And ↪Cheshire's "a thing can't really be otherwise or not," would be a similar sort of reasoning. Dialetheism is normally argued for in the context of paradoxes related to self-reference (as has been the case in this thread). I think critics would argue that these are no more mysterious than our ability to say things that aren't true (which perhaps IS mysterious). At any rate, the "actual" true contradictions that get thrown out, in the SEP article for example, etc. tend to be far less convincing. For example, "you are either in a room or out, but when you are moving out of a room, at one point you will be in, out, both, or neither." — Count Timothy von Icarus
If you want to make use of the term, then you can set out what you take it to mean.
"Correct logic" is not a term defined in formal logic. That's rather the point here. You will not, for example, find a definition of "Correct Logic" in the Open Logic text. But you will find definitions of validity, satisfaction, truth and so on. These are the terms used by logicians when doing logic.it's how she defines the entire problem — Count Timothy von Icarus
You will not, for example, find a definition of "Correct Logic" in the Open Logic text. But you will find definitions of validity, satisfaction, truth and so on. These are the terms used by logicians when doing logic.
Beale and Restall define their pluralism in these terms for instance (and as there being "multiple true logics"), Paseau and Griffith's define their monism in these terms. — Count Timothy von Icarus
I'm asking you to show you have a basic understanding of the topic. — Count Timothy von Icarus
From my OPOk, so you cannot define logical monism or pluralism. — Count Timothy von Icarus
Logical laws are supposed to work in every case. Modus Tollens, non-contradiction, identity - these work in any and all cases. A logical nihilist will reject this.
To be a law of logic, a principle must hold in complete generality
No principle holds in complete generality
____________________
There are no laws of logic.
— Gillian Russell
There are two ways to deal with this argument.
A logical monist will take the option of rejecting the conclusion, and also the second premise. For them the laws of logic hold with complete generality.
A logical pluralist will reject the conclusion and the first premise. For them laws of logic apply to discreet languages within logic, not to the whole of language. Classical logic, for example, is that part of language in which propositions have only two values, true or false. Other paraconsistent and paracomplete logics might be applied elsewhere. — Banno
Just to be clear, for other folk, Tim's question is loaded precisely becasue the notion that there is a "correct logic" for which a definition might be provided is exactly what is denied by both logical pluralism and nihilism.
Well no, — Count Timothy von Icarus
If pluralism denied that there were any correct logics, how would it be distinguishable from nihilism exactly? — Count Timothy von Icarus
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.
Surely, there's an idea of rationality and proper reasoning in general discourse, e.g. we say that we are rationally warranted to hold some beliefs but not others, that we can jointly hold some beliefs but that holding others jointly would be inconsistent, and so on. To deny this would be one of the most fringe positions one could possibly take on anything. And this idea also includes that of in some sense 'proper' and 'improper' inferences (deliberately avoiding the word valid for now). We are supposed to 'accept' some arguments of the form '{premises}, therefore conclusion', that someone might tell us at work, at the family dinner, in politics, but not others. So there's a notion of some consequence relation between propositions that sometimes holds and sometimes doesn't.
The question then simply is whether there is a logic, including in the specific sense of some formal system, whose consequence relation coincides with that of proper reasoning in ordinary discourse, such that we could for example turn to it and use it to settle the validity of an argument in ordinary discourse, period. If there's exactly one such system that gets the job done, that's monism, if there are multiple that have equal claim to something like that, that's pluralism, and if something like that simply doesn't exist, that's nihilism
There are two interwining ways to cash out the phrase "correct logic":
Deontologically, as in there being propositions of e.g. the form, "If it is judged that A, and if it is judged that (if A then B), then it ought to be judged that B." Now, it would not be that there was only one correct logic in the sense of there being only one strictly commanded rule or pattern of inference, but we would claim that only one system of patterns of inference featured such "oughts," and either no other system featured "oughts" but at best only "mays" (you may infer this from that...) or the other systems would in some sense be forbidden.
Ontologically, as in thinking that objective/external reality is itself structured like a complex interlocking set of propositions, which proposition-like entities we usually call by the name of facts. Then some one completely correct logic would be one consisting in all and only inference rules reflected from the interrelations between possible facts.
Deontologically, pluralism is best understood as what we might call "permissivism," i.e. any acknowledged system of logic is permissible. (A pluralist doesn't actually have to acknowledge every system that the word "logic" is applied to, though they are less and less a pluralist, the more and more they limit the range of their acknowledgements.) This is subtly, but genuinely, distinct from logical relativism, which would be that different systems "ought" to be applied to different topics.
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.)
there is more than one sense in which arguments may be deductively valid, that these senses are equally good, and equally deserving of the name deductive validity”.
Some would argue that logic is about natural language reasoning or vernacular reasoning (e.g., Graham Priest has most clearly articulated this view). If that is the case, then the correct logic is the one that correctly captures/represents the consequence relation in natural language or the consequence relation instantiated by reasoning in the vernacular. If there is no single consequence relation of the relevant sort, then one might be led to pluralism. If there is no consequence relation discoverable in natural language, one might be led to nihilism, etc.
Part of what the monism/pluralism/nihilism debate is about, however, is how to conceive of logic. Arguably, despite what I said above, this debate cannot be conducted entirely independently of the background problem about the correct conception of logic. Some pluralists would deny that logic is only or primarily about the consequence relation in natural language or about vernacular reasoning. Logics should model the consequence relation of any legitimate mathematical theory, leaving room for many "correct logics" which get the job done since there are, arguably, many legitimate mathematical theories (this is Shapiro's view).
This is not the purely abstract conception of logic, according to which logic just means pure logic - logics as models of any possible formal language whatsoever. But it is also not the more traditional view, according to which logic should be applied to vernacular reasoning before one can speak of correct logics, either. I say that the latter is the more traditional view because, arguably, in the history of logic, it was typical to assume that logic is normative for human reasoning and not about modeling any possible language whatsoever, mathematical or other.
There are yet other views, according to which logic should represent the logical structure of the fundamental language which carves nature at its joints (Ted Sider's view). That would be one way to cash out the ontological approach to the "application of logic."
"Correct" in that quote basically means appropriate. It has nothing to do with truth.
In order to answer the question about what makes a logic correct one has to address the prior question about what logic is about, i.e., the subject matter of logic. There is one view of logic, according to which a logic is specified by giving a consequence relation for any abstract formal language. There is nothing else to logic. This conception of logic trivializes the debate
What is "appropriateness" then? — Count Timothy von Icarus
First think about the historic development of logic starting with Aristotle, the idea of what logic is supposed to do for us, and the pre-theoretical idea of validity. What is the definition that absolutely every student who takes a course in (formal or informal) logic or critical thinking (or reads a Wikipedia article) learns? Usually, something along the lines of "an argument is valid iff it is impossible for the premises to be true and the conclusion nevertheless to be false". And why did people think this is an important concept? I don't want to talk about Aristotle on my own, so I rely on John Corocan here:
"Every non-repetitive demonstration produces or confirms knowledge of (the truth of) its conclusion for every person who comprehends the demonstration. Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration is an extended argumentation that begins with premises known to be truths and involves a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In short, a demonstration is a deduction whose premises are known to be true. For Aristotle, starting with premises known to be true and a conclusion not known to be true, the knower demonstrates the conclusion by deducing it from the premises—thereby acquiring knowledge of the conclusion."
The last sentence is probably the most interesting one here: thereby acquiring knowledge of the conclusion. Of course, that's how we typically think about logic, long before we think about verification of program correctness, multi-agent systems, games, and 5 million other use cases for dozens of logics these days.
But on a first view, that makes the idea that there is more than one accurate account of logical consequence and that they are equally correct, somewhat problematic. There's a challenge sometimes referred to as "Priest's challenge" by Read and Restall. Imagine there are two equally correct accounts of logical validity, L and K. We agree/know that a set of premises S is true. According to L, p follows from S, according to K it doesn't. Just like most people, the most popular logical pluralists are not relativists about truth, and K and L here are allegedly accurate accounts of validity, not of truth. Further, they don't deny that the most important objective of any logical system is to describe an account for logical consequence. So is p true or not?
To say "it depends" seems unsatisfying. Firstly, it's not clear what that's supposed to mean. Does the set of premises S guarantee the conclusion in the sense of validity or not? The pre-theoretical idea of validity doesn't appear to be relativistic, and the best-known pluralists aren't relativists about truth. The answer "Yes, p is true. K doesn't say it's not true, it just doesn't confirm that it is so. L confirms it" on the other hand, seems to contradict the claim that K and L are equally good accounts of logical consequence. If L tells us more without being incorrect, then L seems better than K.
Closely related to that is the concern about the normative status of logic. Many logicians and philosophers of logic held that logic is normative - it informs us how we ought to reason. That was certainly part of the intellectual background of the development of logic. A word used for logical principles or axioms by German mathematicians like Frege or Zermelo was "Denkgesetz" - a law of thought. Given the pre-theoretical idea of validity, in combination with conceptualizing logical laws as laws of thought, we shouldn't be surprised that one standard articulation of what it means to be a law of logic was that a principle must hold in complete generality - domain independent. Even pluralists have acknowledged that all of that is in obvious conflict.
So, there's quite a bit of explaining to do for the pluralist, as their conception of logic deviates significantly from how people have historically thought about logic and validity for the last 2300 years, even what it means to be a logic in the first place.
The monist's position, on the other hand, is rather 'standard': It seems to follow more naturally from nothing but the conceptualization of validity and logic. They don't have much explaining to do here. The opposite doesn't really hold, or to a lower degree: Many of the things that seem to be prima facie troubling for the monist, must likewise be answered by the pluralist. For example, maybe we want to ask the monist "There's only one true logic? How would you find out what logic that is, and what does this even mean?" This might be a legitimate question, but it needs to be answered by the pluralist as well. Neither Restall & Beall nor Shapiro hold that literally any possible logic (alphabet, formation rules, deductive apparatus) that we can write on a piece of paper is a 'true logic' in their sense.
And can one have correct purposes, or can one's purposes be defined arbitrarily? The purpose here is to capture natural language understandings of good reasoning and valid argument — Count Timothy von Icarus
Surely, there's an idea of rationality and proper reasoning in general discourse, e.g. we say that we are rationally warranted to hold some beliefs but not others, that we can jointly hold some beliefs but that holding others jointly would be inconsistent, and so on. To deny this would be one of the most fringe positions one could possibly take on anything. And this idea also includes that of in some sense 'proper' and 'improper' inferences (deliberately avoiding the word valid for now). We are supposed to 'accept' some arguments of the form '{premises}, therefore conclusion', that someone might tell us at work, at the family dinner, in politics, but not others. So there's a notion of some consequence relation between propositions that sometimes holds and sometimes doesn't.
The question then simply is whether there is a logic, including in the specific sense of some formal system, whose consequence relation coincides with that of proper reasoning in ordinary discourse, such that we could for example turn to it and use it to settle the validity of an argument in ordinary discourse, period. If there's exactly one such system that gets the job done, that's monism, if there are multiple that have equal claim to something like that, that's pluralism, and if something like that simply doesn't exist, that's nihilism
do not think it's plausible to say that trivial logics in which everything expressible can be proven true are only arbitrarily bad for inference for instance. Do you disagree? — Count Timothy von Icarus
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