I flip these values accidentally in my mind all the time. I could just be confusing myself. When stating it in terms of probability space my thought is that we can look at A and its negation as a probability space -- say a quarter that's fair has a 50 percent chance to land heads, and since there is only one other possibility (we could call it "Not-heads") we can deduce that not-heads' probability "is contained within", i.e. determined by, the probability of Heads.

Sort of thinking about future events in analogue to the bag of different colored marbles -- George is late has 99 white marbles, George is on time has 15 red marbles, and George doesn't show up is 1 black marble.

I find the visualization helpful. We're just doing Venn diagram stuff here. — Srap Tasmaner

Yes that's very helpful, thanks. I was getting lost in the idea of a probability space and how that relates to "contains in", but the visualization makes it quite literal and easy to comprehend.

So going back to

Ask yourself this: would "George will not open tomorrow" be a good inference? And we all know the answer: deductively, no, not at all; inductively, maybe, maybe not. But it's still a good bet, and you'll make more money than you lose if you always bet against George showing up, if you can find anyone to take the other side.

"George shows up" may be a non-empty set, but it is a negligible subset of "George is scheduled to open", so the complement of "George shows up" within "George is scheduled", is nearly coextensive with "George is scheduled". That is, the probability that any given instance of "George is scheduled" falls within "George does not show up" is very high. — Srap Tasmaner

The probability space here is the set of possible outcomes we've thus far observed and, under the assumption that the distribution over that probability space has not changed -- George hasn't converted to the church of punctuality, giving us a reason to believe the probability space has changed -- the good bet is he'll show up late.

EDIT:

Wrapping that back to the OP, now...

A -> ~A
A
Therefore ~A

The (probability) space of A is entirely contained within the (probability) space of not-A.


Well, of course it is. That's almost a restatement of the probability of P v ~P equals 1.


Not sure where I'm going with this, just thinking out loud more than anything.

https://web.stanford.edu/class/cs103/tools/truth-table-tool/

Thanks :).



This is a meaty post.

Almost too much for me :D -- one thing that's interesting is your reduction of material implication to set theory. I'm not sure how to understand that, really -- if the moon is made of green cheese then 2 + 2 = 4. That's the paradox, and we have to accept that the implication is true. How is it that the empirical falsehood, which seems to rely upon probablity rather than deductive inference, is contained in "2 + 2 = 4"?

I'm intentionally throwing wrenches/spanners here so kindly tell me to 'ef off if it's uninteresting or simply misinformed. I'm starting to feel the tread in this conversation where I'm in too deep over my head.

I remember enjoying it -- it's something of a lament and criticism of disenchantment as the one true knowledge. The plant studies stuck with me as an interesting bit because it seemed like such an easy thing to test, empirically, so you didn't even need to care if the idea was silly -- it got along with my general attitude of anarchy towards scientific knowledge.

When I say A sarcastically, I mean ~A, of course. And that is equivalent with A -> ~A. But I don't present it like that at all. I just say A and there is an implicit premise that when I say it, I mean its negation. I don't know how even modal logic could capture that. Or maybe, I am saying that A is true in an alternative world and false in the actual world, but even that seems far-flung.

Getting back to Srap Tasmaner, he's looking for a use of A -> ~A in everyday discourse. I don't think your proposal works, since people don't acutually say things of the form A -> ~A to convey sarcasm. It seems to me that you followed an interesting idea, but it doesn't do the job here. — TonesInDeepFreeze

Fair enough. I agree it doesn't fit the form -- people don't actually say the implication, it's only equivalent to the implication (but so are so many other formulas...).

True. The one time he did we all know it's because his wife grilled him the night before and he felt guilty but ever since the divorce it's been same old George: He only opens when he feels worried and ever since the divorce the man is never worried!

:D

This seems the easier approach to making sense of A -> ~A in a commonsense setting.

You mean substitute "George will open the store" with "If George will open the store then George will not open the store"?

Why make that substitution? I don't see how that is what the ironic speaker is saying. — Moliere

I can give you a story that comes to mind in which I'd assert something like that -- say I'm commiserating with a coworkers frustration about George not being as reliable as we'd like, even though he's a good enough fellow.

The substitution is there only because the OP starts with A -> ~A and asks for validity, so substitution seems to work as a model for the sarcastic talking. I agree that the person speaking sarcastically does not in any way mean these logical implications, though -- it's only an interpretation of everyday speech to try and give some sense to the original question that's not purely formal.

What is the conditional? — TonesInDeepFreeze

A = "George is going to open the store tomorrow"

So, by substitution:

George is going to open the store tomorrow implies George is not going to open the store tomorrow.

If it turns out, extensionally at least, that George opens the store tomorrow then the implication is false -- and I don't think that sarcasm means to invoke material implication, but this seems an example of everyday communication which material implication seems to capture. George opens the store tomorrow, so tho I state one and believe another it turns out that my belief is false and the assertion true (attempting to use your intensional definition here) -- so the implication turns out to be false. I'm thinking more baby logic here:

A -> ~A

Put it in a truth table and if A is true then the implication is false.

I like the idea of an irony operator :D

What I want is an example where this conditional is actually false, but is relied upon as a sneaky way of just asserting ~A. — Srap Tasmaner

A thought I have is sarcasm, but in the context of asserting a falsehood mistakenly.

So I can sarcastically say "George is going to open the store tomorrow" to mean that George is usually late and we are the ones who open the store on the regular. But if George opens the store tomorrow then the conditional was false because I asserted A to imply not-A, but in fact A is true so the conditional is false.

I haven't seen anyone define any of the positions in a clear and non-vacuous way, much less go on to argue in favor of one or another. — Leontiskos

If dialethism is true then pluralism is true.
Dialethism is true as it resolves the liar's paradox in a clear, non-vacuous way.
Therefore, pluralism is true.

Of course LNC and LEM are different. — TonesInDeepFreeze

Heh. Well, I'd expect that from you :D -- I'm not sure that the differences between them are at the level of "of course" for the participants here.

I can't find the post about the liar paradox; my own point was merely the technical one that the contradiction of the liar does not require LEM.

I agree. I don't think the liar's needs anything technical at all. For thems who prefer utterances we can frame it in plain language as "I am telling a falsehood right now"

Implications of this theory are far-reaching. It suggests that intelligent species, faced with existential threats, will inevitably develop coping mechanisms. — ContextThinker

I want to attack the notion that this idea is an evolutionary adaptation.

All species develop coping mechanisms, from viruses to us. Some of the species die in the process of natural selection and thems who chose the environmentally-conditioned adaptations which effect reproduction positively for the species are thems who developed the coping mechanisms that passed on.

But evolution has nothing to do with religion, in my opinion. Once we acquired the ability to speak language -- well, I think that's more in the ballpark of why religion exists. But it's pretty hazy since it's not like any of us were there at the dawn of talking/writing.

:rofl:

I don't recall the post, but in this thread (or another?) someone mentioned LEM in relation to the liar paradox. We don't need to refer to LEM for the liar's paradox. The contradiction is obtained even without LEM. — TonesInDeepFreeze

While others may have done so, in this thread that's been me aping Priest.

The idea is to point out a difference between LNC and LEM, as well as to prove that the dialeithic dialethic answer to the liar's is still valid in the sense of using some classical logical laws.

I think thinking in terms of "laws" is probably unhelpful here and I have never seen a monist argument that tries to define itself in this way. If by laws we mean "true for all existing logics," then there are clearly no such laws. The monist doesn't argue that such laws "hold in generality," except insofar as they hold for "correct logic" (as they variously define it; note also that most monists embrace many logics, the question is more about consequence). So, Russell's paper is fine overall, but I think this part has just confused people because it's easy to read it in a way that seems to make the answer trivial. But based on the fact that even pluralists themselves very often claim that they are in the minority, it should give us pause if monism seems very obviously false. — Count Timothy von Icarus

I'm fine with another rendition other than "laws" -- that's just usually the word that comes up. I don't think they are literal laws though, not even in the "laws of nature" sense.

I ought say that I don't think monism is obviously false. I'd say monism is kind of the "default" position when we start logic, if there is a default position at all -- strictly speaking it seems to me that monism/pluralism/nihilism are more philosophies about logic than logic proper. It seems when we're doing strictly logic it wouldn't matter for the purposes of pursing the logic whether there are one or many logics (or consequence relations, as you put it). But the impression that logic gives with its generality seems to indicate there would not be another set of logical rules that lead to different consequences -- that would violate the law of non-contradiction.

I'm thinking this (very consistent!) holding onto the LNC is a part of why these developments have taken so long to be achieved.

I think part of the confusion is that, just as idealism is much more popular on TPF than in metaphysics as a discipline, highly deflationary conceptions of logic's subject matter are also much more common. But one might agree to a deflation of truth for the purposes of doing logic without embracing any robust notion of deflation, e.g. that "on 9/11 the Pentagon was struck by an airliner not a cruise missile," is true or false in a sense transcending any formal construct or social practice. Maybe not, I only know of two surveys on this question, but they do seem to bear this out, as does the way authors actually talk about non-classical logics (i.e. they spend a lot of time making plausibility arguments, which are superfluous of logic is just about formalism). — Count Timothy von Icarus

Oh, certainly*. For my part I think the metaphysics of truth ought to be set to the side for purposes of the question -- I'd say if our metaphysics of truth can't accommodate our logic then it's our metaphysics that are in error. Hence the motivation to develop a logic sans-metaphysics, insofar that it's possible. It seems to me that acknowledging the implications of a logic without commitment is about as close as we can get there. I agree with the part of your quote here:

*EDIT: Certainly, the positions on TPF are a niche that's not representative of the academic community. And though I respect and even rely upon the academy I'm pretty sure my philosophical sympathies are not exactly academic.

Ontologically, the pluralist is going to be the one who thinks that objective/external reality is chaotic or random enough to support all sorts of anomalies and fluxes with respect to the relations between its constituent facts. (Logical nihilism, or rather logical asemanticism, seems more accurate in this context, though, if it is not accurate to think that reality is structured according to any completely specifiable system of logic at all. Or maybe there are a few rules that are universal as such, i.e. exactly those pertaining to universal quantification, if this be doable in an unrestricted way.)

I've mentioned the absurd as my metaphysical stance to kind of hint at why this is interesting to me -- I take the absurd as something of a starting point now-a-days. Reality at least seems chaotic and random enough to support a multiplicity of necessities that disagree.

So, no, my stance is not metaphysically innocent at all. In some ways Priest was appealing because he laid out a more coherent way of talking about these absurdities that seem real but are difficult to put into philosophical words.

I'm very much avoiding basing logic on either science or natural language reasoning even though I think natural language reasoning -- or informal reasoning -- is the origin of formal logic.

It seems to me logic is a bit like math (while not being reducible to math) in the way that it can be developed or "discovered".

My background epistemology of "guess and check", very much inspired by my understanding of science, definitely feeds into my motivation for a pluralistic philosophy of logic -- but I'm trying to avoid claiming either the mantle of science or the common sense of natural language reasoning in making my point. Which is probably why it falls flat.

If pluralism denied that there were any correct logics, how would it be distinguishable from nihilism exactly? — Count Timothy von Icarus

That's a question I ought take up, given I'm defending pluralism and poo-poo-ing the idea of correct logics, at all.

Nihilism states there's no logical laws. Pluralism states there are more than no logical laws, and more than one logical law. Though "law", by the pluralist, is funny here. My thought is that "law" is stipulative -- my suspicion being that all arguments for a logic must beg the question the only way to evaluate a logic is to develop and utilize it in some fashion.

I'm thinking that the monist thinks there is, at the end of the day (ultimately?), only one set of logical laws that cohere together. The pluralist can accept laws insofar that they are limited in a non-lawlike(logical inference rule that fits within the logic) fashion. The nihilist states that all logical so-called laws are matters of preference -- something like a poetry of rhyme, but with ideas.

There's a memoir I read which talked about the effects of music on plants that I wish I remembered the name of. It wasn't the only thing in the memoir -- I remember he visited a person who believed they could talk with whales, but not much else -- but I wish I could remember the author or name of that book.

EDIT: Typing it out helped me remember: https://www.penguinrandomhouse.com/books/319/the-spell-of-the-sensuous-by-david-abram/

Though not to be rude I'm still looking for good points of response @Count Timothy von Icarus, but rather in bits to see if we can stall the sprawl a bit.

Well, that's a fine argument to have. But it gets to the point I tried to make to Banno and fdrake that one cannot retreat into formalism and ignore discussions of truth on this topic. If it would be question begging to assume that logic is about truth-preservation then it would be equally question begging to say that truth depends on / is defined by normative or formal contexts. If the latter is accepted, then of course nihilism is true (or rather true relative to some contexts and false relative to others, depending on our normative games.) — Count Timothy von Icarus

One thing I'm guessing is that arguments for any logic, due to the generality of the topic, will by their very nature always beg the question -- otherwise the logic wouldn't be consistent with itself! And that's a terrible place for a candidate logic to be.

The point from there would simply be to demonstrate more than one logic -- one which results in a "F", where the other results in a "T" or there's perhaps another value other than "F" or "T". The trick is in being able to evaluate the logic without the logic. How can it be done? I think that's the puzzle, in a nutshell.

Oh, certainly. Fair enough.

Frankly, I think such stuff too ill-defined to be done well. — Banno

Now that's when we're doing philosophy! :D

If the liar's sentence is true then the liar's sentence is false.
If the liar's sentence is false then the liar's sentence is true.
The law of excluded middle states there can be no other values for a sentence than true or false.
Therefore the liar's sentence must be true and false, or not-true and not-false.

Though this doesn't get over the hurdle of relevance, which I think has what's mostly been at stake in various responses here -- the liar's sentence isn't useful in some context outside of philosophy and so it seems like a toy which ought to be viewed as such, whereas the knowledge we actually use in the real world is girded by a firm bivalency we not only can stand atop but have not choice but to do so or be in error.

How would you define validity?

"A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid," is the textbook answer from IEP. The textbooks I've used give the same definition.

Stanford's open introduction to logic puts it thus: "Valid: an argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true; if all the premises are true, then the conclusion must be true; it is impossible that all the premises are true and the conclusion is false." — Count Timothy von Icarus

These work just fine by me which indicates we're just talking past one another.


What say you to 's proposal? Does it seem to sidestep something important, in your view?

The reason I've been delving into historical examples, and I have hope I haven't gone too far afield @Banno, was to tie some of the above into the argument for pluralism: if we accept contradiction into our reasoning, and we also reject contradiction in some of our reasoning then we are pluralists.

Moving to that because of the incredulity of dialetheia, which is where originally I staked my flag in defense of pluralism.

Sorry if it was too off topic though.

It's about the number of correct logics (i.e. logics that ensure true conclusions follow from true premises). In general, it's a position about applied logic, which is why monists and pluralists often justify their demarcation of correct logic(s) in terms of natural language, scientific discourse, etc. Nihlism would, by contrast, say there are no correct logics (and also no incorrect ones). This is not to say that reasoning is entirely arbitrary, presumably there are some standards for what constitutes appropriate reasoning. But there is no logical consequence relationship that is appropriate or correct for any particular topic. So, for instance, the intuitionist and his rival in mathematics are both wrong in that neither are "right." — Count Timothy von Icarus

I'm not sure I'd go as far as to say "correct" in describing a logic. What would it possibly mean for a logic to be correct in a non-question begging way? "Correct" seems to already presume some standards of coherency, and I'd say validity is a species of coherency.

That is, we'd be presuming some logic in setting out the correct logic. Now if there were only one logic that would at least be consistent, but then we get to the part on begging the question -- which, I think, is why the puzzle is interesting: Either answer can be made self-consistent (monism or pluralism), but in what sense can the two camps speak to one another?

You could think of this as similar to how there are very many geometries, and unfathomably many possible ones. One can identify what "follows" from their axioms according to whatever logical consequence relationship one cares to use, but this doesn't necessitate that the geometry of the physical world is infinitely variable or that it lacks any "correct" geometries. We tend to think that there would be just one geometry for physics (at least physicists normally do), or that, if there were many, there would be morphisms between them. The claims of the monist in particular are roughly analagous to the claims of the physicist re geometry. For instance, when Gisin recommends intuitionist mathematics for quantum mechanics, he does not mean to suggest that this is merely interesting or useful, but that it in some way better conforms to physics itself in ens reale, not just ens rationis.

[/quote]

Can you fill out this analogy?

Geometry:Physics :: Logic:D

What takes the place of "D" here? I understand the relation between geometry and physics, but also by the time we're talking geometry and physics it seems a logic, an epistemology, an ontology are already in play for the purposes of producing knowledge -- Also I'm not sure that the analogy serves the monist very well because geometers do geometry outside of the bounds of physics, and so we'd presume the same would hold for the logicians?

Normally it gets framed in terms of the entailment relationship. This avoids unhelpful "counterexamples," like competing geometries that use some different axioms, but nonetheless have the same underlying entailment relationship. These are unhelpful because the question isn't about "what specifically is true/can be known to be true given different axioms" but rather "how does one move from true premises to true conclusions." This is why monists might also allow for multiple logics that are "correct," the "correct logic" being more a "weakest true logic." — Count Timothy von Icarus

I'm not sure the entailment relationship ends up being any more stable than the LNC or the principle of explosion. Pick your hinge and flip it!

When you say

These are unhelpful because the question isn't about "what specifically is true/can be known to be true given different axioms" but rather "how does one move from true premises to true conclusions."

There's a quibble I feel that may indicate some miscommunication (or not, we'll see).

The question for logic, IMO, is not "How does one move from true premises to true conclusions?" -- I'd say that's a question for epistemology more broadly -- but rather logic is the study of validity. The big difference here from even introductory logic books is that the truth of the premises aren't relevant, which I'm sure you know already -- the moon being made of green cheese and all that.

So we don't care if the premises are true or not. We only care that if they are true, due to the form of inferences, that the conclusion must be true.

Do you see a difference between the questions?

I'd say your question asks for evidence or rationation, whereas the study of validity will depend upon how we define our logic.\

I don't think Hegel is really a good example here because the Absolute is the whole process of its coming into being, in which contradiction is resolved, and contradictions contain their own resolution. It's examples of contradiction, being's collapse into nothing, etc. are very much unlike the standard examples meant to define dialetheism. — Count Timothy von Icarus

Just to be clear, and I have not been so sorry, I'm not presenting Hegel as a dialetheist, but rather as a philosopher that uses contradiction in his reasoning -- since the conclusion to a contradiction is not "Meaningless" or "simply false" it strikes me as different from the older assumption of the LNC.

Also, you've mentioned it but, what makes Hegel an interesting case is his simultaneous acceptance and modification to the LNC. He accepts the LNC in its own context (i.e. outside of time), but when time gets involved he introduces a new inference -- sublation -- to manage the contradictions of becoming.

This isn't to say that he's a pluralist, either. I agree that if Hegel were anything that "monist" makes sense. It's only to say that in order for us to make sense of Hegel we have to be able to evaluate contradictions without rejecting them out of hand, and so at least the logic which makes sense of Hegel must reject the LNC.

Well you can't say what it means — Leontiskos

I set out the meaning of the liar's here:

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. "This sentence" is a pronoun being used to refer to the entire phrase which the pronoun is a part of. "... is false" is the sort of predicate we apply to statements.

"...is false" is the predicate which yields the value "true" for sentences which are false in a truth-functional sense — Moliere

The objection was given <here>. You tried to answer it by redefining "false" as "fake," and I think we both agreed that that answer failed. That's where things stand, as you never made another attempt. — Leontiskos

What I said was

"Duck is false" and "2+3+4+5 is false" don't work because "Duck" and "2+3+4+5" are not assertions at all, but nouns. — Moliere

It's the object that's different which changes the meaning of "...is false", which is why these examples don't work. Since the liar's sentence is a sentence the usual meaning of "...is false" works just fine.

I didn't redefine the predicates but pointed out how your counter-example didn't stick.

Sure: if dialetheism is true, then strong logical pluralism is true. — Leontiskos

Cool. Then it seems that an argument for dialetheism is very much on topic then, and the liar's sentence is what I'm proposing as a dialetheia

No, they don't. This is equivocation. Neither one has anything like the standing contradictions of dialetheism. Tensions which go on to get resolved are nothing like the stable contradictions of dialetheism. — Leontiskos

I disagree. The moment of sublation in either Hegel or Marx is not a singular moment which is separable from their negations, but is rather the composition of negations and the negation of that composition. Without recognizing the unity of the opposites -- contradiction -- sublation wouldn't be recognizable as a distinct moment in the logical process.

Now that may very well be the case in fact, but conceptually speaking it seems you at least have to accept contradictions which are operable in some fashion in the logics of each philosopher -- not two opposing things that happen to yield a third thing, but rather the two opposing things very opposition is connected to this third thing in a relationship of inference, where the contradiction is part of the inference, and is not a reductio.

That's an interesting background explanation for why the "Liar's paradox" tempts you, but what I am hearing is that you are interested in playing a game that has nothing to do with reality. . — Leontiskos

Reality is what's interesting here -- what I don't want to do is define reality within my logic, though. And I don't think that logic needs to restrict itself to objects since reality is not composed of objects and objects only -- it also contains sentences.

You have not answered the objections, and I don't see that Marx and Hegel have much at all to do with this issue

As I see it right now the objection is we don't agree on what a pluralist logic would even mean. I've asked you if you'd accept a defense of dialetheism, the belief that there are true contradictions, as a basis for making the inferences that there is more than one logic.

Unless you answer that question it becomes rather hard to answer your objections since we don't have an agreed upon notion of pluralism. I've already laid out, with the liar's sentence, why I accept dialetheism. Marx and Hegel are philosophers which, like the liar's, utilizes contradiction in their reasoning. My thinking here is to ask if you'd accept that as a basis for dialetheism.

So what do you say?

I believe you've misunderstood, or I've not explained myself clearly. Wherever the fault lies doesn't matter to me.

My thinking is that the mind is not the body. My foot is not my mind. I still have a mind for all that. And when I think about a donut that does not make me the donut. Thus far I believe we agree.

The part I'd point out is that my mind is influenced by whether my foot itches, hurts, etc -- and is even influenced by things like how much sugar or water I presently have in my body. It's much easier to be amiable when I'm feeling pleasure than it is when I'm feeling pain.{

so I conclude that my body and mind, while not being one, are connected.

After that it has to do with stupid theological shit that need not be brought up in this question.

EDIT: I ought say that "stupid theological shit" includes my own atheism and all that.

:heart: :nerd:

I hope to do so :).

Naw. "Mind" and "Identity" are different.

For instance if I'm looking for some keys then my mind is occupied with keys, but I am not the keys.

I wish I could tell you the "because", so I'm sorry for piquing your curiosity here without having an answer.

I'm still interested in the problem of consciousness, and slowly reading Sartre's B&N as an effort to think through the metaphysics of consciousness (cuz Chalmer's kind of just leaves it in the air)

Where's the evidence that the mind is the body? Without assuming that the mind is the body - which is question begging - what evidence is there that the mind is part of the body? — Clearbury

What's evidence to you?

That's probably where disagreement lies, by my guess.

The evidence I'd point to with respect to the mind being a part of the body -- and only a part (my foot is not a mind) -- is that what we normally think of as mind is influenced by physical things. The world feels different when drunk. If I've eaten a big meal that I ought not to have I get feeling tired and want to sleep. Even the smells and sounds of an environment seem to effect my mind. (you need not trust my word on it: fast for several days and you'll see what I'm talking about, if you desire not to utilize these various methods and want to rely upon your body and your body alone for feedback)

When I pay attention to why I'm doing what I do it's hard to rule out that the body does not relate to what we like to call the mind.

I can say, with certainty, that the Moliere posting on the old TPF is not the same person as the new TPF, but at the same time is the same person as the Moliere of the old TPF.

And I can say that I have a body, and have had a body the entire time, and that when my body is gone I believe that I'll be gone too.

So -- going into the transporter may turn me into light and recreate me on the other side, but my folk belief about the metaphysics of consciousness is that the "I" I'm experiencing now would cease to exist.

In that sense then only one person named Moliere has been on TPF, and the old PF. The ship of Theseus still belongs to Theseus -- but not because of the bits we can name.

Could be. Maybe we're uploadable. — frank

Taking this one up in favor of the OP:

If we invented a Transporter in the way Star Trek seems to indicate I would not enter it.

It's science fiction so we can invent whatever: My understanding is that the Transporter converts your physical make-up into "information", and then translates that information into light which can quickly travel to the surface of a planet and re-create you.

But I think the "new you" would behave exactly like you, but the you which experiences things would disappear. It's basically a death machine for convenience, by my guess. (which is only a guess -- this is somewhat a pop-sci explanation of the problem of consciousness in a nutshell)

Blasphemy! — frank

I mean I have a type of thinking I keep going back to and it's often labeled as Blasphemy :D

I, for one, do not trust math.

We may be immortal for all that. (EDIT: And it looks like a cool book that I'd enjoy reading)

M'kay. Then my example would not convince you of dialetheism, and at this point in the debate I'd ask -- if dialetheism were somehow justified would that then justify logical pluralism?

Can you think of any examples of a sentence wherein both A and not-A are true in the same sense or context? For example I could be said to be both old or tall and not old or tall but not in the same senses or contexts. — Janus

The liar's sentence.

"This sentence is false" is the liar's sentence.

This doesn't fit your "for example", though, because it's not about a person, but a sentence.

Since the sentence can be said in any context, and it's basically about words and how we describe them, we can place them within the sense of logic.

The sense of logic can be informal or formal, and insofar as we understand one another well enough it need not be specified.

Though I'm wondering if I've just lost you at this point?

My point was that within any valid logical argument of whatever stripe there must be consistency between the premises and the conclusion. If a premise contradicts another premise or the conclusion then the argument cannot be valid. That sort of thing. — Janus

Your choice of words here has me wondering if I can or not.

But I can give a straightforward answer to your question which may be aside from the point.

Can you explain how dialetheism rules out the LNC? — Janus

Quoting the SEP here:

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true. If falsity is assumed to be the truth of negation, a dialetheia is a sentence which is both true and false.

I've been advancing the argument that the LEM holds -- because there is nothing in between truth and falseness so we cannot choose some in-between or other -- but the liar's sentence is best treated as a dialetheia.

If one accepts that then the LNC cannot hold because the LNC says "A & ¬A" is false. Since ¬A and A, as a dialetheia, are both true and false, together, the LNC is rejected.

However I do remember someone asking whether there were any logical laws that applied to all forms of logic. How about validity and consistency? Or which is basically the same as far as I can tell—the law of non-contradiction? — Janus

I'm a defender of dialetheism, thus far.

Which rules out the LNC.

Hence, the notion of pluralism -- at least so far no one has said that the logics which include the LNC are the same as the logics which exclude the LNC.

Heh. I wouldn't go that far at least. I think @Leontiskos and @Count Timothy von Icarus would want us to come up with a notion of logical monism which is interesting enough for their concerns.

Thus far I've gathered that they both would like to relate to knowledge generation? I think?

This is what motived by earlier response about why the problem is interesting with respect to knowledge generation.