I think the people doing the stats have found that the police are largely neither to blame nor praise when it comes to movement in violent crimes. While I agree with you that deterrence is something important, it isn’t the act of policing that drives deterrence (or many other kinds of deterrence policy), but the perception of being caught and/or actual imposition of consequences. So yes, arresting domestic abusers would be great, but I am not that concerned about low levels of murderers not getting arrested. I am interested in seeing people called into society and given a vested interest in its success. Putting lots of cops in the street could increase a murderer’s sense that he (because it is generally a he) will be caught, but the cost of increased police presence to prevent a murder or three (rather than to solve a murder or three) is the increased policing of POC for meaningless low level crimes combined with the continuation of seeing the system as an oppressor rather than a vehicle for personal and familial success.

Sure, ruling with an iron fist sounds amusing, but it isn’t based in the sorts of policy that I would hope animate policy in the United States.

Like 5 per 100,000? Maybe nationally, but not by state, and not by city. — Bitter Crank

That nasty place of Louisiana? High was 20 in 1993 and is like 12 today.

https://www.disastercenter.com/crime/lacrime.htm

Do you think it was the police force that halved the murder rate?

The police activity that is missing in many communities is detective-led investigations leading to the arrest of people committing murder and manslaughter. — Bitter Crank

I’m curious why this is of such concern to you.

https://www.disastercenter.com/crime/uscrime.htm

In 1960, the murder rate was 5.1. Today it is 5.0. There was a peak in 1980 of around 10.


https://www.brennancenter.org/our-work/analysis-opinion/americas-faulty-perception-crime-rates

It seems an aweful lot like sociological factors are behind the change in crime rates far more than particular policing theories or interventions.

https://www.brennancenter.org/our-work/research-reports/what-caused-crime-decline

More important were various social, economic, and environmental factors, such as growth in income and an aging population. The introduction of CompStat, a data-driven policing technique, also played a significant role in reducing crime in cities that introduced it.

The report concludes that considering the immense social, fiscal, and economic costs of mass incarceration, programs that improve economic opportunities, modernize policing practices, and expand treatment and rehabilitation programs, all could be a better public safety investment. — “Brennan Center”

Do you have sources you find compelling to counter narratives such as this?

…

My work looks most closely at where crime is happening, not at individual victims. But there are some things we think we know. Intimate-partner violence increased in 2020. So did hate crimes against Asians. But the overall demographics of victims is incredibly consistent over time. It’s young people of color, particularly young men of color. I don’t see anything yet to indicate that’s changed dramatically.

…

My argument is that in areas where communities go through periods of disinvestment and where institutions break down, people feel like they’re on their own. This creates conditions where violence becomes more likely. As a place becomes more violent, people change their behavior. They become more likely to interpret uncertainty in an aggressive way, more likely to carry a weapon, more likely to act quickly or first if they feel threatened. This is how the presence of violence creates more violence. This cascading effect, where violence begets violence, has been reinforced in the past year.

Last year, everyday patterns of life broke down. Schools shut down. Young people were on their own. There was a widespread sense of a crisis and a surge in gun ownership. People stopped making their way to institutions that they know and where they spend their time. That type of destabilization is what creates the conditions for violence to emerge.

…

When a social order depends on the police dominating public spaces, and that form of social order is questioned and starts to break down, it can lead to a surge in violence. It doesn’t mean that protests cause violence. It means that when you depend on the police to dominate public spaces and they suddenly step back from that role, violence can increase.

… — “Atlantic Interview of Patrick Sharkey”

https://www.theatlantic.com/ideas/archive/2021/03/is-americas-great-crime-decline-over/618381/

Nothing in realism locks the realist into a particular logical system. — Banno

:up:

a relative lack of police services in black communities. — Bitter Crank

This is painful, BC. The solution to very little is increasing police presence in over-policed communities. How about we legalize drugs and end the non-sense monopolies we keeping giving to rich folk to legally sell the same drugs that the non-rich folk have had their lives destroyed for selling. You might find that as we create a freer society (you know, one in which people can sleep with/marry whomever they want and put whatever substances they want into their bodies) the extra-social organizations (like crime rings), lose funding and power. Throw in a bit of social services (including support of women and children) and see what that does for domestic violence.

We have enough people incarcerated. We can’t keep jailing people to solve the problems the criminal laws were (in theory) instituted to avoid.

If one is concerned with people of color being murdered, then black-on-black violence is relevant; — ToothyMaw

Again, why are you mentioning it? If it is to stop systemic forces legitimizing/creating the circumstance of power in which violence is unethically directed towards particular oppressed (or politically weak) groups, then black-on-black violence isn’t relevant unless you can directly tie it to the systemic forces being discussed. If you believe that discussions of systemic racism are wholly coequal with discussions of how to stop people of color being murdered, I believe you are mistaken. An ethically just system of power will likely have problems with people acting unethically - a situation it shares in common with ethically unjust systems of power. Indeed, as the social circumstance of entrenched racism is redressed, you may very well find that crime against all people (POC or otherwise) decreases.

You need to focus not on whether black-on-black violence is an issue (of course it is), but whether it is a helpful topic in the context of the discussion at hand. I would imagine that if you find yourself in a room full of people discussing systematic racism, you should probably be pointing them towards POC engaged in self-advocacy that are identifying what features of systemic racism are important to them and, in the fortunate circumstance that you are talking to POC, you should encourage them to continue speaking without telling them what you believe they should be speaking about. If you are a POC and you think that the more important issue is something other than what they are discussing, you might exercise the general level of appropriate social decorum and talk about the topic that the organizers intended, talk about the topic that others have already introduced, or, when made aware that others don’t believe that your topic of choice is useful for the group, move on.

The “you” here is intended to be generalized and not about you as an individual. I know nothing about you nor do I pretend to. What I do know is that the people talking about systemic racism have made it abundantly clear that black-on-black violence is not something they want to spend time discussing and that it categorically comes across as deflection.

but black-on-black crime is also worth paying attention to — ToothyMaw

If we are paying attention to systemic racism, do you respond what about breast cancer? Surely breast cancer is something worth paying attention to. And what about feminism generally and the plight of children in Eastern Europe? Bringing something unuseful up in an unrelated context because that unseful thing is important is a waste of time, i.e. a deflection. I think you’d find it unlikely that serious people exclaim that black on black violence is always a deflection, but that the only time they hear certain people talk about it is in response to a conversation about (or action against) systemic racism.

But according to intuitionism objects and numbers can also be lawless, where an object is said to be "lawless" if it's existence and/or value isn't decided by the formal system it is part of, but by something not described by, and external to, the formal system. — sime

Lots of great things about your post. I did a really bad job of trying to highlight truth of a system and truth external to the system in another post and how when those two systems share a one way relation (external can set values internally but internal cannot set values externally), one can construct a variety of internal systems to predict/interpret the inputs from the external system, and choose the system that works best in the context employed rather than attempt to have the internal system account wholly for the lawless external values.

Hence, according to Devitt, "no doctrine of truth is constitutive of realism". — Banno

Which is what I am badly saying elsewhere.

DO you thin this somehow incompatible with realism? — Banno

I was responding to this question. Perhaps I misunderstood the tone.

Ideally, fending against informal logical fallacies should protect one against being duped (and, if one is very nice, make one refrain from duping others). — baker

I want very much to like this, but there are times when informal fallacies are useful - like appeals to authority or ad hominem when it is so much more trouble to show why the person is wrong. If an informal fallacy gets you to the same end with more expedience, I question why they shouldn’t be given the same status as any other heuristic.

There are some alternative mathematical logics which account for the (un-)provability problem by eliminating the tertium-non-datur and the law of the double-negation by saying "x" means that "a proof can be contructed for x" and "not(x)" means "a proof can be constructed for not(x)". Doing this a failure to construct a proof for "not(x)" no longer necessarily implies "x", which makes the logic weaker (and suitable for an open world). — Heiko

So this is a type of motivation of mine - to understand that where we have warrant for both X and ~X, that we shouldn’t somehow dismiss the warrant of one or the other for fear of contradiction. Although not fully explicated here, the thought is that the way that we speak of truth is neither about coherence nor correspondence, but about achieving our ends. We can grant the realist his state of affairs for rTruth, move into why rTruth is utterly meaningless for epistemology, and then get on with the business of thinking well about solving our problems. It would be nice, however, if the realist would cease their reproach of logics that don’t meet their aesthetic based upon the faulty belief that logic is about the state of affairs.

Indeed, why not makeEristische Dialektik our Bible? — baker

Well I don’t understand the Bible in Latin or German, why should another German book that I don’t understand fail to qualify as a bible? The title sounds grand though.

Banno may tell you that he never laughs at my jokes.

Persuade the Audience, Not The Opponent
This is chiefly practicable in a dispute between scholars in the presence of the unlearned. If you have no argument ad rem, and none either ad hominem, you can make one ad auditores; that is to say, you can start some invalid objection, which, however, only an expert sees to be invalid. Now your opponent is an expert, but those who form your audience are not, and accordingly in their eyes he is defeated; particularly if the objection which you make places him in any ridiculous light. People are ready to laugh, and you have the laughers on your side. To show that your objection is an idle one, would require a long explanation on the part of your opponent, and a reference to the principles of the branch of knowledge in question, or to the elements of the matter which you are discussing; and people are not disposed to listen to it. For example, your opponent states that in the original formation of a mountain-range the granite and other elements in its composition were, by reason of their high temperature, in a fluid or molten state; that the temperature must have amounted to some 480 degrees Fahrenheit; and that when the mass took shape it was covered by the sea. You reply, by an argument ad auditores, that at that temperature - nay, indeed, long before it had been reached, namely, at 212 degrees Fahrenheit - the sea would have been boiled away, and spread through the air in the form of steam. At this the audience laughs. To refute the objection, your opponent would have to show that the boiling-point depends not only on the degree of warmth, but also on the atmospheric pressure; and that as soon as about half the sea-water had gone off in the shape of steam, this pressure would be so greatly increased that the rest of it would fail to boil even at a temperature of 480 degrees. He is debarred from giving this explanation, as it would require a treatise to demonstrate the matter to those who had no acquaintance with physics. — “The Art of Being Right”

My inclination is to say simply that we can choose whatever logic suits our purpose. DO you thin this somehow incompatible with realism? — Banno

I am suggesting quite the opposite - that if truthmakers are states of affairs, then logic should not be faulted for its failure to ensure rTruth. In other words, realists should feel free to use whatever logic they want including the acceptance or denial of any particular rule no matter how much of a sacred cow it is. If a logic occasionally produces an useful result, we just use a different one. If our concern is about preserving lTruth, then we apply a different criteria to our logic than if our concern is predicting the behavior of light through a slit as it spins our radiometer.

Universal logic which is responsible both for rTruth and lTruth feels much like ancient baggage. Thinking can be dynamic and free and so long as our methods achieve our ends, what more can we ask of them? If you want realism, it doesn’t require the baggage of a particular logic.

If you read ~ as an intuitionist, as Dummett would, then ~p only says that you haven't demonstrated p, and ~~p only says that you haven't demonstrated that you haven't demonstrated p. — Srap Tasmaner

I appreciate that, however I am not sure that Michael was saying that. And yes, I should have asked him if he is rejecting the law of the excluded middle rather than focusing on the principle of bivalance to be more to the point. I stand corrected.

Intuitionist Logic from SEP

Intuitionistic logic can be succinctly described as classical logic without the Aristotelian law of excluded middle:
A∨¬A(LEM)

or the classical law of double negation elimination: . . .

Not having verified p isn’t the same as having verified not-p. You need to verify not-p for p to be false. — Michael

So you are abandoning the principle of bi-valance?

Also, I think you are about to engage in a dangerous game when you suggest that P can be true and ~P can be true because they are separate propositions. The tilda, which stands for "not", is a logical operator, not a feature of the proposition being negated (i.e. the tilda is the logical operator that means that the atomic or complex formula represented by P is not true).

Other than that - I do not understand your concept of rTruth completely: E.g. If you feel a poke in the back, is there "really" something that pokes you? I guess the answer is "no": it is a conclusion that everything has cause. I am not sure that all realists would reduce reality to just the given content of consciousness. In another thread I pointed out that (following e.g. Heidegger) reality seems to be purely negative - that it is mainly what _prevents_ you to assume something. In logics this would be a statement not(x) where x is the "state of affairs as assumed". — Heiko

Realism, as being used here, is about people who think that what makes a proposition true is its relation to the states of affairs. I am not a realist. I am, however, interested in non-binary, relevant, paraconistent, etc. logics and how they solve real world problems that classical logic (however slightly modified) cannot (or perhaps they solve such problems more efficiently). I see logic more as a tool of thinking than a thing capable of governing the world (i.e. logical necessity/entailment/possibility does not preclude otherwise efficacious behavior).

Yet again, if the verificationist hasn’t verified the square root of 123 then he isn’t omniscient. It’s that simple. — Michael

If the verificationist hasn't verified it, it isn't true. The nice thing about being omniscient is that knowing everything that is true (i.e. every proposition that has been verified) neatly discloses everything that is false (every proposition that hasn't). It isn't like I'm the person that said that Fitch's paradox of knowability is a problem for verificationists. This type of omniscience is precisely the naive anti-realism that is required when the middle way gets hoisted on Fitch's petard.

The operative concept of “knowability” remains elusive but is meant to fall somewhere between equating truth uninformatively with what God would know and equating truth naively with what humans actually know. Equating truth with what God would know does not improve intelligibility, and equating it with what humans actually know fails to appreciate the objectivity and discoverability of truth. ...

The great problem for the middle way is Fitch’s paradox. It is the proof that shows (in a normal modal logic augmented with the knowledge operator) that “all truths are knowable” entails “all truths are known”... — "SEP

Because under verificationism that isn’t sufficient to be omniscient. Omniscience requires having verified every proposition or their negation. — Michael

You keep saying this. Who says that verificationism doesn't require omniscience? If omniscience is knowing every true thing and every true thing is known....

It is however the contrapositive of Theorem 5 that is usually referred to as the paradox:
(K Paradox)∀p(p→◊Kp)⊢∀p(p→Kp).

It tells us that if any truth can be known then it follows that every truth is in fact known. — SEP on Fitch

Fitch’s paradox of knowability (aka the knowability paradox or Church-Fitch Paradox) concerns any theory committed to the thesis that all truths are knowable. Historical examples of such theories arguably include Michael Dummett’s semantic antirealism (i.e., the view that any truth is verifiable)

No I don’t. Verificationism doesn’t permit unknown truths. It permits unverified propositions. — Michael

So why do you say that verificationism doesn't require omniscience? All truths are known.

You mean this definition?

But verificationism holds that p is true if and only if it has been verified.

And it follows that everything that is true has been verified. — Banno

So Banno's verificationism says that everything that is true has been verified and you say that verificationism permits unknown truths. Please give an example of something that is verified true but is unknown. As of yet unverified propositions are necessarily not true according to Banno's account and, so far as I can tell, a not true thing is false on the typical account. So which P is unverified, true, and unknown to be true.

I'm not arguing that robots experience things here. I'm arguing that it's a superfluous requirement. But even if you do add this superfluous requirement, it's certainly not the critical element. To explain what brings me the bananas when I ask for them, you have to explain how those words makes something bring me bananas. — InPitzotl

I'm not so sure that Daemon accepts that the understanding is in the doing. A person and a robot acting identically on the line (see box, lift box, put in crate A, reset and wait for next box to be seen) do not both, on his view, understand because the robot is explicable (since he, or someone else, built it from scratch and programmed it down to the last detail). He is after minds as the locus of understanding, but he seems unwilling to accept that what has a mind is not based on explicability. It is a bit like a god of the gaps argument that grows ever smaller as our ability to explain grows ever larger. We will have minds (and understanding) only so long as someone can't account for us.

If for example, the grass is wet, it has to have become wet somehow. If we were in a world where this can only happen by rain, the conclusion clearly is that it must have rained. — Heiko

And this is the type of tension that I think the realist has - that logic is supposed to give warrant for the belief in rTruth, but the world doesn't function deductively (from generalizations to specifics), rather it just is. Probabilistic, stochastic, etc. logics which can account for the variance between premises and conclusions are deemed insufficient to give warrant (let alone certainty) for the realist, but logic can never demonstrate other than which what was assumed. So if we demand binary truth values (for unitary propositions or compound propositions), but our best methods for predicting/accounting for the world are not perfectly accurate, what is the role of such logics for the realist? It cannot do what it sets out to do (make an rTruth) and its predictive and truth preservation properties are inherently disconnected from the way that rTruths appear to relate to themselves, so what is the allure?

I am looking for an argument of what logic does for the realist besides act as a useful heuristic. In particular, I am looking for an argument as to why anyone should feel compelled to accept classical logical (or minor variations) as somehow more useful as a heuristic than any other logic.

The difference is that normally we use the material implication as an actual implication, as in the truth of the antecedent implies the consequent. Being a bachelor implies being an unmarried man. Being a man implies being mortal. Winning 270 Electoral College votes implies becoming the next President of the United States. — Michael

You seem stuck in social conventions and definitions. Forget social conventions and focus on mind-independent stuff, you know, the pre-interpreted states-of-affairs. If you are a realist and you wish to avail yourself of the power of logic to determine rTruth, can it do so?

On whose account of anti-realism? What is true that is unknown on their account and how does their account differ from realism?

Logic can determine that a set of premises /cannot/ be true or show that the truth of a given conclusion holds under given premises and derive such already implied conlusions. — Heiko

That is the bit that most people lose, I think, that all conclusions are of necessity assumed in the premises. Logic is useful revealing novel relations given a particular set of rules, but cannot reveal rTruths. Logic then is descriptive and not normative, no matter how well the logic (or math) predicts the rTruths. But is this a problem for logic or just for non-logicians?

Nothing. Your argument has no practical use. I have to evaluate the truth of your conclusion to evaluate the truth of your premise. — Michael

This feels much like a circle. Yes, there is no point to a logical argument about states of affairs because what makes propositions about states of affairs true are the states of affairs, not our rules of logic. Nevertheless, people want to use logic to dictate how states of affairs can be. What lTruth can you produce that relates to an rTruth? If you are happy to concede from go that logic is just the formalistic manipulation of symbols, I won't complain.

The argument form is already valid and isn't the least bit interesting. The "what makes it sound" part is what I am discussing. If soundness is judged by reference to the world (and that includes evaluating the propositions contained in the conclusion since they must have appeared among the premises), what work is the proof doing for you viz-a-viz the rTruth of the propositions in the conclusion?

(That is, while the argument form may be valid, the interesting bit - whether the consequence is true - is directly evaluated by reference to the facts. In this respect, soundness is a coincidence of valid form and fact.) — Ennui Elucidator

I'll even quote myself in the OP.

So how do you evaluate soundness?

You have to prove your premises true to prove your conclusion. — Michael

That isn't how logic works. A premise is assumed, not proven. The valid conclusion is of the form "If the premises are true, the conclusion must be true".

You proved that 1 is true, you haven't proved that 2 is true. How do you prove that if 2 + 2 = 4 then the cat is on the mat? — Michael

It is a premise, I don't have to prove it to assume it.

It isn't. The argument is only a proof if you can prove 1 and 2 to be true. A deductive argument can have false premises after all. How do you prove 2 to be true? By proving that 2 + 2 = 4 and that a cat is on the mat. You need "the world" to do this. — Michael

But that is what my example shows you, I provided what is essentially a tautology in 1 and a claim about the world as a consequent of a conditional. The only way to show that 2 is false (and thereby show the argument is unsound) is to evaluate whether the consequent is true, which is precisely what the proof appears to be proving. So the proof adds nothing to the rTrue of the consequent and indeed is just a symbols game.

it's not paraconsistent logic - which holds that A, ~A ⊨ B is not a valid inference; this is the view usually associated with anti-realism. — Banno

I believe this is where we diverge. Anti-realism isn't concerned with explosion as a logical matter, it (the middle-way anti-realism) is concerned with how all truths are known yet some truths are unknown (anti-realism plus non-omniscience) in a meaningful (non-incoherent/useful) way. I thought my quotes pointed strongly in the direction that paraconsistent logic is not, in and of itself, the issue, but the paradox:

Beall suggests that the knower gives us some independent evidence for thinking Kp∧¬Kp, for some p — “SEP on Fitch’s Paradox”

I am not sure how anti-realism plus denying explosion would solve the knower's paradox as a philosophical matter, it would just say let anti-realists say, "Yes, there is a contradiction, but you can't prove anything else as a result." If the anti-realist does not want to permit contradictions in the first place (How absurd!), non-explosion doesn't do the necessary work. I grant I could be missing a nuance.

Michael's claim regarding multiple truth values was addressed by Priest in the article when he discussed "value of" as a relation rather than a function. So yes, what Michael suggests is not classical logic, but it is a possibility accounted for in paraconsistent logics which leads me to think that paraconsistent logics reject the principle of bivalence in-so-far as it requires a proposition have only one truth value. This is distinct, I believe, from having a third truth value, i.e. paraconsistent logics are not necessarily multi-valued logics, cf. multivalued paraconsistent logics .

I'm not sure there's really a problem then. If premise 1 is true then premise 2 is true only if the cat is on the mat. So the realist can say that the realist account of truth is required for premise 2 to be true. — Michael

That is the backwards part. Yes, rTrue for the world. But can 1 and 2 make 3 rTrue? If we want to know if 3 is rTrue, how is a proof used as a proxy for the world?

Anytime you look to rTrue for the premises, you are focusing on the wrong spot. Pick any argument you want,

If my finger isn’t in my nose then my hand has five fingers.
My finger isn’t in my nose.
Therefore my hand has five fingers.


P then Q
P
Therefore Q

I assure you, my hand has five fingers and my finger isn’t in my nose. Why is Q true?

So let’s try to fix some of my ambiguity.

The statement "the cat is on the mat" is definitionally true — TheMadFool

This is exactly contrary to the way I am using “true.” Something is true when it is the state-of-affairs. When we find the cat is on the mat, we aren’t satisfying definitions, it is simply the case that the cat is on the mat. Part of what this post is about is highlighting the equivocation between true by virtue of state of affairs and true by virtue of definition (but entirely avoiding the analytic/synthetic framework). Maybe we can refer to this version of truth as “rTrue” (for realist truth).

You're addressing the discrepancy with natural language? — Michael

You aren’t completely off here, but I had hoped that my reference to entailment (rather than logical implication) might help avoid focusing on the difficulty of mapping natural language to symbolic logic. I am more focused on logical consequence, i.e. what it means for a conclusion to follow from its premise, and trying to contrast it with the requirements of a realist account of truth. In order to facilitate this distinction, I will add another term, “lTrue” to mean the conclusion of a valid deductive argument (by use of whatever logical system you desire).

Perhaps we can think of this post as something like, what is the relation between rTrue and lTrue for any proposition, P. Critically, I am not interested in the semantic content of P, whether “P” can stand in relation to rTrue, or what the magic is that causes P to make “P” rTrue (that is, for us to articulate a truth rather than just observe, or potentially observe, one).

As a side note, much like the linked article, I am going to focus on deductive validity rather than inferential validity. Also, this is a maybe helpful quote:

A closely related analysis for formality is that formal rules are totally abstract. They abstract away from the semantic content of thoughts or claims, to leave only semantic structure. The terms ‘mother’ and ‘cousin’ enter essentially into argument (5). On this view, expressions such as propositional connectives and quantifiers do not add new semantic content to expressions, but instead add only ways to combine and structure semantic content. Expressions like ‘mother’ and ‘cousin’, by contrast, add new semantic content.

[/quote[

. — “SEP on Logical Consequence”

how does one account for the existence of irrationality, abstraction, subjectivity and opinion via logical/ reasonable means? — Benj96

I like this question, but I think it is a bit aside from my current focus. This seems like a problem of constructing a useful logic that can account for such things more than investigating the relation of logical consequence to the state of affairs in the first instance (i.e. logic may not have to account for all rTruths but I am asking it can account for some).

IS it that (2) already seems to evaluate "the cat is on the mat"? — Banno

I’m not sure what you mean by “seems to evaluate” in this case. My hope was that by using a mathematical truth as the antecedent, that we could highlight that any true premises plus valid form makes “P” true of logical necessity. Logic is, perhaps, about establishing (discovering?) the rules by which the truth value of one proposition relates to the truth value of another. Classical logic, where any proposition can stand in for any other proposition with the same truth value, leads to many intuitively unsatisfactory “proofs”.

And harkening to your questions about realism, here is another snip from the logical consequences article:

Perhaps there is a reason to allow the notion of logical consequence to apply even more broadly. In Gentzen’s proof theory for classical logic, a notion of consequence is defined to hold between multiple premises and multiple conclusions. The argument from a set X of premises to a set Y of conclusions is valid if the truth of every member of X guarantees (in the relevant sense) the truth of some member of
Y. There is no doubt that this is formally perspicuous, but the philosophical applicability of the multiple premise—multiple conclusion sense of logical consequence remains an open philosophical issue. In particular, those anti-Realists who take logical consequence to be defined in terms of proof (such as Michael Dummett) reject a multiple conclusion analysis of logical consequence. For an Anti-realist, who takes good inference to be characterised by the way warrant is transmitted from premise to conclusion, it seems that a multiple conclusion analysis of logical consequence is out of the question. In a multiple conclusion argument from A to B, C, any warrant we have for A does not necessarily transmit to B or C: the only conclusion we are warranted to draw is the disjunction B or C, so it seems for an analysis of consequence in terms of warrant we need to understand some logical vocabulary (in this case, disjunction) in order to understand the consequence relation. This is unacceptable if we hope to use logical consequence as a tool to define that logical vocabulary. No such problems appear to arise in a single conclusion setting. (However, see Restall (2005) for a defence of multiple conclusion consequence for Anti-realists; and see Beall (2011) for a defence of certain sub-classical multiple-conclusion logics in the service of non-classical solutions to paradox.)
— “SEP on Logical Consequence”

Truthfully, this whole truth bit is complicated, but I don’t find logical proof among the things that make propositions true in articles like this. and yet it so often seems that people say that some proposition is “true” by virtue of some logical argument.

I don't think that quite right - rather it accepts that the height is neither known nor unknown; and hence paraconsistent. — Banno

Not to dwell on the disagreement, but I think the motivation to paraconsistent logics is precisely about explosion rather than about propositions without a truth value. We may get off on the wrong foot if we think that Beall is not asking us to accept the contradiction implied by Fitch’s paradox, but to do so in a logical system where such contradiction doesn’t lead to “triviality”, i.e. adopt a paraconsistent logic.

In the literature, especially in the part of it that contains objections to paraconsistent logic, there has been some tendency to confuse paraconsistency with dialetheism, the view that there are true contradictions (see the entry on dialetheism). The view that a consequence relation should be paraconsistent does not entail the view that there are true contradictions. Paraconsistency is a property of a consequence relation whereas dialetheism is a view about truth. The fact that one can define a non-explosive consequence relation does not mean that some sentences are true. The fact that one can construct a model where a contradiction holds but not every sentence of the language holds (or where this is the case at some world) does not mean that the contradiction is true per se. Hence paraconsistency must be distinguished from dialetheism (though see Asmus 2012).
— “SEP on Paraconsitent Logics”

Beall suggests that the knower gives us some independent evidence for thinking Kp∧¬Kp, for some
p, that the full description of human knowledge has the interesting feature of being inconsistent. With a paraconsistent logic, one may accept this without triviality. And so it is suggested that one go paraconsistent and embrace Kp∧¬Kp as a true consequence of the knowability principle. Beall concludes that Fitch’s reasoning, without a proper reply to the knower, is ineffective against the knowability principle.
— “SEP on Fitch’s Paradox”

A is both true and false. Which is... different. — Banno

And in case you didn’t read the Priest article I linked, here is a quote that you may find interesting.

At the core of the explanation, one has to grasp a very basic mathematical distinction. I speak of the difference between a relation and a function. A relation is something that relates a certain kind of object to some number of others (zero, one, two, etc). A function, on the other hand, is a special kind of relation that links each such object to exactly one thing. Suppose we are talking about people. Mother of and father of are functions, because every person has exactly one (biological) mother and exactly one father. But son of and daughter of are relations, because parents might have any number of sons and daughters. Functions give a unique output; relations can give any number of outputs. Keep that distinction in mind; we’ll come back to it a lot.

Now, in logic, one is generally interested in whether a given claim is true or false. Logicians call true and false truth values. Normally, and following Aristotle, it is assumed that ‘value of’ is a function: the value of any given assertion is exactly one of true (or T), and false (or F). In this way, the principles of excluded middle (PEM) and non-contradiction (PNC) are built into the mathematics from the start. But they needn’t be.

To get back to something that the Buddha might recognise, all we need to do is make value of into a relation instead of a function. Thus T might be a value of a sentence, as can F, both, or neither. We now have four possibilities: {T}, {F}, {T,F} and { }. The curly brackets, by the way, indicate that we are dealing with sets of truth values rather than individual ones, as befits a relation rather than a function. The last pair of brackets denotes what mathematicians call the empty set: it is a collection with no members, like the set of humans with 17 legs. It would be conventional in mathematics to represent our four values using something called a Hasse diagram, like so:

{T}
↗ ↖
{T, F} { }
↖ ↗
{F}

Thus the four kotis (corners) of the catuskoti appear before us.

In case this all sounds rather convenient for the purposes of Buddhist apologism, I should mention that the logic I have just described is called First Degree Entailment (FDE). It was originally constructed in the 1960s in an area called relevant logic. — “Priest on Beyond True and False”

3.5 in particular, yes? But my sense is that you don’t want a discussion of what is presented there, but a reaction. I further suspect that my reaction is going to go sideways, so I apologize in advance.

In brief, people don’t like the idea of anti-realism in-so-far as it relates truth to knowledge because clearly there must be things that are true that we don’t know, yet anti-realism suggests that all truths are necessarily known, i.e. there is nothing that is true that we don’t know (Fitch’s Paradox). Your classic case of the height of Mt. Everest before it was surveyed (a discrete fact seemingly manifested in the “real” world) seems to embody this type of unknown truth for which anti-realism cannot account.

So how does paraconsitent logic help anti-realism? It pulls an interesting trick - rather than denying that Mt. Everest has a height if no one knows it, somehow it accepts that the height is both known and unknown. So we can satisfy both the intuition that not all truths are known and the requirement of anti-realism that all truth be known. This much I assume (or perhaps hope) we can more or less agree on.

My suspicion is that you would be amenable to anti-realism if the “middle way” was not absurd (e.g. leads to a contradiction either in logic or intuition). Given that paraconsistent logic seems to save the middle way in anti-realism, you are questioning what else you must commit to if you accept a type of this logic.

Are we on the same page as to where we are and the sort of response you are looking for to “where now?”


P.S. On pain of equivocation (and certainly not to agree with him) I am vaguely reminded of the great perceiver required by the idealism of Berkeley. If this were the case, that there were actually two categories of perceivers (humans as traditionally conceived and something transcendent), it could be analogous to how something could be both known and unknown in a meaningful way and not of necessity collapse the middle way into naive anti-realism. I think there is a little ambiguity in what qualifies as a “knower” for Fitch’s paradox to the extent that our intuition is that humanity (collectively) is not omniscient and yet there are truths that are unknown by us.

Another strategy, however, is suggested by Berkeley’s reference in PHK 3 and 48 to “some other spirit,” a strategy summarized in a further limerick:

Dear Sir, your astonishment’s odd
I am always about in the Quad
And that’s why the tree
continues to be
since observed by, Yours faithfully, God
— “SEP on Berkeley”

Fitch article in SEP — Banno

Sorry for being dense, what is the title of the article?

For the sake of expedience, I am just going to assume you mean the one on Fitch’s Paradox of Knowability.