy is either. If every logic is on the same level, then pluralism must be true. Logical monism and logical pluralism strike me as equally silly.

You've made it plain that you don't accept Dialetheism, and will give no reason, so the point is moot. — Banno

You've made it plain that you won't offer any arguments, only assertions. Moliere tried and I answered his.

It's like "This sentence has six words" in some ways — Banno

"In some ways."

Unlike "...is false," "...has six words" does not require an assertion/claim.

(Moliere and yourself are doing what I would call Dialetheist apologetics. You've heard objections to the "Liar's paradox" and you are responding to those objections, regardless of the fact that my objection is quite different.)

- So for Griffiths and Paseau "logical monism" holds that there is one true formalization. I have not seen anyone on TPF hold this theory, and I certainly do not. He is also talking about consequence rather than inference. "Logical monism" does not look at all like the classical view.

Again, for Aristotle logic is the solution to the problem of the Meno. It is how discursive knowledge is achieved. It is primarily a matter of inference. Aristotle was quite clear that his formalization was not identical to logic in this fundamental sense.

If someone wants to argue for logical pluralism I would want to know exactly what they mean by that term, because it has been unhelpfully ambiguous all throughout this thread.

Point well-made and taken. That should have been further qualified as all spherical lines of circumference. That's what I meant. That's what I was thinking. Evidently a few synapses misfired. — creativesoul

Well, one might accept it. I don't see any of these objections as straightforward. I don't think there is a "verbatim" meaning, to use @fdrake's word.

Does the circumference of a (Euclidean) circle encircle space? Yes, two-dimensional space. But then does the great circle's encompassing space make it a non-circle? Apparently not. Unless what we mean is that the great circle encompasses three-dimensional space, in which case this does make it a non-circle.

Just wondering if I've understood something. — creativesoul

Fair enough, and I meant to ask in a broader way and include fdrake.

My interest was piqued by the claim that a line of circumference around a sphere was a circle. — creativesoul

I am quite fine with that claim. Apparently I think the coplanar points of the great circle contain a circle (and a two-dimensional plane).

fdrake effectively puts words in my mouth in declaring victory, "Ah, when you say 'great circle' you mean something which does not contain a two-dimensional plane, therefore when you say 'great circle' you don't mean a Euclidean circle." But I never assented to any of these sorts of interpretations.

---

My position was that there are circumstances in which it makes sense to say there are square circles, perhaps even that there are circumstances in which one can correctly assert that there are square circles, not "there are square circles" with an unrestricted quantification in "there are". — fdrake

So you are ("perhaps") willing to say that there are circumstances in which one can correctly assert that there are square circles, but you won't commit yourself to there being square circles. This is odd.

The idea behind this sort of thinking seems to be that every utterance is limited by an implicit context, and that there are no context-independent utterances. There is no unrestricted quantification. There is no metaphysics. I take it that this is not an uncontroversial theory. Here is an example of a statement with no implicit formal context, "There are no Euclidean square circles." You would presumably agree. But then to be wary of the claim that there are no square circles, you are apparently only wary of ambiguity in the terms. You might say, "Well, maybe someone would say that without thinking of Euclidean geometry." But we both know that there is no verbatim meaning of "square" and "circle," at least when subjected to this level of skepticism. This is a nominal dispute, but it won't touch on things like logical pluralism, for that question has to do with concepts and not just names. A new definition of "circle" will not move the needle one way or another with respect to the question of logical pluralism. As noted, the taxicab case involves equivocation, not substantial contradiction.

I am still wondering:

I'm not really sure what you are arguing, fdrake. It doesn't sound like you hold to logical nihilism or logical pluralism in any strong or interesting sense. Am I wrong in that? — Leontiskos

Is that wrong somehow? — creativesoul

I don't see why one must accept this:

All lines of circumference encircle space. — creativesoul

Nevertheless, if the great circle is a torus—a three-dimensional object—then it is not a (Euclidean) circle. If it is not a torus then it may well be a circle. Yet perhaps it is not a torus but is nevertheless a set of coplanar points, falling on an implicit plane which possesses a spatial orientation. Is it a circle then? Not strictly speaking, because two-dimensional planes do have not a spatial orientation.

But what is the point here? Recall that @fdrake's desired conclusion was that there are square circles.

Because I'd say that just from a plain language sense "This sentence is false" is clear to a point that it can't be clarified further. — Moliere

So be honest. When you say, "This sentence is true/false," do you think you are saying something meaningful? Would you actually use that phrase, speak it aloud, and expect to have said something meaningful?

What does it mean to "say something"? — Moliere

A sentence says something if it presents a comprehensible assertion. It says something if its claim is intelligible.

Now when you say, "X is false," I can think of X's that fit the bill. I might ask what you mean by X, and you might say, "2+2=5." That's fine. "...is false" applies to claims or assertions. If there is no claim or assertion then there is no place for "...is false." For example, "Duck is false," "2+3+4+5 is false," "This sentence is false."

I suppose the flip-side would be that there is no relationship between concepts of truth. I can't help but think this would make truth arbitrary, or at least have major philosophical ramifications, maybe not. — Count Timothy von Icarus

It is also another departure from natural language. We do not speak of truth as having various species with no relation to each other. Nor does the term "logics" jibe with the idea that the various logics have nothing in common.

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. — Leontiskos

Now in a given philosophy we'll want a particular logic, or particular logics for particular ends, but the logician need not adhere to one philosophy. — Moliere

Banno has so thoroughly poisoned the well that it becomes difficult. Here is what I said to this idea:

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. — Leontiskos

-

It's the name for a sentence.

A name denotes an individual.

The individual is an English sentence.

The sentence is "This sentence is false"

(1) is a shorthand to make it clear what "This sentence" denotes. — Moliere

So again:

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. — Leontiskos

In order for a sentence to be true or false it must say something. That is what it means to be a sentence. "This sentence is false," does not say anything. It is not a sentence. It is no more coherent than, "This sentence is true," or, "This sentence is that."

One answer, which you've provided, is that the sentence means nothing.

It's not the only one though. — Moliere

If you think that answer is wrong then you'll have to tell us what the sentence means.

And yet Dialetheism. You at least need to make a case, rather than an assertion. — Banno

Er, do you ever take your own advice?

It might not be a confusion, it could be an insistence on a unified metalanguage having a single truth concept in it which sublanguages, formal or informal, necessarily ape. — fdrake

A good move away from the strawmen. :up:

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

Logic is that which reliably produces knowledge, via rational motion or inference. This is not limited to a single formal system - that is Banno's strawman. But knowledge and truth are one. There cannot simultaneously be knowledge both of X and ~X. Therefore logical pluralism is false.

Russell's approach is largely telling logical nihilists not to throw the baby out with the bathwater — fdrake

This is what always seems to happen with these shiny new theories. It is motte and bailey. The controversial claims that stimulated attention dissipate upon closer examination.

I'm not really sure what you are arguing, fdrake. It doesn't sound like you hold to logical nihilism or logical pluralism in any strong or interesting sense. Am I wrong in that?

You talk a lot about the great circle:

the great circle might be taken as a countermodel for Euclid's definition of a circle — fdrake

Let's suppose it is a countermodel. How does the logical pluralism arise? I can only see it arising if we say that a "circle" means both Euclid's definition and the great circle countermodel, and that these two models are incompatible. Is that what you hold?

-

Our dispute was similar to the former - we both have the same pretheoretical intuitions about what a circle is. Agreeing on Euclid's and on the great circle's satisfaction of it. And we'd probably agree on the weird examples containing deleted points too, they would not be circles even though if you drew them they'd look exactly like circles. — fdrake

Given that I disagree with all of this, does it follow that you were the sophist and not the sadistic genie?

and I kept asking you to repair it. — fdrake

I kept asking you to offer a reason why it needs to be repaired, because it "clearly" was fine. You are begging the question in your own favor with words like "clearly."

Why are we to believe that a three-dimensional abstraction (i.e. the great circle) does not contain a two-dimensional abstraction (i.e. a circle)? In any case, the easier disagreement here is over the question of whether one can delete a point.

Whereas your examples do not insist on taking the conceptual content of what's said for granted, indeed they're attempting to distort it. Allegorically, the logic of shit testing is that of a particularly sadistic genie - taking someone at their word but exactly at their word, using whatever pretheoretical concepts they have. The logic of your sophist is closer to doubting the presuppositions which are necessary for the original problem to be stated to begin with. — fdrake

This is helpful, but I'm not convinced it is cogent. The sadistic genie is not taking them at their word by being overly pedantic, he is just being a sophist. I see the distinction you are making, but I would say that the sadistic genie is a sophist, even if not every sophist is a sadistic genie.

I saw my cousin who has Asperger's, "Your hair is long, how long has it been growing?" "Since I was born!" He is fun, and this is an example of the sadistic genie, but it is not a non-example of a sophist. Taking someone "exactly at their word" is a good way not to take them at their word.

Where's the issue? — fdrake

To take a few, you haven't defined the operations, commutativity relations, numbers, variables, etc.

To be clear you would have been compelled to deny the great circle was a circle by only using Euclid's definition of it verbatim, I would not have! — fdrake

I don't follow, but you seem to think "verbatim" is a fix; a quibble-proof solution; a univocal meaning. I don't think the buck stops there or anywhere else. Literal meaning is a puzzle as much as anything else. To use the word "verbatim" and assume you have won the argument will not do.

Good posts, though. I have to run but I hope to come back to this soon.

In effect the nihilist doubt machine gets going by noticing that there's arbitrary degrees of contextual variation — fdrake

I think the univocalist extreme of splicing everything apart and analyzing it separately is representative of sophistry (or nihilism?). Namely, the methodology precludes reasoning and knowledge. If one does not admit analogical predication in one form or another then they can deny but they can never affirm. They have created a method that can only deny; a skepticism machine.

For example:

1) Gillian is in Banf.
2) Therefore, I am in Banf.

to

1) Gillian is in Banf
2) I am Gillian
3) Therefore, I am in Banf — fdrake

Has it been fixed? The "sophist" would say no, and can quibble endlessly. They might ask you to specify what exactly "I am Gillian" means; what 'I' means; what a name is; what the predication of amness means (all difficult questions). They might splice (1) and (2) into different contexts, pointing out that (1) is a third-person description and (2) is a first-person description, and that it is not clear that these two discrete contexts can produce a conclusion that bridges them. "Shit-testing" seems to have no limits and no measure.

There is an interesting question about the great circle, but the method which outright denies that the great circle is a circle can outright deny anything it likes. It is the floodgate to infinite skepticism. I think we need to be a bit more careful about the skeptical tools we are using. They backfire much more easily than one is led to suppose.

Edit:

you can tell it to sod off by specifying the exact mess you're in — fdrake

Can you? There is an idea that floats around, according to which one can give quibble-proof arguments. I don't think this is right. I'd say the idea that there is some quibble-proof level of exactness won't cash out.

The problem is that we never know for sure whether or not something other than A might bring about the occurrence of B. — Metaphysician Undercover

So you seem to think that atheists should go ahead and pray. It doesn't make sense. If someone believes that person X does not exist then they should not petition person X. A petition/prayer is not offered in generality, to no one in particular.

There are all sorts of hypothetical entities that could answer prayers; devils, angels, fairies, wizards, extremely advanced aliens, the universe branching into a new timeline in accordance to one's will, etc. There's no reason to believe that it can only be the working of some sort of monotheistic creator deity (and certainly no reason to believe that it can only be the working of a specific religion's deity). — Michael

Eh. If I ask you to do something and someone else does it then you haven't fulfilled my request. Pretty basic. Has my petition been granted? No, I don't think so, unless the petition was somehow made to no one in particular.

When you choose to enguage with the articles cited, I'll be happy to join in. — Banno

Can't you do philosophy in your own words, and answer simple questions put to you?

• In an OP with three different articles, you post first, ignore the entire OP and its articles, post your own article, and derail the thread.
• In an OP on Kimhi and Frege, you post first, ignore the OP, and derail the thread with an anachronistic post on illocutionary force. Later on in the thread you were explicitly asked more than once to try to engage the arguments on their own terms.
• In this thread, you literally took a conversation between Srap and I, transplanted it into this thread while calling me out, and then went on to complain that I haven't addressed the OP of this thread.

This shit just happens over and over and over. The double standards are wild. I have a reminder from August 6, "Put Banno on ignore." I had some technological difficulties in the meanwhile, but it's probably time to honor that reminder and start focusing on people who are sincerely interested in philosophy. ...Interested in engaging ideas other than their own.

We say that prayers being answered is the effect, and God's existence is the cause of this effect. God's existence causes prayers to be answered. However, it's an inverse fallacy to say that if prayers are answered then God exists. — Metaphysician Undercover

So you are saying that your prayers might still be answered even if God does not exist? So that an atheist could be justified in praying?

- Okay, well thanks for answering the question. Given that I have an outstanding reply to @Moliere in this thread and Baden elsewhere, I'm going to leave it there as far as our dialogue is concerned. I can't maintain too many conversations at the same time. Take care.

Implied by stating it's violation is a destruction. — Cheshire

Okay, so you think the PNC can be violated without being destroyed?

I disagree with the first premise. They could have systematic disagree and remain consistent in there conclusions. Somehow, presumably. — Cheshire

I'm not really following. Presumably you think the first premise presents a false dichotomy.

Again, I would suggest focusing on the argument I gave, not some argument you are afraid I will give at some point in the future.

- Remember back when you thought this was an "interesting question"? Now you refuse to look at it.

But how we might deal with a case where, say, two logics over the same domain reach opposite conclusions remains an interesting question. — Banno

Have you stopped beating your wife yet? — Banno

You want to talk about logical pluralism without talking about the PNC? All that means is that you don't want to talk about logical pluralism. You are pretending.

it would turn this thread away form the mere bitch session it is becoming — Banno

Bitch session? It's just another rerun of, "Banno refuses to do philosophy." This is why I said I wanted a thread on Srap's logical pragmatism instead of Banno's logical nominalism. I've seen the episode too many times.

They aren't logical without total adherence seems strong — Cheshire

Where do you find that claim, "They aren't logical without total adherence"?

I have asked Banno multiple times whether he agrees or disagrees with the argument, but he is being his usual coy self.

Can you answer the question? Do you agree with the argument? If you disagree then please explain which premise you oppose.

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. — Leontiskos

No, Leon. If you are going to use the claim to reject there being contradictory logics — Banno

But I never did that, so that makes you wrong four times in a row now. Shoot. I can't have begged the question with a claim I never made.

( - Yep)

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.