What is Logic? — Count Timothy von Icarus

Best answer might be that it is rules of grammar; rules for stringing symbols together.

But I would draw your attention to logical pluralism: the view that there are no "Laws" of logic.

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.

A few counter-examples of logical principles that might be thought to apply everywhere.

Identity: ϑ ⊧ ϑ; but consider "this is the first time I have used this sentence in this paragraph, therefore this is the first time I have used this sentence in this paragraph"

And elimination: ϑ & ϒ ⊧ ϑ; But consider "ϑ is true only if it is part of a conjunction"... — Banno

Pick the logic that works for the sort of discussion which you are involved - a grammar for your argument.

But your statement “Logic is a set of formal systems; it is defined by the formalism” (which is neither a logic formula nor a logic tautology) seemed to offer a definition for “Logic”. And valid definitions should not be tautological in the sense that what is to be defined should not occur in what is defining. Yet your other claims made your definition of “logic” look tautological (even claiming “Logic is all about tautologies” would sound tautological if it equates to “Logic is all about logic”).

It's like formalism in mathematics; there are rules for manipulating symbols and nothing else. The most austere definitions of logic I've seen tend to take the line that logical systems are like Chess, they are a set of rules that have been developed. Their relation to what they are used for in the world (e.g. the sciences) is pushed off to the side (which you see a lot in definitions of mathematics as well). I don't particularly like these definitions, but I don't think/hope I'm not misrepresenting them. The rub seems to be, "the system is what it is because that is how it is defined," and then we go from there in talking about the properties the systems have in virtue of their rules.

This isn't the only type of austere definition. There is also "logic as the study of logical truths," that is the identification of the most general truths that must be true under all conditions. This seems even more tautological, but you can make it at least more descriptive by saying it's about the truths that follow from an empty set of premises.

I’m not persuaded by the deflationary theories of truth so I can’t share your assumption.

Me either. I'm just trying to explain the bucket of answers to "what is logic," that I was trying to group together with point 1.

So “abstract systems“ refers to the possibile result of such cognitive task. I guess that’s the understanding suggested by your claim, right?

Yeah, in general. Again, I was just trying to explain what seems to be a popular collection of definitions of logic, so it's hard to generalize. In general, from my limited poking around, this does seem to be the type of "abstract" that people have in mind. That said, I have come across the argument that the "landscape of mathematical systems," are the real Platonic objects that mathematicians study, and so I imagine someone has probably made the same argument about logical systems at some point.

Indeed, I’m not even sure that such views would even justify anybody saying “a system can produce descriptions”, since the notion of “description” to me conceptually implies the idea that representations of states of affairs are distinct from the states of affairs in the world as the former refers to the latter (not the other way around), and the idea that the former can correctly or incorrectly apply to the latter (hence the distinction between “true” and “false”).

Good point.

If you mean that this thread is specifically about naturalist views of logic, then I didn’t get it but I will take it into account from now on.

No, by no means. Your replies have been interesting. I just find it interesting that naturalism is so dominant in culturally and in philosophy writ large, but that the subfield of logic seems fairly well insulated from this.

Concerning the "Scandal of Deduction", even though I do not share your naturalist assumptions, my way out is somehow similar to yours. We do not have the full list of valid representations of the world in our mind simultanously. We process them progressively according to some logic/semantic rules. And we may also fail in doing it.

Gotcha. But then why do we only progress through these rules so quickly and why are some people much faster than others at doing so? Or why are digital computers so much quicker than any person? I'm curious how that can be answered without reference to the physical differences between people or people and machines.

Sure we may be unable to describe many of our experiences to any arbitrary degree of detail. For example there are many varieties of “red” and yet we can refer to all of them simply as “red”. That’s not the point, the point is that in order to talk meaningfully about experiences we can’t put into words, we still need to apply correctly a sufficiently rich set of notions and make inferences accordingly: e.g. that the varieties of red are not varieties of grey, they are colors and not sounds, that they are phenomenal experiences and not subatomic particles, that one normally needs functioning eyes and not functioning ears to experience them, etc.

That makes sense to me. I thought you were drawing some distinction between "the world as it actually is, which might lack anything corresponding to the order we see in phenomena" and our view of things. I think I may have misread that.

The term “influence” may express an ontological notion of causality, but I find this notion problematic for certain reasons. On the other side, if we talk in terms of nomological regularities, surely I do believe that certain external facts (e.g. the light reaching our retina) correlate with visual experiences which then we have learned to classify in certain ways. That would be enough for me to talk about “influence” but at the place of ontological causal links, there are just nomological correlations plus a rule-based cognitive performance.

Yeah, I think that works for what I'm thinking of. I don't really like eliminative views on causation, e.g. Russell's "a complete description of the solar system includes no room for cause," but even accepting his view it seems like there are still relations of a sort between the world and beliefs. But this to me suggests that our perceived order corresponds to an order that exists outside of our perceiving it.

But is it logic by which physical states seem to orderly evolve into only other certain configurations of future physical states? I feel like a different word should be used because "logic" is more associated with definitions 1 and 2 I laid out. It is certainly very common in the natural sciences to read phrases like "because of the logic of thermodynamics...." etc., but it's obviously not a reference to thought in those cases.

Since they are mostly primitive concepts they can not be questioned or explained away without ending up into some nonsense or implicitly reintroducing them.

I'm reading Terrance Deacon's "Incomplete Nature," right now and it makes the same sort of argument. I'm really enjoying it, and I think he has a point here.

But Deacon is also coming from a naturalist frame, so he has different ideas about where to go from there. He has what I thought at first glance was a good argument against nominalism and the idea that all our categories are products of mind "in here," as opposed to reflections "out there." Perhaps not directly relevant to what we're talking about, since he is focused on how universals can have causal efficacy, but somewhat related:

Even if we grant that general tendencies of mind must already exist in order to posit the existence of general tendencies outside the mind, we still haven’t made any progress toward escaping this conceptual cul-de-sac. This is because comparison and abstraction are not physical processes. To make physical sense of ententional phenomena, we must shift our focus from what is similar or regularly present to focus on those attributes that are not expressed and those states that are not realized. This may at first seem both unnecessary and a mere semantic trick. In fact, despite the considerable clumsiness of this way of thinking about dynamical organization, it will turn out to allow us to dispense with the problem of comparison and similarity, and will help us articulate a physical analogue to the concept of mental abstraction.

The general logic is as follows: If not all possible states are realized, variety in the ways things can differ is reduced. Difference is the opposite of similarity. So, for a finite constellation of events or objects, any reduction of difference is an increase in similarity. Similarity understood in this negative sense—as simply fewer total differences—can be defined irrespective of any form or model and without even specifying which differences are reduced . A comparison of specifically delineated differences is not necessary, only the fact of some reduction. It is in this respect merely a quantitative rather than a qualitative determination of similarity, and consequently it lacks the formal and aesthetic aspects of our everyday conception of similarity.

To illustrate, consider this list of negative attributes of two distinct objects: neither fits through the hole in a doughnut; neither floats on water; neither dissolves in water; neither moves itself spontaneously; neither lets light pass through it; neither melts ice when placed in contact with it; neither can be penetrated by a toothpick; and neither makes an impression when placed on a wet clay surface. Now, ask yourself, could a child throw both? Most likely. They don’t have to exhibit these causal incapacities for the same reasons, but because of what they don’t do, there are also things that both can likely do or can have done to them.

Does assessing each of these differences involve observation? Are these just ways of assessing similarity? In the trivial example above, notice that each negative attribute could be the result of a distinct individual physical interaction. Each consequence would thus be something that fails to occur in that physical interaction. This means that a machine could be devised in which each of these causal interactions was applied to randomly selected objects. The objects that fail all tests could then get sorted into a container. The highly probable result is that any of these objects could be thrown by a child. No observer is necessary to create this collection of objects of “throwable” type. And having the general property of throwability would only be one of an innumerable number of properties these objects would share in common. All would be determined by what didn’t happen in this selection process.
As this example demonstrates, being of a similar general type need not be a property imposed by extrinsic observation, description, or comparison to some ideal model or exemplar. It can simply be the result of what doesn’t result from individual physical interactions. And yet what doesn’t occur can be highly predictive of what can occur. An observational abstraction isn’t necessary to discern that all these objects possess this same property of throwability, because this commonality does not require that these objects have been assessed by any positive attributes. Only what didn’t occur. The collection of throwable objects is just everything that is left over. They need have nothing else in common than that they were not eliminated. Their physical differences didn’t make a difference in these interactions.

I'm just trying to explain the bucket of answers to "what is logic," that I was trying to group together with point 1. — Count Timothy von Icarus

All right, I think I got it now. In my own words, your summary amounts to pointing at 3 ways of approaching the question “what is logic?”:
1. The formalist, which understands logic as a system of rules independently from any reference to mental processes or the world.
2. The psychologist (comprising behaviourist, cognitivist, neurologist views), which understands logic as an empirical description of “laws of thought”.
3. The realist, which understands logic as metaphysical description of meta-empirical principles.

Concerning the "Scandal of Deduction", even though I do not share your naturalist assumptions, my way out is somehow similar to yours. We do not have the full list of valid representations of the world in our mind simultanously. We process them progressively according to some logic/semantic rules. And we may also fail in doing it.


Gotcha. But then why do we only progress through these rules so quickly and why are some people much faster than others at doing so? Or why are digital computers so much quicker than any person? I'm curious how that can be answered without reference to the physical differences between people or people and machines. — Count Timothy von Icarus

Your questions about cognitive performance in processing logic inferences are empirical questions not conceptual ones. So they deserve an empirical answer as offered e.g. by cognitive sciences.
What is crucial to me here is the distinction between empirical and conceptual questions. Naturalist views tend to conflate them. The co-existence between two distinct domains (the empirical and the conceptual) is undigestible for naturalists. Naturalists are mostly reductionists or eliminativists (there are also the mysterianists though) about the mental.

The term “influence” may express an ontological notion of causality, but I find this notion problematic for certain reasons. On the other side, if we talk in terms of nomological regularities, surely I do believe that certain external facts (e.g. the light reaching our retina) correlate with visual experiences which then we have learned to classify in certain ways. That would be enough for me to talk about “influence” but at the place of ontological causal links, there are just nomological correlations plus a rule-based cognitive performance.


Yeah, I think that works for what I'm thinking of. I don't really like eliminative views on causation, e.g. Russell's "a complete description of the solar system includes no room for cause," but even accepting his view it seems like there are still relations of a sort between the world and beliefs. But this to me suggests that our perceived order corresponds to an order that exists outside of our perceiving it.

But is it logic by which physical states seem to orderly evolve into only other certain configurations of future physical states? I feel like a different word should be used because "logic" is more associated with definitions 1 and 2 I laid out. It is certainly very common in the natural sciences to read phrases like "because of the logic of thermodynamics...." etc., but it's obviously not a reference to thought in those cases. — Count Timothy von Icarus

The empirical method obliges scientists to check their theories against the facts, therefore the confidence one can scientifically grant to scientific theories remains conditional for any empirical theory no matter how successfully it looks in competition to other theories.
Anyways I too find the expression “because of the logic of thermodynamics” a bit confusing (e.g. “logic of thermodynamics” is not yet another a logic system distinct from “propositional logic”), however I find it harmless if it simply equates to claiming: “Given the premises of the theory we call ‘thermodynamics’, we can logically infer this and that”.

Since they are mostly primitive concepts they can not be questioned or explained away without ending up into some nonsense or implicitly reintroducing them.


I'm reading Terrance Deacon's "Incomplete Nature," right now and it makes the same sort of argument. I'm really enjoying it, and I think he has a point here.

But Deacon is also coming from a naturalist frame, so he has different ideas about where to go from there. He has what I thought at first glance was a good argument against nominalism and the idea that all our categories are products of mind "in here," as opposed to reflections "out there." Perhaps not directly relevant to what we're talking about, since he is focused on how universals can have causal efficacy, but somewhat related. — Count Timothy von Icarus

Unfortunately I didn’t read "Incomplete Nature". And I find that passage rather obscure, even in relation to what I said. From what I gathered around he seems to support a peculiar notion of causality that would allow to bridge the gap between mental phenomena and physical explanation, so I guess it might be an interesting reading.

I have my own ideas but I figured I'd open with the simple question: what is logic? (there is more on this than "what is computation," but a lot of it does not seem to address the big questions) — Count Timothy von Icarus

Logic seems best defined as a set of rules forming the axiomatic basis of correct reasoning.
Tarski Undefinability, Gödel Incompleteness and the Principle of Explosion seem to indicate
issues with current systems of logic.

My unique contribution to this is that the above issues can be easily abolished by simply
requiring all conclusions to be a semantically necessary consequence of all of their premises.
Copyright 2023 PL Olcott

The key change that this requires is to fully integrate model theory into the notion of formal systems.

In computer programming, the word "logic" is a reference to the,

...set of rules, algorithms, and conditions that determine the behavior of a program. It's the part of the code that makes decisions, performs calculations, and controls the flow of data.

While there are industry-wide standards for how programs (and any related logic) should be structured, Developers are able to build anything they want, anything they can imagine. And as long as their work meets requirements, such a thing/process is an example of software.

Based on these observations and similar experiences, I have come to conclude that "logic" is primarily "applied values".

...which has me wondering what an unapplied value might be.

Logic, i.e., propositional logic is about correct reasoning. It's about the process of collecting reasons (i.e., propositions) and drawing conclusions based on those reasons/evidence. Logic sets out the rules for doing just this. So logic is concerned with the justifications used to support conclusions. It's not about laws of thought or thinking processes, that's a matter for psychology.

That's an interesting question. In programming an unapplied value is generally considered wasteful and ultimately ignored.

But your statement “Logic is a set of formal systems; it is defined by the formalism” (which is neither a logic formula nor a logic tautology) seemed to offer a definition for “Logic”. And valid definitions should not be tautological in the sense that what is to be defined should not occur in what is defining. Yet your other claims made your definition of “logic” look tautological (even claiming “Logic is all about tautologies” would sound tautological if it equates to “Logic is all about logic”). — neomac

I think this is exactly right. "Logic is a set of formal systems," does not approach a coherent definition of logic. The question that immediately comes to mind is, "Which set of formal systems?" It's much like saying, "Hyenas are a set of animals." It gives the genus without a specific difference. The specific difference of logic is related to (2), namely that logic aims to provide us with a means of reasoning well and arriving at previously unknown truths.

Those who study formal systems as some sort of end in themselves are doing meta-logic, not logic. It would be like if a traffic engineer became so interested in traffic lights that he comes to focus on the lights themselves, independently of traffic. At that point he is no longer a traffic engineer—he is just a guy who studies a specific sort of light. I think this sort of detachment from reality is a big problem in contemporary philosophy.

If the thread is about cataloguing the different ways that the word 'logic' is used, then (1) has a place. If it is about logic, then I think it doesn't.

But there is no way for me to make sense of “true” as applied to “logic” since the notion of “truth” is built in the “logic” rules themselves, in other words the meaning of “truth” is determined by “logic rules” too. — neomac

On the other hand, I don't agree with this. Logic can be said to be true insofar as it does what it is supposed to do: aid us in reasoning well. Currently our central criterion is validity, where the truth of the premises ensures the truth of the conclusions. So if I take a logical system and I scrupulously follow the rules, beginning with true premises, but then arrive at false conclusions, the logical system is bad or false. It is false in the sense that it is not doing what it was meant to do (i.e. preserve truth). Truth is not built in logic; it transcends it.

But there is no way for me to make sense of “true” as applied to “logic” since the notion of “truth” is built in the “logic” rules themselves, in other words the meaning of “truth” is determined by “logic rules” too. — neomac


On the other hand, I don't agree with this. Logic can be said to be true insofar as it does what it is supposed to do: aid us in reasoning well. Currently our central criterion is validity, where the truth of the premises ensures the truth of the conclusions. So if I take a logical system and I scrupulously follow the rules, beginning with true premises, but then arrive at false conclusions, the logical system is bad or false. It is false in the sense that it is not doing what it was meant to do (i.e. preserve truth). Truth is not built in logic; it transcends it. — Leontiskos

Notice that quote of mine was questioning the notion of “true logic” if applied to different logic systems or different sets of logic rules which are all supposed to “preserve truth“. On the other side if your claim is supposed to question my claim that “the notion of ‘truth’ is built in the ‘logic’ rules themselves”, then you are failing since your own notion of logical system as a set of truth preserving rules is also grounded on the notion of “truth”. That doesn’t compromise the distinction between valid and sound deduction, by any means.

On the other side if your claim is supposed to question my claim that “the notion of ‘truth’ is built in the ‘logic’ rules themselves”, then you are failing since your own notion of logical system as a set of truth preserving rules is also grounded on the notion of “truth”. — neomac

If something is meant to preserve another thing, then it is not building or creating that thing.

Trouble is, truth does not enter into formal systems until they are given an interpretation.

That is, there are logical systems that do not involve truth.

It follows that logic cannot be defined only in terms of preserving truth.

Well, I never said that logic can only be defined in terms of preserving truth. But that someone makes up a formal system that has nothing to do with truth and calls it 'logic' is not much of a counterargument. Logicians can temporarily and usefully prescind from truth, but entire detachment is something different.

Best answer might be that it is rules of grammar; rules for stringing symbols together. — Banno

But logic is not merely rules for stringing symbols together. If I make rules for stringing symbols together I have not necessarily done anything related to logic.

Formalists need to take a step back and consider why the formal systems were constructed in the first place.

But that someone makes up a formal system that has nothing to do with truth and calls it 'logic' is not much of a counterargument. — Leontiskos

Well, that would mean that, say, an uninterpreted explication of propositional calculus does not count as part of logic.

The point here is just that logic is bigger than the preservation of truth in an argument.

But logic is not merely rules for stringing symbols together. If I make rules for stringing symbols together I have not necessarily done anything related to logic. — Leontiskos

I wouldn't be so quick to draw that conclusion. We do say strings such as:

☐☐◇☐☐◇◇☐☐◇◇◇

"have a certain logic to them...".

Logic has advanced somewhat since the middle ages.

Well, that would mean that, say, an uninterpreted explication of propositional calculus does not count as part of logic. — Banno

I added to my last post, "Logicians can temporarily and usefully prescind from truth, but entire detachment is something different." There are more proximate and more remote relations of logic to truth, but something with a perfect non-relation to truth is not logic.

The point here is just that logic is bigger than the preservation of truth in an argument. — Banno

This is an ignoratio elenchus, as I already noted.

"have a certain logic to them..." — Banno

This is a metaphorical use of the term, similar to what I pointed out <here>. Logic depends on order, and thus ordered things are sometimes called "logical." But logic is more properly an art of ordering, not mere order. You are appealing to usage, but the etymology and the historical usage point very clearly to logic as an art of reasoning.

They say that one of the best ways to learn something is to teach it. A few weeks ago I looked at your thread which is intended to teach propositional calculus (link). It's no coincidence that in your third substantial post you were already into truth tables. But even in your first substantial post you said, "What we want to do is to examine the relations between these propositions, rather than their contents." It seems to me that it would have been more apt to say that we want to examine the relations that obtain between these propositions based on their content. Relations hold or fail to hold in light of the content of the relata, and this has everything to do with truth.

Now a pedagogue might choose to introduce the rules of logic before introducing the purpose of logic, much like you could teach a child to kick a ball before introducing them to the game of soccer. Of course I am not convinced that this is sound pedagogy.

Logic has advanced somewhat since the middle ages. — Banno

Do you have any actual acquaintance with the logic of the middle ages?

This has degenerated into rhetoric rather than anything interesting.

Take a look at Gillian Russell's work. Let me know what you think.

If logic is "rules for stringing symbols together," then these rules can either be arbitrary or non-arbitrary. If they are non-arbitrary, then logic must itself be connected to the non-arbitrary determination of these rules.

I see that Russell defines logic in terms of the preservation of truth, so that's an interesting start. "Logics are theories of validity: they tell us, for different arguments, whether or not that argument is of a valid form" (SEP). (She appeals to the Generalised Tarski Thesis to define validity.)

I'm guessing I might agree with much of what she thinks. But 'logical pluralism' feels a bit like 'situation ethics', in that it gets at something true but mixes up epistemological and metaphysical spheres. I clearly think formalized systems have significant limitations, so if "logical monism" is the view that there is some formalized system without limitations then I am not a logical monist. It's not hard to think that two different 'logics' "can be getting things right."

"Logics are theories of validity: they tell us, for different arguments, whether or not that argument is of a valid form" — Leontiskos

The next sentence is "Different logics disagree about which argument forms are valid". There is some considerable subtlety here.

Russell is playing with Logical Nihilism, rather than pluralism. https://gilliankrussell.files.wordpress.com/2018/05/logicalnihilism-philissues-v3.pdf
The picture is of an organic logic, which grows by lemma incorporation.

If something is meant to preserve another thing, then it is not building or creating that thing. — Leontiskos

"Built-in" is a figure of speech, we are talking semantics. So the point is that the notion of truth is semantically built in the idea of correct inference. This holds even if we occasionally fail to process the inference or if the inference is simply valid but not sound.

Trouble is, truth does not enter into formal systems until they are given an interpretation. — Banno

Notice that the opening post takes "formalisation" to be but one approach to answer the question of "what is logic?" so we are not just talking about logic in formal systems or just formal systems.
I can get that "formal systems" do not all make explicit use of the notion of truth and false (e.g. algebra). But my claim is more radical than it appears. Indeed, I take the notion of "truth" to be so primitive and pervasive along with the notion of "logic" that I take the concept of "truth" to be built-in that of "logic" ALSO independently from ANY interpretation. Indeed, any rule-based manipulation of symbols would still have a correct or incorrect application and this necessarily equates (even if it may not be identical) to answering the question: "This application conforms to the rules, true or false?". Besides if the meaning of "logic" (classic and non-classic) is not stretched to the point of not being about propositions/sentences (in other words representations), then it is still linked to possible interpretations.

The social role of logic does bring up an interesting issue re the concept of group minds. If we take as a given that organizations can exhibit their own emergent form of intelligence, problem solving techniques, and goal directed behavior, such that organizations' goals are not merely the sum of the goals of their individual members' goals (and even cut against the goals of the individuals who compose the organizations), then doesn't the social rules of one level of organization become the "rules of thought," for the higher level entity?

No doubt many will find the idea of organizations behaving like group minds to be metaphysicaly dubious. We would need a whole thread to get into that issue in particular. I will just note that it is an idea with significant support in the realm of theories of embodied cognition and some areas of the life sciences. Ant and bee "hive minds" would be a potent example, and there is decent evidence to support the contention that the human mind itself is emergent from a number of surprisingly distinct systems. There also doesn't appear to be clear cut "levels" to group mind organization, so this would be more a sort of fractal process through which different levels of community give rise to different levels of mind.

Yes, this is the view I was getting at with approach #1, which is the most common in the study of logic itself. But I think there are obvious isomorphisms between all three definitions that are worth exploring. More on this later when I have a bit more time!

"Built-in" is a figure of speech, we are talking semantics. So the point is that the notion of truth is semantically built in the idea of correct inference. This holds even if we occasionally fail to process the inference or if the inference is simply valid but not sound. — neomac

This just isn't right. It is not true that, "[T]he notion of 'truth' is built in the 'logic' rules themselves, in other words the meaning of 'truth' is determined by 'logic rules' too" ().

The notion of truth is not semantically built in the idea of correct inference. Truth is something beyond inference and beyond validity. Validity can be formally defined, but truth cannot be formally defined. Of course we can talk about "truth" qua some logical system, but this is technically an equivocation. This sort of "truth" is different from actual truth, and we do not hesitate to call it false in certain instances.

---

The next sentence is "Different logics disagree about which argument forms are valid". There is some considerable subtlety here. — Banno

But they do not disagree that logic is about validity, and that validity is about the preservation of truth. So what you say here is not to the point.

This just isn't right. It is not true that, "[T]he notion of 'truth' is built in the 'logic' rules themselves, in other words the meaning of 'truth' is determined by 'logic rules' too" (↪neomac
).

The notion of truth is not semantically built in the idea of correct inference. Truth is something beyond inference and beyond validity. Validity can be formally defined, but truth cannot be formally defined. Of course we can talk about "truth" qua some logical system, but this is technically an equivocation. This sort of "truth" is different from actual truth, and we do not hesitate to call it false in certain instances. — Leontiskos

Apparently you disagree with yourself. Indeed you yourself wrote “Currently our central criterion is validity, where the truth of the premises ensures the truth of the conclusions” so you determined the meaning of “valid inference” by explicitly referring to the notion of truth. If a valid inference must be truth-preserving then the notion of truth is built in that of valid inference. Q.E.D.

If a valid inference must be truth-preserving then the notion of truth is built in that of valid inference. Q.E.D. — neomac

Again, "If something is meant to preserve another thing, then it is not building or creating that thing" ().

Let's apply your reasoning to mortuary. "A mortician is concerned with preserving bodies. Therefore a mortician builds/creates bodies. Q.E.D."

Let's apply your reasoning to mortuary. "A mortician is concerned with preserving bodies. Therefore a mortician builds/creates bodies. Q.E.D." — Leontiskos

"Built-in" is a figure of speech. We are talking semantics. Let's apply MY reasoning to mortuary "A mortician is concerned with preserving bodies so the notion of 'body' is semantically built in the notion of 'mortician'".

- That's enough for me. Take care.

But they do not disagree that logic is about validity, and that validity is about the preservation of truth. So what you say here is not to the point. — Leontiskos

The contention I criticises was that logic consists in the preservation of truth.

I pointed out that parts of logic do not involve truth. For example the sequent calculus consists in a bunch of rules setting out what you can write down next - or previously. Truth doesn't enter until the tack, and even then it's the false that is introduced...

A valid argument is one that follows the rules. Yes, that usually also means that if the argument is given an interpretation, truth will be preserved, but that is incidental.

I am not claiming that preservation of truth does not enter in to logic.

I'm saying that there is a difference between a valid argument and a sound argument.

The contention I criticises was that logic consists in the preservation of truth. — Banno

For a third time now, that "contention" is a figment of your imagination. Do you think that when I spoke about the "central criterion" as validity in our current day, I was saying that logic "consists" in validity? Or that logic is "defined only in terms of preserving truth"?

Russell, on the other hand, asserts that "Logics are theories of validity..." (my emphasis). If there is anyone who thinks logic consists in validity, it is Russell, at least if we can take this general statement from her SEP article to reflect her views.

I pointed out that parts of logic do not involve truth. For example the sequent calculus consists in a bunch of rules setting out what you can write down next - or previously. Truth doesn't enter until the tack, and even then it's the false that is introduced... — Banno

But your argument here is no good. There are rules in logic which must be attended to, but from this it does not follow that this part of logic is unrelated to truth or validity (I happen to think that logic is more consistently related to truth than validity, but your argument fails on both scores). The rules are themselves related to truth and validity.

To take an analogy, language is about meaning. Someone might say, "Ah! But when we utilize rote memorization to teach children to spell words we are not teaching them about meaning." True enough, but the whole reason we teach children to spell words is so that they can use the words in sentences and paragraphs to convey meaning. The spelling of a word is not unrelated to meaning, and the rules of a formal system are not unrelated to validity. To think otherwise would be to fundamentally misunderstand language and logic.

A valid argument is one that follows the rules. — Banno

According to what definition of validity? Russell prefers the Generalized Tarski Thesis to define validity, and this is altogether at odds with the definition you now offer.

I'm saying that there is a difference between a valid argument and a sound argument. — Banno

I think most anyone would agree with such an innocuous claim. Yet according to Russell logic is about validity, not soundness. Such is the received view, and I have not challenged it here.

For a third time now, that "contention" is a figment of your imagination. — Leontiskos

Well...

There is also "logic as the study of logical truths,"... — Count Timothy von Icarus

2(a). Logic is a description of the ways we make good inferences and determine truth, or at least approximate truth pragmatically. — Count Timothy von Icarus

The purpose of logic is to provide an analytic guide to the discovery of demonstrated truth — James A. Weiseipl, Preface

the truth-preservation that is validity — Leontiskos

The post at https://thephilosophyforum.com/discussion/comment/834084 wasn't directed specifically at you. I was simply making a general observation; seems it hit a nerve.

...but from this it does not follow that logic is unrelated to truth or validity — Leontiskos

And again, (third time?) yes, I agree. There are bits of logic that involve truth, and bits that don't. Truth alone will not suffice to define logic.

The post at https://thephilosophyforum.com/discussion/comment/834084 wasn't directed specifically at you. I was simply making a general observation; seems it hit a nerve. — Banno

You were making a general observation? About truth-preservation? When I was the only one who had brought up or defended the idea of truth-preservation in the entire thread? :brow:

And again, (third time?) yes, I agree. — Banno

Realizing that the analogy might not suffice, I amended that sentence to make the idea clearer, but I think we are agreed that we should be done in this thread, no? We're not going anywhere.