Boring answer but I think the possibility you alluded to is correct, the word has separate definitions and the meaning depends on the context.

A consistent definition that works within all the different contexts will poorly represent what the word means in each of those different contexts.

But here is the big question: do we think that these are all different things? That we use the same word out of a sort of confusion? Or is there actually a similarity between these types of "logic?" — Count Timothy von Icarus

I posted a thread on stackexchange about the relationship of logic and causation. It turns out they’re different topics. Logic is the relationship between propositions whereas physical causation involves many factors. You can find the discussion here. The very first response notes that the ‘because’ of logical necessity is not the same as the ‘because’ of causation. And a lot hangs on this distinction, it turns out.

Another point is, apropos of the other thread on Schopenhauer - his ‘fourfold root of sufficient reason’ also differentiates between the logic of being knowing (which approximates to what we are calling logic) and the logic of becoming (which approximates to physical causation.)

I personally am very drawn to your (3) - that there is a logic in order of things, as the Greek intuition has it. I think the issue with that is that it seems to contravene the naturalist assumption of there being no telos. But also notice that related to this concern, the whole concept of ‘natural law’ is nowadays called into question. See for example There are no laws of Physics. I *think* this mirrors a confusion, but I’ll leave it there for now.

But this brings up the question, "does the absence of a 'one true logic' necessitate deflating logic into formalism? — Count Timothy von Icarus

I think you didn't clarify much what you mean by "formalism". As a starter, I take "formalism" to be broadly speaking the symbolic codification of a set of logic rules. If there are one or many sets of logic rules, this is a distinct issue.
"Formalism" to me is required to standardize a given set of rules and remove ambiguities of ordinary language for certain syntactic terms (e.g. we can attributing different meanings to “to be“, “if…,then…”, “not”, “or” or “all” in logic).
Said that, I find the expression "one true logic" nonsensical. One may be willing to count "logic" by counting the number of "set of ‘logic’ rules" we want to distinguish (for example in geometry different set of postulates can different geometries the same can go for logic see e.g. non-classical logic). 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. One might be tempted to see “logic rules” as a description of how things are, but that’s a categoric confusion to me: “logic rules“ are rules, not description of facts. To me.

Or can we meaningfully speak of things like the logic of cause? — Count Timothy von Icarus

Broadly speaking yes, if you mean by "logic of cause" the set of semantic rules that govern the notion of “cause”. However, more strictly speaking, "logic" refers to rules governing synthatic terms (like propositional operators, quantifiers, modal operators, etc.)

And if we can meaningfully speak of things, what is the relationship between the formalism and the referents? — Count Timothy von Icarus

Formalism helps us discriminate better different ways allowing us to meaningfully speak of things according to various sets of “logic” rules.

When we say: "you're acting illogically? "or "that doesn't follow logically," we often mean something different from: "you are not acting according to a formal system," or "I am not aware of any formal system where the inference you are making works." Rather, we tend to be criticizing someone for failing to think in a way that is sufficiently rational.. — Count Timothy von Icarus

What does one mean by “being sufficiently rational”? To me, appeal to “rationality” is nothing other than an appeal to the set of rules that must be satisfied in order to make things intelligible to somebody. And this may certainly include logic rules, too.

1. Logic is a set of formal systems; it is defined by the formalism.
2(a). Logic is a description of the ways we make good inferences and determine truth, or at least approximate truth pragmatically.
2.(b). Logic is a general description of the features or laws of thought. (This is more general than 2(a).
3. Logic is a principle at work in the world, its overall order. Stoic Logos, although perhaps disenchanted. — Count Timothy von Icarus

Following what I wrote, I disagree with all 3 responses to "what is logic?" partially or totally:
1. Logic is not defined by formalism. Formalism is a way to express a set of logic rules.
2. Logic is not a description of the ways we make good inference or laws of thought, if this is taken to be an empirical enterprise like a scientific theory.
3. Logic refers to rules that make the world intelligible to us.

That's probably fair. But it seems like there is a sort of general principle, perhaps one of necessity or one of "sufficient reason," that undergirds the other. I'd say "Logos" would be a good term, but it has mystical connotations too.

It seems to me like this question often produces three types of responses:
1. Logic is a set of formal systems; it is defined by the formalism.
2(a). Logic is a description of the ways we make good inferences and determine truth, or at least approximate truth pragmatically.
2.(b). Logic is a general description of the features or laws of thought. (This is more general than 2(a).
3. Logic is a principle at work in the world, its overall order. Stoic Logos, although perhaps disenchanted. — Count Timothy von Icarus

My abbreviated answer to "what is Logic" might be : Mathematics with Words. Note the connection of Greek Logos with the notion of Words as encapsulated ideas about the world and how it works. The values of Math are expressed in abstract numbers (quantity), while the values of Logic are expressed in terms of statistical probabilities (oughts).

Mathematics is the formalism of the physical structure (interconnections) and natural laws (relationships) of the material world. Just as mathematical Physics allows humans to predict the outcome of physical processes, mental Logic allows us to infer (educated guess) a future state of human metaphysical processes, such as Politics. Unfortunately, as with the order-within-chaos of weather patterns, human freewill makes even logical forecasts (e.g. inferences by think tanks) of political outcomes dicey. :smile:

I posted a thread on stackexchange about the relationship of logic and causation. It turns out they’re different topics. Logic is the relationship between propositions whereas physical causation involves many factors. You can find the discussion here. The very first response notes that the ‘because’ of logical necessity is not the same as the ‘because’ of causation. And a lot hangs on this distinction, it turns out.

Excellent point. Causation and logic are different areas of philosophy, for sure. That logic and causation are completely different things I think is open to question.

Where do most people turn for their best, most fundamental theories on physical causation? (And does it even make sense to talk of non-physical causation?) They go to physics. And in modern physics, the idea that the universe is computable, and behaves like a computer is extremely popular (Landauer, Lloyd, Deutsch, Davies, Tegmark, etc.).

But then what is computation, how is it defined? Partly in terms of logical operators, stepwise symbolic manipulations that occur according to rules such that prior states of some system entail the system's future states (or entail either a range of states in quantum indeterminacy or, in a multiverse, many existing states). This is how Leibnitz saw computation in his pronouncement that one day all disagreements could be settled through such symbolic manipulations-- "let us calculate!"

You can't separate the definitions of computable functions and computation from logic, and it increasingly seems hard to separate computation, or a process that is computation-like (perhaps involving real numbers?) from physics. But then this makes logic deeply intertwined in how we understand cause, and moreover, what we think cause actually is, sans our experience of it.

We see cause coming together with logic from another angle with categorical quantum mechanics and quantum logic as well.

So, IMO, the separation of the philosophy of causation and logic has more to do with the history of philosophy than the two being fully unrelated concepts. But this is exactly what frustrates me in the literature. There is a move to treat logic as divorced from reality to make it manageable, but then logic is used by other disciplines to justify statements about reality.

Well, at some point you have to make the connection in the other direction. As natural creatures, the products of natural selection, there should be some explanation of where our sense of logic comes from and why we can use it to describe causality so well, and why we can use it to create science and technology. Why does the use of logic and computation allow us to manipulate reality so well if logic is just disembodied systems without relevance to the world? Why would we, and other animals, show evidence of having a "logic sense?" If the connection between logic and cause is merely our construction, there should still be an explanation as to why we construct things in such a way.

Another point is, apropos of the other thread on Schopenhauer - his ‘fourfold root of sufficient reason’ also differentiates between the logic of being knowing (which approximates to what we are calling logic) and the logic of becoming (which approximates to physical causation.)

There is a similar move in Hegel's Greater Logic with the objective logic, although it's not clear that the logic of being is contained to just the objective logic. The problem with Hegel's insights is that they are hard to formalize and are grounded in speculation, observing bare thought without presupposition (at least as best he could). In this sense, it's not backed up by the type of evidential support or argument that modern philosophy is particularly comfortable with, at least not analytical philosophy.

I personally am very drawn to your (3) - that there is a logic in order of things, as the Greek intuition has it. I think the issue with that is that it seems to contravene the naturalist assumption of there being no telos. But also notice that related to this concern, the whole concept of ‘natural law’ is nowadays called into question. See for example There are no laws of Physics. I *think* this mirrors a confusion, but I’ll leave it there for now.

Great point! But do we need a mind for telos? This is a huge problem in the sciences. Terrance Deacon's Incomplete Nature (which I'm still in) looks at just this issue and the diagnostic section of the book, which looks at the ways in which homunculi crawl their way into even eliminitivist theories is pretty spot on.

Obviously, there is something like a "logic" to the way our world progresses because we believe that past states dictate future states. We don't think the universe just popped into existence 10 seconds ago. We don't hop off our beds in the morning and fear we will fall through the floor; there are seeming entailments between before and after. There is not randomness, there is order. All of science relies on this fact. If experimental results gave us no reason to suppose we have learned something about how the world would act in the future than the entire argument against telos from scientific findings crumbles along with the rest of the scientific edifice.

The move against "laws of nature" always seemed more to me about thinking that regularities in the way the world works in due to an intrinsic set of properties (i.e., Kirpke's response to Hume re induction) That is, things do what they do, or the world progresses like it does, because of its traits, not because of any external Platonic laws that guide interactions. That makes perfect sense to me, but the move to intrinsic properties doesn't fix the problem of why the properties are such that they are intelligible and state progression is orderly and can be described with computable laws so well.

I think you didn't clarify much what you mean by "formalism". As a starter, I take "formalism" to be broadly speaking the symbolic codification of a set of logic rules. If there are one or many sets of logic rules, this is a distinct issue.

"Formalism" to me is required to standardize a given set of rules and remove ambiguities of ordinary language for certain syntactic terms (e.g. we can attributing different meanings to “to be“, “if…,then…”, “not”, “or” or “all” in logic).

Fair point; I worry about making my OPs too long and sometimes gloss over some areas. I agree with your definition. By formalism I mean "the rules" not merely their particular expression, or to borrow a term from information theory, the "encoding." There can be many formalisms that map on to the same rules.

Said that, I find the expression "one true logic" nonsensical. One may be willing to count "logic" by counting the number of "set of ‘logic’ rules" we want to distinguish (for example in geometry different set of postulates can different geometries the same can go for logic see e.g. non-classical logic). 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. One might be tempted to see “logic rules” as a description of how things are, but that’s a categoric confusion to me: “logic rules“ are rules, not description of facts. To me.

Good points, and we have the problem, per Tarski, of being able to define truth from within a system. But my understanding of the search for the "one true logic" was that the pioneers of post-Aristotelian logic were looking for something that would be both a rigorous system and which would reflect facts perfectly. From the 19th century view, where it looked like all the world would soon be explainable in a rigorous way, this makes sense. They hadn't run into undecidability, the entscheidungsproblem, incompleteness, undefinability, etc. yet.

However, I feel like the response to the aforementioned list might have been to throw the baby out with the bath water, since we've now disembodied logic in a sort of neo-Platonism. This is my problem with "game" theories of language as well. Maybe I'm just too much of a close-minded naturalist, but I tend to think that rules exist out in the world, in minds that are natural themselves, and that the rules must thus have natural causes.

In any event, I've seen more recent appeals to a "logic of being" that work off the idea of systems whose rules change over time, evolving based on meta-principles, essentially being paraconsistent and allowing for dialetheism. The details went over my head though.

Broadly speaking yes, if you mean by "logic of cause" the set of semantic rules that govern the notion of “cause”. However, more strictly speaking, "logic" refers to rules governing synthatic terms (like propositional operators, quantifiers, modal operators, etc.)

Right, but generally in the sciences we think that if a formal system very closely (or ideally, perfectly) describes something in the world, and if it allows us to make good (or ideally, perfect) predictions, this is because the formalism corresponds to something in the world. We don't think our language is magic, that it is sorcery that causes the world to correspond to it (else why all the failed formalisms, right?). But we also don't think our systems can have no connection to the world, because then science isn't about the world at all, its about language and formalisms. Except it also seems to tie to our experiences and have huge pragmatic value, so that doesn't seem right.

Of course, we can justify the sciences on pragmatic grounds, but it feels worthwhile to ask "why is it pragmatically valuable?" Presumably, because our formalisms, e.g. Newton's laws, the Schrodinger equation, etc. correspond to external reality in some way. But then if logical rules correspond to reality, it seems reality has some rules.

Formalism helps us discriminate better different ways allowing us to meaningfully speak of things according to various sets of “logic” rules.

Right, but then the question is: why do some formalisms work for meaningfully speaking of things better than others? And why is it that breaking our inference rules, committing logical fallacies, computing incorrectly, etc. all cause our models to fail at predicting what we see in the world? If there is no mapping between the formalism and the world, then using inappropriate inferences, bungling our computations-- these shouldn't necessarily be a problem for predicting nature. They are just violations of a game we invented.

What does one mean by “being sufficiently rational”? To me, appeal to “rationality” is nothing other than an appeal to the set of rules thatmust be satisfied in order to make things intelligible to somebody. And this may certainly include logic rules, too.

If something needs to satisfy certain rules to be intelligible, and we think the world is intelligible (sort of a prerequisite of the scientific project), then doesn't that mean the world must, in at least many key respects, satisfy such rules too?

3. Logic refers to rules that make the world intelligible to us.

I'm most interested in this one. If this is the case, are there rules out in nature that shaped us such that we need said rules to make the world intelligible to us? That is, why would natural selection endow us with such a need if such rules only exist in our minds? This is what I find most puzzling and hard to wrap my mind around; it's hard to know what a satisfactory answer to the puzzle looks like.

I'd like to buy into pancomputationalist physics as much as I used to because that seems to explain things well, but the bloom is off the rose for me.

But here is the big question: do we think that these are all different things? That we use the same word out of a sort of confusion? Or is there actually a similarity between these types of "logic?" — Count Timothy von Icarus

Two quotes that may be helpful:

The purpose of logic is to provide an analytic guide to the discovery of demonstrated truth and all its various approximations throughout the philosophical sciences. In the words of St. Albert the Great, logic “teaches the principles by which one can arrive at the knowledge of things unknown through that which is known” (De Praedicab., tr. I, c. 5, ed. Borgnet 1, 8b). St. Thomas defines logic as an art “directive of the acts of reason themselves so that man may proceed orderly, easily and without error in the very act of reason itself” (Foreword). Logic is thus a construct based on the natural processes of the mind invented for a very specific use, namely, scientific reasoning. — James A. Weiseipl, Preface

And the extended quote from Thomas Aquinas:

As the Philosopher says in Metaphysics I (980b26), “the human race lives by art and reasonings.” In this statement the Philosopher seems to touch upon that property whereby man differs from the other animals. For the other animals are prompted to their acts by a natural impulse, but man is directed in his actions by a judgment of reason. And this is the reason why there are various arts devoted to the ready and orderly performance of human acts. For an art seems to be nothing more than a definite and fixed procedure established by reason, whereby human acts reach their due end through appropriate means.

Now reason is not only able to direct the acts of the lower powers but is also director of its own act: for what is peculiar to the intellective part of man is its ability to reflect upon itself. For the intellect knows itself. In like manner reason is able to reason about its own act. Therefore just as the art of building or carpentering, through which man is enabled to perform manual acts in an easy and orderly manner, arose from the fact that reason reasoned about manual acts, so in like manner an art is needed to direct the act of reasoning, so that by it a man when performing the act of reasoning might proceed in an orderly and easy manner and without error. And this art is logic, i.e., the science of reason. And it concerns reason not only because it is according to reason, for that is common to all arts, but also because it is concerned with the very act of reasoning as with its proper matter. Therefore it seems to be the art of the arts, because it directs us in the act of reasoning, from which all arts proceed. — Thomas Aquinas, Foreword to Commentary on the Posterior Analytics

Looking at your categorization:

1. Logic is a set of formal systems; it is defined by the formalism.
2(a). Logic is a description of the ways we make good inferences and determine truth, or at least approximate truth pragmatically.
2.(b). Logic is a general description of the features or laws of thought. (This is more general than 2(a).
3. Logic is a principle at work in the world, its overall order. Stoic Logos, although perhaps disenchanted. — Count Timothy von Icarus

It seems to me that (2) is primary, and that (1) is derivative with respect to (2). A formal system is just an attempt to delineate the "laws of thought," and logic pertains more to the "laws of thought" (art of reasoning) than to any formal system.

But what about (3) and the question of computation that you eventually raise? I would say that to describe nature or computers in terms of logic is to use a metaphor. To talk about the "logic of natural selection" is to talk about the determinate and predictable nature of natural selection. It is metaphorical in the sense that it anthropomorphizes the process of natural selection as if it were an agent following rules of logic, and the case of computers is similar.

It may be worth noting that the causative rules we use for computation are not the same as logic. They were made to mimic logic, and this is very helpful, but (for example) philosophers seem convinced that material implication is at best a poor approximation of actual implication, and yet computers "make due" with material implication. Of course there has also been an interesting reciprocal causality between computers and the field of logic, such that it is more difficult to separate the two now than it was in the past.

It is metaphorical in the sense that it anthropomorphizes the process of natural selection as if it were an agent following rules of logic, and the case of computers is similar.

Does rule following entail intentionality? That's an interesting idea; it would seem to indicate a tie in between the external world and conceptions of subjectivity at a fairly basic level. For instance, ribosomes seem to be "rule following." They "transcribe," and have all sorts of mechanisms for "proof-reading." But while they are part of life, it doesn't seem like they should be conscious.

But the gap between intentional rule following and natural rule-like behavior seems like it would be tough to delineate. How complex does an organism need to be before rule-like behavior is supplanted by intentionality? How might intentional rule following evolve from rule-like mechanism? When does the human fetus or infant transition between these modes?

Interestingly, some behaviors we engage in unconsciously in a rule like way, but at will we can also lend them intentionality. For example, normally we are unaware of our breath, but we can "take control" of it. But the way the heart beats is more an unconscious sort of rule-like behavior. We can do intentional things to slow our heart rate, but we can't "hold our heartbeat" like we hold our breath; consciousness is cut off from stopping the heart, even though the brain could theoretically achieve this through signaling.

It may be worth noting that the causative rules we use for computation are not the same as logic

Interesting, I'm not familiar with the term "causative rules." I always thought the current definition of computation was defined by mathematical logic, and that this is why infinite alphabets and infinite strings aren't allowed for Church-Turing computation, but I also haven't explored that history all the way to the foundations of the idea.

but (for example) philosophers seem convinced that material implication is at best a poor approximation of actual implication, and yet computers "make due" with material implication. Of course there has also been an interesting reciprocal causality between computers and the field of logic, such that it is more difficult to separate the two now than it was in the past.

Exactly! I feel like this is a big reason for the "Scandal of Deduction," the finding that deductive reasoning shouldn't be informative because all the information in any conclusion must be contained in the premises of a deductively valid argument. To my mind, the entire Scandal is simply the result of confusing abstract, timeless entailment and the type of entailments we see in causality. If you think of our understanding things, or a computer's producing an output given some inputs, in causal terms, then it makes total sense that all the implications of some set of premises or messages aren't clear to us immediately. Thinking through implications requires time, information processing, neurons firing. We don't have any thoughts in "no time at all." Any implications we understand, we understand through time, not as eternal relations.

Hintikka and Floridi's responses to this (surface vs depth information, or virtual information) are super technical and complex and I think this obscures the fallacy right in front of our eyes, which is mistaking our (Platonic) abstractions for causal reality. Theories that reach for explanations in computational complexity miss that really simple arithmetic is also such that we don't know the answers until we do the computations. And they can't explain fallacies, why sometimes, even with simple surface-level syllogisms, we can think information is in our premises that isn't really there, e.g. affirming the consequent.

But, if we think nature comes prior to the human, and that it shapes the human, then its the causal rule following that seems more fundamental.

Does rule following entail intentionality? — Count Timothy von Icarus

If it does, then I think my point about the usage in (3) being metaphorical would hold. Are you thinking that if it does not entail intentionality, then (3) is therefore not metaphorical? That if something could follow rules without intention or agency, then (3) might not be metaphorical, and could therefore be a more central meaning of logic? I'm trying to be sure I understand how this relates to the OP.

Interesting, I'm not familiar with the term "causative rules." — Count Timothy von Icarus

Oh, I was only thinking of the underlying hardware of computing technology—the physical, causal mechanisms that underlie software. Basically we began with some rules of logic and we instantiated those rules into computer hardware so that software would then be able to appeal to those "rules" in order to manipulate the state of the machine. The basis of a computer is, I think, a (simple) formal system instantiated in hardware. But my point is that because all formal systems of logic have limitations, so too do computers (e.g. material implication).

Exactly! I feel like this is a big reason for the "Scandal of Deduction," the finding that deductive reasoning shouldn't be informative because all the information in any conclusion must be contained in the premises of a deductively valid argument. — Count Timothy von Icarus

I would want to return to Aquinas' claim that logic is the art of human reasoning, and that it involves a movement from what is known to what is unknown. The reason this does not make sense in a computational paradigm is because it is not clear that computers can know, and therefore for a computer there can be no movement from known to unknown. The proper context of a deduction is the human mind (or at least a rational mind), and when it is removed from that context it becomes opaque.

More generally, this is the problem of the Meno that Aristotle takes up at the very beginning of Posterior Analytics.

Thinking through implications requires time, information processing, neurons firing. We don't have any thoughts in "no time at all." Any implications we understand, we understand through time, not as eternal relations. — Count Timothy von Icarus

That's right, and Aquinas saw this because he was thinking in terms of God, angels, humans, animals, plants, and non-living matter. He would say that human knowledge is distinct because it is conditioned by time and movement, whereas angelic or divine knowledge is not conditioned in that way. This is why logic is a human art (or an art of temporal creatures). It would be of no use to angels or God.

But, if we think nature comes prior to the human, and that it shapes the human, then its the causal rule following that seems more fundamental. — Count Timothy von Icarus

I should look into the materials that Quixodian provided, but I tend to agree with him that logic and causation are different things. I would want to say that causal rule following, even in the higher animals, is not logic because it is not concerned with truth (or more strictly the truth-preservation that is validity). For example, even if we wish to attempt to make a non-metaphorical claim that natural selection follows rules, I think it would certainly be incorrect to go a step further and claim that natural selection follows the rules of logic. Natural selection is not following a set of rules related to truth, and this is one way to conceive of logic.

One of the responses to my question about the relationship of logical necessity and physical causation on Stack Exchange was as follows:

Wittgenstein famously states that (Tractatus Logico Philosophicus, proposition 5.1361) : "The events of the future cannot be inferred from those of the present." and "Superstition is the belief in the causal nexus."

Later (Propositions 6.37, 6.371 and 6.362) "A necessity for one thing to happen because another has happened does not exist. There is only logical necessity. At the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena. So people stop short at natural laws as at something unassailable, as did the ancients at God and Fate. And they both are right and wrong. But the ancients were clearer, in so far as they recognized one clear conclusion, whereas in the modern system it should appear as though everything were explained."

A Wittgensteinian answer to this question would that there is no such thing as physical causation as is generally understood in modern science, but that physical causation is an a priori intuition, which is useful for hypotheses, but which tells us nothing about the world in-itself or its meaning.

I have real trouble accepting this, but then, it is Wittgenstein, so who am I to question it? I myself have often appealed to the ‘illusion that the so-called laws of nature are explanations of natural phenomena’ in arguing against scientific realism but this response taken as a whole seems unreasonably sceptical to me. I mean, there are innumerable ways in which modern existence relies on what we understand as scientific laws (even if the term ‘law’ might be problematic.) It seems to me that Wittgenstein’s argument is similar to Hume’s in denying the necessity of inductive logic. I suppose it’s something to do with the fact that causality - a causing b - is neither deductively true nor directly observable. But isn’t this where ‘Kant’s answer to Hume’ is supposed to apply i.e. causality as being a necessary condition of reason?

I think where it seems wrong to me is that it presumes that because causation only pertains to the phenomenal sphere, then it says nothing about ‘the world in itself or its meaning’. I think that’s an unreasonable inference. But I’m interested in what others have to say about it.

As a rule, I have coffee in the morning, but if there is no coffee I'll have tea, just as the peasants will eat cake if there is no bread. I used to have a cigarette with the coffee, but that rule has lapsed. Likewise, the rules of planting times for gardeners are changing because the climate is changing.

It seems to me that mathematics is the study of form in the abstract. Existence must have some form or other, even if it is entirely random, and therefore some mathematics will always apply to it, in the sense of describing its form.

But the notion of change, of succession, of time itself can only arise in the context of stability. A stable self has a cigarette, and then does not have a cigarette. A stable Earth has a change of climate. Without the stable background there would be nothing to make the 'order of succession' — I cannot have coffee in the morning if there is never again a recognisable morning, and a recognisable me. Time and cause depend on that stability. If tomorrow, everything were different, there would be nothing to say it is tomorrow and not a billion years hence, or a billion years ago, or another timeline altogether.

Language, (mathematics is an abstract language) presumes and requires a context of stability and change. Names are given to things that persist, and stand out from the background. And then to processes that recur. To name something is to make a distinction between what is named and 'the rest'.

And that distinction, of 1 from 0, or observer from observed, gives rise to a logical language that can describe all the forms of the world, and all possible worlds.

http://www.siese.org/modulos/biblioteca/b/G-Spencer-Brown-Laws-of-Form.pdf

:pray:

Very lucid explanation.

I’ve noticed ‘Laws of Form’ but when I tried reading it, found it quite daunting. Maybe we should start a discussion group on it.

I’ve noticed ‘Laws of Form’ but when I tried reading it, found it quite daunting. Maybe we should start a discussion group on it. — Quixodian

I'd love to have a go at it, but I too find it daunting. A logician, a mathematician, and an electrical engineer would be useful contributors. @Anyone?

I'd love to have a go at it, but I too find it daunting. A logician, a mathematician, and an electrical engineer would be useful contributors. Anyone? — unenlightened

I read the prefaces and the introduction, and I'm an electrical engineer who would be happy to contribute to such a thread if I saw a way to do so. I'm not sure I'm willing to make the time commitment of reading the whole book, although sufficiently interesting contributions from other posters might compel me to do so. :wink:

With such great encouragement, how could I not start a thread? Here it is:

https://thephilosophyforum.com/discussion/14599/reading-the-laws-of-form-by-george-spencer-brown

Tell all your friends.

I would say logic is the organization of thoughts and identities at an attempt to arrive at conclusions that are concurrent with reality. This is done using deduction. This is logic.

I think where it seems wrong to me is that it presumes that because causation only pertains to the phenomenal sphere, then it says nothing about ‘the world in itself or its meaning’. I think that’s an unreasonable inference. But I’m interested in what others have to say about it. — Quixodian

From my Information-based perspective, I think your intuition is correct. There is a connection between phenomena (world) and noumena (mind). However, the meaningful "connection" is not a phenomenal object, but a noumenal relationship : a logical link. It's a relationship between "world in itself" and meaning in the observer.

As Hume noted*1, Causation is an inference, not an observation ; a conception, not a perception. What we observe is changes in material objects from T1 to T2. But the causal force we call Energy is invisible & intangible, hence unobservable. We attribute the power of causation to some imperceptible enforming Force at T1 to explain the perceived Effect at T2. A phenomenal event is a physical transformation from state A to state B. As in physical Phase Transitions (e.g. liquid water to solid ice), the before & after states are are observable, but the intermediate cause that connects them is only inferrable. And Logic is the ability to imagine plausible interrelationships between things & events.

For a zombie, Causation may "only pertain to the phenomenal sphere". But for rational beings Causation is significant to the observer, not just for what happened to an object, but for what could happen to the subject*2. That a physical change has occurred in the non-me world is meaningful to me because I am an integral part & participant in that objective world.

Phenomenal Change is what we interpret as Noumenal Causation*3. Change is physical & material, but Causation is metaphysical & mental. Perhaps the notion of causation says as much about the the subject as the object. Without change in the world, to which we accredit causation, there would be no meaning in the mind. :smile:

*1. Causation as conjunction of states :
Causation is a relation between objects that we employ in our reasoning in order to yield less than demonstrative knowledge of the world beyond our immediate impressions.
https://iep.utm.edu/hume-causation/

*2. Objective Data vs Subjective Information :
Data is a collection of facts, while information puts those facts into context. While data is raw and unorganized, information is organized. Data points are individual and sometimes unrelated. Information maps out that data to provide a big-picture view of how it all fits together.
https://bloomfire.com/blog/data-vs-information/
Note --- Context includes observed and observer

*3. EnFormAction :
The novel concept of Enformation is also a synthesis of both Energy and Information. So I invented a new portmanteu word to more precisely encapsulate that two-in-one meaning : “EnFormAction”. In this case though, the neologism contains three parts : “En” for Energy, “Form” for Shape or Structure or Design, and “Action” for Change or Causation. But Energy & Causation are basically the same thing. And the “En-” prefix is typically used to indicate that which causes a thing to be in whatever state or form or condition is referred to.
https://bothandblog2.enformationism.info/page29.html

I have real trouble accepting this, but then, it is Wittgenstein, so who am I to question it?

I don't think Wittgenstein would have thought this was a good reason to accept what he said. In any event plenty of other philosophers with at least as much cachet would say he is simply wrong about this. In the Investigations, Wittgenstein is trying to reframe questions, think outside the box, and so solve issues the generations of great minds ended up banging their heads against. I think it's fair not to expect that he succeeds in all respects.

I myself have often appealed to the ‘illusion that the so-called laws of nature are explanations of natural phenomena’ in arguing against scientific realism but this response taken as a whole seems unreasonably sceptical to me.

The idea of the "laws of nature" having causal efficacy does seem open to critique. As Cartwright points out, Newton's "immutable" laws fall apart when we add three or more bodies or imperfect spheres, meaning they are clearly only approximations. Paul Davies among others has offered pretty solid arguments against thinking of "the laws of physics," as Platonic statutes that causally interact with the world.

But this doesn't torpedo scientific realism because we can also think of such "laws" as merely describing the way things interact due to properties that are essential to them. That is, the causal nature of such laws areintrinsic to reality as a whole, or to parts of that whole, rather than laws being something outside nature that guides nature (the extrinsic view popularized by Newton, which Hume was critiquing).

For example, "water is H2O is an a posteriori analytical truth. It is true by definition, but we had to discover it empirically. Water, by this view, will behave like water whenever it interacts with "stuff" like the "stuff" of our world because of what water is due to its intrinsic properties. Just like how 2 is an even number by virtue of what 2 is. So here, the laws are just mathematical descriptions of the standardized properties of being that are internal to being qua being. What might be surprising here is that:

A. Such properties are intelligible to us and so readily describable in mathematics and logical formalisms.

B. That such properties exist at all. After all, we can well imagine a random universe (although we would only exist by chance in one). A random universe is certainly mathematically describable, but we don't see a random universe. We see a universe that always seems to move according to principles. And moreover, the principles exhibit a certain type of fractal recurrence such that disciplines such as chaos theory and complexity studies can identify general principles at work in extremely diverse systems, such as how fireflies decide to blink, hurricane formation, how the heart generates a beat, how earthquakes form, etc.

https://www.oxfordphilsoc.org/Weekend/2003/2_EileenWalker.pdf

It seems to me that Wittgenstein’s argument is similar to Hume’s in denying the necessity of inductive logic. I suppose it’s something to do with the fact that causality - a causing b - is neither deductively true nor directly observable. But isn’t this where ‘Kant’s answer to Hume’ is supposed to apply i.e. causality as being a necessary condition of reason?

Yes, and Leibnitz had the Principle of Sufficient Reason before Kant. Denying PSR gets very dicey vis-a-vis the cosmological argument because it opens opponents up to John Edwards' argument that: "if things can just start existing that didn't exist at any prior state, why don't things start to exist all the time." And moreover, with the intrinsic view: "if things don't initially occur due to any reason, why should they have one set of properties and not another." I don't shake up my water bottle and expect it to become a nice Scotch for instance, or expect that second moon wil pop into existence in the sky some night.

I think Wittgenstein and Hume have a massive pragmatic hurdle. If cause isn't real and induction is invalid, why the hell does it work so damn well? It certainly seems like logical models and mathematics correspond to how the world works.

But really, my views on Wittgenstein are mixed. Genius insights, and a great warning about the problems that come with attempting to theorize, especially theorizing about philosophy like it is the natural sciences. But at the same time, the self-described "purist" reading of Wittgenstein (per Rorty's label) ends up trying to use language to explain everything in the very way Wittgenstein warns against in the same book.

I think where it seems wrong to me is that it presumes that because causation only pertains to the phenomenal sphere, then it says nothing about ‘the world in itself or its meaning’. I think that’s an unreasonable inference. But I’m interested in what others have to say about it.

:up: Right, if you believe we are the products of natural selection, then claiming we only see cause because we construct it is a half answer. Ok, then why would we evolve to see cause? Why is it so useful? Why do animals seem to have a basic logical and causal sense? If we are natural, why did nature shape us to hallucinate causation from whole cloth? Why shouldn't we expect vision is the same way, that what we see has no correspondence with the world as it really is? Down this road seems to lie solipsism.

This is my problem with the linguistic turn, it seems to think that because you can't pin language down with a formalism that this entails that it isn't underpinned by nature in a way that is intelligible. This inclination is helped along by some findings in linguistics, namely Chomsky's universal grammar, but I think Chomsky is simply wrong here in terms of the causal origins of such rule-like behaviors.

Maybe this gets us too far afield, but its sort of like how all stem cells from an early fetus can become any type of cell. Tissues only differentiate, organs only develop, because of a complex feedback cycle between cells with the same DNA. It's all epigenetic, not hard coded at all. Kids don't learn language if they don't get exposed to it. We, as fully formed humans, are closer to chimps or even horses then a clump of our fetal cells, given they develop in a different environment, because that clump can be grown into nothing but a giant group of liver cells given the right signals. Hell, scientists can even turn animal stem cells into new synthetic creatures with little in common with the animals they share 100% of their DNA with. Point being that language is probably nothing suis generis, but natural like anything else, and so subject to the same causal principles.



:up: Plus, how do creatures like ourselves develop in a world without stability? It doesn't seem they can, we'd only have various types of "Boltzmann Minds." Our world is stable, and it has a certain type of stability, and that type of stability appears to be what gives rise to us and our languages. So, that's where I see an opening for a base level of "logic" that is posterior to our subjective logic, but perhaps it requires a different name so as to not to confuse the two.

But there appears to be morphisms between the two types of "logic." E.g., Leibnitz comes up with the Principle of Sufficient Reason because of the type of world he experienced and the type of animal that world made him to be. The fact that we understand necessity at all seems to imply something about us and about the world. If you explain necessity to a toddler, you're probably going to use empirical examples. Indeed, I'd argue we understand the abstract from the empirical sort of necessity found in cause, that abstract necessity is posterior to knowledge of causal necessity. E.g. "if you don't eat your dinner, it will necessarily get cold (because of the Second Law of Thermodynamics).

But I’m interested in what others have to say about it. — Quixodian

I think philosophy erred in taking Hume too seriously, and this had a big impact on Kant and (apparently) Wittgenstein. A related problem is that such individuals basically started with a critique, and then interpolated their more systematic views on that basis of that critique. This is a particularly poor way to do philosophy. A critique or a problem is not the basis for a systematic approach.

Obviously I will need to brush up on Hume since so many participants on forums such as this one take him for granted, but in general when presented with a Humean premise the response should just be, "Why think that?" The Humean premises are implausible and the conclusions are absurd, and at the end of the day the Humean ends up being schizophrenic because they want to have their cake and eat it, too (i.e. they want both their skeptical philosophy and the scientific enterprise that it undermines). I'd say that we need to be a bit more skeptical of Hume's skepticism, and that newcomers to philosophy need to feel free to question Hume or Wittgenstein when they say silly things.

On a related note, I have Jamal's piece on my reading list, "An Argument for Indirect Realism."

A necessity for one thing to happen because another has happened does not exist. There is only logical necessity. — Wittgenstein

It is fascinating to me that Wittgenstein sees himself, in saying this, as repudiating a modern error. Rather, it seems to me that he has captured the error of modernity in a remarkably pithy formula. But I would want to read more to further understand his context and intentions. He may be arguing against certain deformations.

To my point above, imagine saying something like this to a scientist, such as a biologist. It is a truly absurd claim to anyone familiar with reality. There is an important way in which the causal realities known to the biologist are much more real than the logical necessity of the logician. When one has no spectacles besides modal necessity with which to view the world, the majority of the world itself evaporates from before their eyes.

By formalism I mean "the rules" not merely their particular expression, or to borrow a term from information theory, the "encoding." There can be many formalisms that map on to the same rules — Count Timothy von Icarus

.

Your way of talking looks confusing to me. If you say in the latter statement that there can be many formalisms mapping on the same rules, then formalism is distinct from rules. And surely, by formalism, you could mean to refer to the logic rules as you also stated. But were this the case the following claim of yours “1. Logic is a set of formal systems; it is defined by the formalism” would equate to “1. Logic is a set of logic rules; it is defined by the logic rules” which sounds, if not tautological yet, very little informative.
To me it’s more clear to simply say that formalism is the symbolic codification of logic rules as opposed to the natural language codification of such rules. My substantial points here are that one thing is the subject of our representations (logic rules) another is our representations (formalised vs natural) and that formalisation would be a fix for natural language ambiguities. Wrt these points the observation that for exactly the same set of logic rules one can have many symbolic or natural language codifications is correct but marginal.

Good points, and we have the problem, per Tarski, of being able to define truth from within a system. — Count Timothy von Icarus

Independently from the merits of Tarski’s semantic theory of truth for formal systems, if the price for it is to relativize the notion of truth to a given (object) language, my problem with it is: what does “if and only if” in the T-condition mean? If the be-conditional requires the notion of “True” to be understood as a logic operator, but the notion of true can not be applied at the same language level in which the bi-conditional is expressed, then what does that bi-conditional even mean? Besides asserting p (in the most basic object language and since it’s a language it can offer just representations of facts not facts themselves) doesn’t mean that p is true.

But my understanding of the search for the "one true logic" was that the pioneers of post-Aristotelian logic were looking for something that would be both a rigorous system and which would reflect facts perfectly. From the 19th century view, where it looked like all the world would soon be explainable in a rigorous way, this makes sense. They hadn't run into undecidability, the entscheidungsproblem, incompleteness, undefinability, etc. yet. — Count Timothy von Icarus

I see your point. But I think it is relatively easy to realign it with what I said. Indeed the “rigorous system” condition can reflect the need to have a system that doesn’t suffer from the ambiguities which e.g. the natural language suffers from. And the “reflect facts perfectly” condition refers to the fact that a certain set of logic rules can serve science better than other conceivable set of logic rules, as much as a set of mathematical analysis rules can serve science better than other conceivable mathematical rules.

However, I feel like the response to the aforementioned list might have been to throw the baby out with the bath water, since we've now disembodied logic in a sort of neo-Platonism. This is my problem with "game" theories of language as well. Maybe I'm just too much of a close-minded naturalist, but I tend to think that rules exist out in the world, in minds that are natural themselves, and that the rules must thus have natural causes. — Count Timothy von Icarus

All I can say at this point is that if your naturalist assumptions play a role in your understanding of logic, then they deserve to be addressed as well.

Right, but generally in the sciences we think that if a formal system very closely (or ideally, perfectly) describes something in the world, and if it allows us to make good (or ideally, perfect) predictions, this is because the formalism corresponds to something in the world. We don't think our language is magic, that it is sorcery that causes the world to correspond to it (else why all the failed formalisms, right?). But we also don't think our systems can have no connection to the world, because then science isn't about the world at all, its about language and formalisms. Except it also seems to tie to our experiences and have huge pragmatic value, so that doesn't seem right.

Of course, we can justify the sciences on pragmatic grounds, but it feels worthwhile to ask "why is it pragmatically valuable?" Presumably, because our formalisms, e.g. Newton's laws, the Schrodinger equation, etc. correspond to external reality in some way. But then if logical rules correspond to reality, it seems reality has some rules. — Count Timothy von Icarus

Without directly joining the debate between idealists and realists, my point is that if we develop tools (formal systems) to better serve a purpose (to describe the world), then we shouldn’t be all that surprised if these tools serve that purpose. What you may be tempted to say instead is that if there are representational tools that can successfully represent the world, then the world must be such that our representational tools can succeed in representing it. But this claim does very much sound like claiming that we can represent the world that we can represent, doesn’t it?

Formalism helps us discriminate better different ways allowing us to meaningfully speak of things according to various sets of “logic” rules.


Right, but then the question is: why do some formalisms work for meaningfully speaking of things better than others? And why is it that breaking our inference rules, committing logical fallacies, computing incorrectly, etc. all cause our models to fail at predicting what we see in the world? If there is no mapping between the formalism and the world, then using inappropriate inferences, bungling our computations-- these shouldn't necessarily be a problem for predicting nature. They are just violations of a game we invented. — Count Timothy von Icarus

Logic rules allow us to infer some conclusions from some premises. Such rules ensure that if the premises are true, then the conclusion is true. And that’s possible because from premises to conclusions we are manipulating our own representations so that, semantically speaking, there is no more truth in the conclusion than there is in the premises, there is no more information in the conclusion than there is in the premises. The mapping to the world can be done by the premises. But logic would work even without any such mapping. E.g. Premise 1: squares are triangles; Premise 2: triangles are circles; Conclusion: squares are circles.

What does one mean by “being sufficiently rational”? To me, appeal to “rationality” is nothing other than an appeal to the set of rules thatmust be satisfied in order to make things intelligible to somebody. And this may certainly include logic rules, too.


If something needs to satisfy certain rules to be intelligible, and we think the world is intelligible (sort of a prerequisite of the scientific project), then doesn't that mean the world must, in at least many key respects, satisfy such rules too? — Count Timothy von Icarus

It’s not the world that satisfies such rules, but our representations of the world. While we can represent and logically process representations of state of affairs that do not map into reality and do not correspond to facts, are there real states of affairs that we can not represent ? But how can we answer such question without possibly representing such state of affairs? What are we picking with the notion “state of affairs“ for whatever goes beyond our means of representation (so including the notion of "state of affairs" itself)?

3. Logic refers to rules that make the world intelligible to us.


I'm most interested in this one. If this is the case, are there rules out in nature that shaped us such that we need said rules to make the world intelligible to us? That is, why would natural selection endow us with such a need if such rules only exist in our minds? This is what I find most puzzling and hard to wrap my mind around; it's hard to know what a satisfactory answer to the puzzle looks like.

I'd like to buy into pancomputationalist physics as much as I used to because that seems to explain things well, but the bloom is off the rose for me. — Count Timothy von Icarus

I guess that these questions are all the more pressing because of your naturalist assumptions which I’m afraid I do not share. My assumptions have been more shaped by a certain reading of Wittgenstein’s views, especially in his later phases, and according to such reading there are reasons to be skeptical about both platonism and naturalism.
Concerning your claims, let me list just the points I’m having problems with: 1. if by “rules out in nature” you are literally referring to the “laws of nature” then I find your usage conceptually confused, because the former concept is conceptually distinct and irreducible to the latter. And rules are not “in our minds” if this means a private phenomenon, something only a given subject can possibly have access to. I won’t elaborate further such claims now 2. If by “laws of nature” you are referring to some theory of natural selection then I’m not sure we have such a theory for logic rules. Notice that logic rules can be used to justify anti-natalism, human killing and suicide depending on the premises so both for human beings’ survival as much as for their extinction. Besides natural selection can be used to explain also failures to follow logic rules, think of our cognitive biases (and more radically, if you remember, even Nietzsche claimed that the notions causality, will, subject, substance are false representations of the world which we have to survive).
Anyways, as far as I’m concerned, a more Humean understanding of “laws of nature” plus some form of “emergentism” may help us make the coexistence of “laws of nature” and “rule following” less untreatable.

@Gnomon - I moved your comments about Law of Form to the new thread on that topic https://thephilosophyforum.com/discussion/14599/reading-the-laws-of-form-by-george-spencer-brown

Quotidian or whatever didn't do the job? Wayfarer is far more wistfully wise.

Why thanks. Put it down to a sudden rush of blood to the head. Kept the icon though.

If you say in the latter statement that there can be many formalisms mapping on the same rules, then formalism is distinct from rules. And surely, by formalism, you could mean to refer to the logic rules as you also stated. But were this the case the following claim of yours “1. Logic is a set of formal systems; it is defined by the formalism” would equate to “1. Logic is a set of logic rules; it is defined by the logic rules” which sounds, if not tautological yet, very little informative.

Sure, it's tautological. That was the position of Russell and the Vienna Circle. Moreover, by this view, all of mathematics is itself tautological. This is logic as defined as: "the study of certain mathematical properties of artificial, formal languages. It is concerned with such languages as the first or second order predicate calculus, modal logics, the lambda calculus, categorial grammars, and so forth. The mathematical properties of these languages are studied in such subdisciplines of logic as proof theory or model theory."

(quote from https://plato.stanford.edu/entries/logic-ontology/#DiffConcLogi)

The rules define what the system is. And per deflationary theories of truth, that tend to go along with this sort of view, truth is itself simply something defined in terms of such systems. That is, truth is "neither metaphysically substantive nor explanatory. For example, according to deflationary accounts, to say that ‘snow is white’ is true, or that it is true that snow is white, is in some sense strongly equivalent to saying simply that snow is white, and this, according to the deflationary approach, is all that can be said significantly about the truth of ‘snow is white."

E.g., many axiomatic theories of truth: https://plato.stanford.edu/entries/truth-axiomatic/

The most austere versions of "logic as formalism" seem to deny any direct relation to thought or metaphysics. Many versions aren't quite so austere, but the general idea is that logic is about abstract systems, not thought and certainly not the world or metaphysics.Logic might inform our metaphysics, but our metaphysics (or philosophy of mind) should not inform our consideration of logic.

(After being very impressed by the North Holland Handbook of the Philosophy of Complex Systems I was excited to grab their book on the Philosophy of Logic, but it seemed to hew fairly close to these sorts of views throughout the submissions, which was the impetus for this thread.)

To me it’s more clear to simply say that formalism is the symbolic codification of logic rules as opposed to the natural language codification of such rules.

This seems right to me. What I wanted to get at with description 1 is the conception above.

Independently from the merits of Tarski’s semantic theory of truth for formal systems, if the price for it is to relativize the notion of truth to a given (object) language, my problem with it is: what does “if and only if” in the T-condition mean? If the be-conditional requires the notion of “True” to be understood as a logic operator, but the notion of true can not be applied at the same language level in which the bi-conditional is expressed, then what does that bi-conditional even mean? Besides asserting p (in the most basic object language and since it’s a language it can offer just representations of facts not facts themselves) doesn’t mean that p is true.

Right. Or what does it mean to "describe things" at all in a language we are pretending is completely divorced from anything else in reality? At a certain point, when you get into very deflationary views, you're no longer describing "things." All you can say is that "a system can produce descriptions."

All I can say at this point is that if your naturalist assumptions play a role in your understanding of logic, then they deserve to be addressed as well.

Sure, and I can totally see how my concerns might be irrelevant for people who are less concerned with naturalism. But most philosophers are naturalists, so it doesn't seem too outlandish.

What you may be tempted to say instead is that if there are representational tools that can successfully represent the world, then the world must be such that our representational tools can succeed in representing it. But this claim does very much sound like claiming that we can represent the world that we can represent, doesn’t it?

It sounds similar; I don't think it's identical. First, if we posit that any intelligibility we find in the world is hallucinatory, something we project onto a world that lacks it, I don't see how this doesn't slide into the territory of radical skepticism. The steps to get us to "how do you know cause and effect exist? Maybe your mind creates all such relationships," seem like they should also get us to "why do you think other minds exist?" Or "why should we think an external world exists outside of our perceptions?" Afterall, don't we suppose that others have minds because of how those minds seem to effect their behaviors?

The fact that animism is pretty much universal in early human cultures (e.g., "the river floods because it wants to"), and that children tend to provide intentional explanations for natural phenomena ("the clouds came because the sky is sad") seems to show we can "hallucinate" other minds to some degree. But if we think all of the intelligibility we find in the world is simply projected, then I'm not sure how solipsism isn't a problem.

Most philosophers are naturalists though, and most think the natural sciences are one of the best sources of information we have about how the world is though. And if we accept we are formed by natural selection, then it is prima facie unreasonable to think how we "make the world intelligible" has nothing to do with how the world is.

Second, what is the point of positing aspects of reality that we cannot ever, even in principle, experience? To be sure, people have experiences all the time that they say they cannot put into words. That makes perfect sense; we do more than just use language. But aspects of reality we can never know? They are like Penrose's invisible fire breathing dragon who is flying around our heads and not interacting with anything. We can imagine an infinity of such entities. But as long as they are, in principle, forever unobservable, their being or not being seems identical. When we move to the existence of that which cannot even be thought it seems even weirder. It's the inverse of radical skepticism, instead of seeing a way to doubt everything, now we can posit anything (so long as we can never know of it).

Logic rules allow us to infer some conclusions from some premises. Such rules ensure that if the premises are true, then the conclusion is true. And that’s possible because from premises to conclusions we are manipulating our own representations so that, semantically speaking, there is no more truth in the conclusion than there is in the premises, there is no more information in the conclusion than there is in the premises. The mapping to the world can be done by the premises. But logic would work even without any such mapping. E.g. Premise 1: squares are triangles; Premise 2: triangles are circles; Conclusion: squares are circles.

This gets to the "Scandal of Deduction." If in all valid deductive arguments all information in the conclusion is contained in the premises, what exactly is the point of deduction? It tells us nothing. So why does deduction seem so useful? Why can't we memorize Euclid's axioms and then immediately solve every relevant geometry problem we come across?

This is probably the best example I know of where thinking of logic as completely abstract runs into problems. A lot of ink has been spilled trying to figure out some sort of formal solution to the Scandal, because the idea is that any solution has to lie within the scope of the abstract systems themselves.

I don't think this works. Floridi and D'Agostino put a lot of work into their conception of virtual information, trying to figure out how it is that at least some inference rules introduce new information in an analysis. But it seems like such a project is doomed. As both they and Hintikka agree, Aristotelian syllogisms only deal with surface information, information explicit in the premises. The problem is that we can still find this type of analysis informative, just as we can not know the answers to very simple arithmetic problems until we pull out a pencil and start computing.

Naturalist approaches have no problem here. We don't see things and immediately know what they entail because thought is a complex process involving a ton of physical interactions, all of which occur over time-- simple as that.

It’s not the world that satisfies such rules, but our representations of the world. While we can represent and logically process representations of state of affairs that do not map into reality and do not correspond to facts, are there real states of affairs that we can not represent ? But how can we answer such question without possibly representing such state of affairs? What are we picking with the notion “state of affairs“ for whatever goes beyond our means of representation (so including the notion of "state of affairs" itself)?

Not everything can be put into words. I'm not sure if it makes sense to posit things that can be known in any way though.

Anyhow, would you agree that the world has an influence on how we represent it? This is the logic behind using mathematical patterns to contact extra terrestrials. If the representations of intelligent life forms aren't the result of bidirectional influence, then of course this won't work of course. But then if nature doesn't shape our representations than I don't get why even members of the same species should understand each other.

One way to get logic without compromising your naturalism is to push it away from basic brain function and toward social interaction.

I don't think you have to look for logic in the world at all. You can instead say that there are regularities in the world -- I just don't know any way around this -- and our minds are built pretty much entirely around making predictive inferences based on these regularities.

But neither are the domain of logic. We can approximate the sort of things our minds get up to, but it's not logic; it's probability, Bayesian inference, that sort of thing. (And the most we can say about the world is something statistical.)

If that mathematical formalism is in some ways a simplification of what our minds do (and also of how the world is), logic is a further simplification, even exaggeration, of that, and its use is not primarily in our prediction-generating and updating machinery, but in discussion.

We present our views to others in a drastically simplified form -- even more simplified than the form in which we ourselves become aware of our own beliefs. Some of that may be down to the nature of language, built as it is on conceptual generality, but some of it is strategic: we need only bring to the discussion a view, with the expectation that others will bring other views, and the cooperative process of comparison and critique will lead to a more-heads-are-better-than-one conclusion.

We're each biased toward our own ideas, and notoriously bad at judging how well supported those ideas are. Others make better judges of the soundness of our thoughts.

Around here is where it makes some sense to talk about logic, in the critique of the reasons others offer in support of their views, and in the contest between positions that are presented as more perfectly opposed than they really are. It's efficient and productive to present and critique ideas this way, and the process should lead not only to a better view than any individual would produce on their own, but through the exchange and critique of supporting reasons and evidence, to a view that gets buy-in from participants. Reasons need to be persuasive because it's not just the least wrong belief we want; it's cooperative behavior reliant on a shared point-of-view.

Some of this can be supported by research, and probably some of it can't yet, but it's the overall story I lean toward these days. The inferences that we think of as 'belief formation' aren't really much like any sort of formal logic, so there's no such process that would be isomorphic to some logical structure of nature. Even single-cell organisms can display behavior we might as well call 'rational' in avoiding danger and seeking nutrients. But they don't deal in reasons and persuasion and counter-arguments and counter-examples and all that stuff that logic is useful for.

Some of this can be supported by research, and probably some of it can't yet, but it's the overall story I lean toward these days. The inferences that we think of as 'belief formation' aren't really much like any sort of formal logic, so there's no such process that would be isomorphic to some logical structure of nature.

What do you think of computational theory of mind? I'm not totally sold on it, but it remains the most popular theory of how consciousness emerges (Integrated Information Theory is fairly similar too).

If these theses are mostly true, then logic absolutely can be used to describe all our beliefs and how we come to them, since these theories take mind to be a product of computation. It's simply that forming such a complete description of how said computation works is very difficult because parallel processing is harder to follow and because we're talking about quadrillions of operations per second (at lower end estimates).

Even single-cell organisms can display behavior we might as well call 'rational' in avoiding danger and seeking nutrients. But they don't deal in reasons and persuasion and counter-arguments and counter-examples and all that stuff that logic is useful for.

If computation is symbolic manipulation based on logical rules then it seems like simple organisms use computation all time time. But I get your point. It squares with views that computation only occurs in virtue of a human observers recognizing a process as such. E.g., "Chat GPT doesn't "compute," computing is just a label we project on to what the machines running the program are doing."

This particular example I find puzzling because the same thing can be said about all our concepts. For example, "burning" is a human concept and label we attach to a class of phenomena. All incidences of combustion are actually different events, but we don't tend to say "wood doesn't really burn." I suppose the difference here is supposed to be that computation necessarily requires intentionality, but I've never been convinced about why this should be the case. My phone seems to compute.

I find the "computation requires intentionality," view less convincing because I haven't seen one that can define how sentient an observer needs to be before they can "view computation," nor one that explains why mental constructs should be causally disconnected from the rest of the world. Presumably, under intentional versions of computation, when my cat is looking at my computer, it doesn't see something that is computing. Likewise, when my son plays with my phone, he doesn't understand that it is computing, so for him it isn't computing. But how well does he have to understand the process before he is projecting computation onto the phenomena? This is not a way we tend to think about other processes such as combustion or acceleration. "Reading" might be analogous though: does a ribosome "read" DNA? Does a license plate scanner "read" license plates?

In biology, the idea that simple organisms compute is fairly mainstream. If a bacteria computes, then there is a sense in which logic, or a very similar sort of thing, plays a role in organisms that we tend to think lack intentionality and social organization, at least in any way that is qualitatively like our own.

But in biology and biosemiotics there is often a move to cut off the definition of "computation," at the domain of life. Cells compute, self-replicating silicone crystals do not. Digital computers might compute, but only in virtue of their having been designed by living things.

The problem here is that the definition of life is squishy, and this doesn't seem that much less arbitrary than saying computation and logical manipulation only occur in organisms that are "sentient and social enough."

Plus, paired with findings that give rise to the popularity of computational theory of mind, the view of computation as something that only occurs in sentient consciousness starts to get a little wonky. Presumably, I am computing if I am not a math wiz and have to consciously think about the steps involved in summing some list of figures. But then am I not computing if the entire process happens unconsciously and I just know the outcome by glancing at the symbols? Do I compute when I consciously try to read French, but acomputationally experience when the meanings of English words fly into my awareness with no conscious effort? If unconconcious computation is possible within a human, it seems harder to justify it not existing outside the mind. But then knowing the answer to 3+7, 2+2, etc. doesn't seem to require anything conscious or intentional on our part.

Another way to look at it: containment gets you a surprising number of logical relations.

Socrates is a man
All men are mortal
Socrates is mortal

Can be explained as:

Socrates is contained in "men"
"Men" are contained in "mortals"
If Socrates is inside "men" then Socrates is necessarily inside "mortals" because "men" is inside "mortals."

But containment seems like a concept that is harder to bracket off as existing only in the subjective sphere than "reading," or "computation." A box doesn't need to be conscious to contain anything. And if boxes only contain things in virtue of our observing them then it seems like all factual statements must not truly be about the world sans our experiences of it. "If a box is alone in a forest, can it contain a rock?"

Unless we want to say that the containment relations we discuss in mathematics are in fact a different sort of "containment," than physical containment.

Plus, paired with findings that give rise to the popularity of computational theory of mind, the view of computation as something that only occurs in sentient consciousness starts to get a little wonky. Presumably, I am computing if I am not a math wiz and have to consciously think about the steps involved in summing some list of figures. But then am I not computing if the entire process happens unconsciously and I just know the outcome by glancing at the symbols? Do I compute when I consciously try to read French, but acomputationally experience when the meanings of English words fly into my awareness with no conscious effort? If unconconcious computation is possible within a human, it seems harder to justify it not existing outside the mind. But then knowing the answer to 3+7, 2+2, etc. doesn't seem to require anything conscious or intentional on our part. — Count Timothy von Icarus

:up:

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)

It seems to me like this question often produces three types of responses:
1. Logic is a set of formal systems; it is defined by the formalism.
2(a). Logic is a description of the ways we make good inferences and determine truth, or at least approximate truth pragmatically.
2.(b). Logic is a general description of the features or laws of thought. (This is more general than 2(a).
3. Logic is a principle at work in the world, its overall order. Stoic Logos, although perhaps disenchanted. — Count Timothy von Icarus

These all seem to be, as you say, common definitons of 'logic'. The question that arises for me is whether these definitions have a common element or thread running through them.

Is logic as a set of formal systems not a set of formulations built based on what we do naturally when we think deductively, "the ways we make good inferences and determine truth, or at least approximate truth pragmatically", a making explicit of what is implicit in our practice of consistent thinking?

Are these formulationsnot all built on a few basic principles. consistency, non-contradiction and excluded middle, which may be thought of as 'laws of thought"?

And do these principles not reflect our experience of the world? It doesn't seem that we see things in the world being inconsistent, such as appearing as a tree then morphing into an animal, or contradictory, being an apple and the same time not being an apple (unless maybe we have partaken of some psychedelic).

If we think of the laws of nature as formulations of the perceived regularities which abound in the natural world, just as the laws of thought are formulations of the natural ways we think, then why can we not say there is a logic, a logos, at work in the world?

I take it by "disenchanted" you mean that we have come to see this natural order as an immanent nature and not as imposed from on high, by a transcendent or divine order?

If you say in the latter statement that there can be many formalisms mapping on the same rules, then formalism is distinct from rules. And surely, by formalism, you could mean to refer to the logic rules as you also stated. But were this the case the following claim of yours “1. Logic is a set of formal systems; it is defined by the formalism” would equate to “1. Logic is a set of logic rules; it is defined by the logic rules” which sounds, if not tautological yet, very little informative.


Sure, it's tautological. That was the position of Russell and the Vienna Circle. Moreover, by this view, all of mathematics is itself tautological. — Count Timothy von Icarus

Certain logic formulas are tautologies e.g. "( P ⇒ Q ) ⇔ ( ¬ P ∨ Q )" in the sense of being always true whatever is the truth value of the variables P and Q. However not all logic formulas are tautologies (e.g. P ⇒ Q). The idea that logic (and mathematics to the extent it is reducible to logic) is tautological basically comes from the idea that logic theorems can prove only tautological formulas. And this is in line with what I also said about deductive reasoning “from premises to conclusions we are manipulating our own representations so that, semantically speaking, there is no more truth in the conclusion than there is in the premises, there is no more information in the conclusion than there is in the premises.“
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”).

The rules define what the system is. And per deflationary theories of truth, that tend to go along with this sort of view, truth is itself simply something defined in terms of such systems. That is, truth is "neither metaphysically substantive nor explanatory. For example, according to deflationary accounts, to say that ‘snow is white’ is true, or that it is true that snow is white, is in some sense strongly equivalent to saying simply that snow is white, and this, according to the deflationary approach, is all that can be said significantly about the truth of ‘snow is white.” — Count Timothy von Icarus

I’m not persuaded by the deflationary theories of truth so I can’t share your assumption. The most intuitive objection I can make against it is that, asserting p doesn’t mean nor implies that p is true.

the general idea is that logic is about abstract systems, not thought and certainly not the world or metaphysics.Logic might inform our metaphysics, but our metaphysics (or philosophy of mind) should not inform our consideration of logic. — Count Timothy von Icarus

Notice that “abstract” in “abstract systems” may also have a metaphysical connotation: namely, being out of space and time. And this understanding would lead us to a form of platonism about logic (which is also a metaphysical view). However “abstract” can simply refer to the result of a cognitive task by which we are focusing on certain set of characteristics or type of information while ignoring others. So “abstract systems“ refers to the possibile result of such cognitive task. I guess that’s the understanding suggested by your claim, right?

Independently from the merits of Tarski’s semantic theory of truth for formal systems, if the price for it is to relativize the notion of truth to a given (object) language, my problem with it is: what does “if and only if” in the T-condition mean? If the be-conditional requires the notion of “True” to be understood as a logic operator, but the notion of true can not be applied at the same language level in which the bi-conditional is expressed, then what does that bi-conditional even mean? Besides asserting p (in the most basic object language and since it’s a language it can offer just representations of facts not facts themselves) doesn’t mean that p is true.


Right. Or what does it mean to "describe things" at all in a language we are pretending is completely divorced from anything else in reality? At a certain point, when you get into very deflationary views, you're no longer describing "things." All you can say is that "a system can produce descriptions.” — Count Timothy von Icarus

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”).

But most philosophers are naturalists, so it doesn't seem too outlandish. — Count Timothy von Icarus

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. On the other side, if you mean that this thread is about views on logic and your views on logic are grounded on popular naturalist assumptions, then I’ll confirm what I said that I do not share such popular views and I’m open to discussing them.

What you may be tempted to say instead is that if there are representational tools that can successfully represent the world, then the world must be such that our representational tools can succeed in representing it. But this claim does very much sound like claiming that we can represent the world that we can represent, doesn’t it?

It sounds similar; I don't think it's identical. First, if we posit that any intelligibility we find in the world is hallucinatory, something we project onto a world that lacks it, I don't see how this doesn't slide into the territory of radical skepticism. The steps to get us to "how do you know cause and effect exist? Maybe your mind creates all such relationships," seem like they should also get us to "why do you think other minds exist?" Or "why should we think an external world exists outside of our perceptions?" Afterall, don't we suppose that others have minds because of how those minds seem to effect their behaviors?

The fact that animism is pretty much universal in early human cultures (e.g., "the river floods because it wants to"), and that children tend to provide intentional explanations for natural phenomena ("the clouds came because the sky is sad") seems to show we can "hallucinate" other minds to some degree. But if we think all of the intelligibility we find in the world is simply projected, then I'm not sure how solipsism isn't a problem.

Most philosophers are naturalists though, and most think the natural sciences are one of the best sources of information we have about how the world is though. And if we accept we are formed by natural selection, then it is prima facie unreasonable to think how we "make the world intelligible" has nothing to do with how the world is.

Second, what is the point of positing aspects of reality that we cannot ever, even in principle, experience? To be sure, people have experiences all the time that they say they cannot put into words. That makes perfect sense; we do more than just use language. But aspects of reality we can never know? They are like Penrose's invisible fire breathing dragon who is flying around our heads and not interacting with anything. We can imagine an infinity of such entities. But as long as they are, in principle, forever unobservable, their being or not being seems identical. When we move to the existence of that which cannot even be thought it seems even weirder. It's the inverse of radical skepticism, instead of seeing a way to doubt everything, now we can posit anything (so long as we can never know of it). — Count Timothy von Icarus

I’m not positing “that any intelligibility we find in the world is hallucinatory”, I’m not a radical skeptic, I’m not a solipsist. My point is more that we have a network of concepts (like representation, world, truth, fact, possible fact, logic/semantic inference) that enable us to talk meaningfully and reflectively about our own cognition. Since they are mostly primitive concepts they can not be questioned or explained away without ending up into some nonsense or implicitly reintroducing them. To me “realism” about the existence of the external world (that can be experienced or referred to by other minds beside mine) is matter of conditions to talk meaningfully about the external world, so any attempt to question the existence of the external world sounds nonsensical to me as much as any attempt to demonstrate it, because one needs demonstration were things can be questioned meaningfully.
On the other side, our representations of the world may not correspond to what is the case, and may refer to mind dependent facts (as human linguistic conventions or social institutions). Unfortunately we may hold more false beliefs than we are able to detect or wish to admit. And human representations and logic/semantic inferences may serve human biological extinction as much as they can serve human biological survival.

Logic rules allow us to infer some conclusions from some premises. Such rules ensure that if the premises are true, then the conclusion is true. And that’s possible because from premises to conclusions we are manipulating our own representations so that, semantically speaking, there is no more truth in the conclusion than there is in the premises, there is no more information in the conclusion than there is in the premises. The mapping to the world can be done by the premises. But logic would work even without any such mapping. E.g. Premise 1: squares are triangles; Premise 2: triangles are circles; Conclusion: squares are circles.


This gets to the "Scandal of Deduction." If in all valid deductive arguments all information in the conclusion is contained in the premises, what exactly is the point of deduction? It tells us nothing. So why does deduction seem so useful? Why can't we memorize Euclid's axioms and then immediately solve every relevant geometry problem we come across?

This is probably the best example I know of where thinking of logic as completely abstract runs into problems. A lot of ink has been spilled trying to figure out some sort of formal solution to the Scandal, because the idea is that any solution has to lie within the scope of the abstract systems themselves.

I don't think this works. Floridi and D'Agostino put a lot of work into their conception of virtual information, trying to figure out how it is that at least some inference rules introduce new information in an analysis. But it seems like such a project is doomed. As both they and Hintikka agree, Aristotelian syllogisms only deal with surface information, information explicit in the premises. The problem is that we can still find this type of analysis informative, just as we can not know the answers to very simple arithmetic problems until we pull out a pencil and start computing.

Naturalist approaches have no problem here. We don't see things and immediately know what they entail because thought is a complex process involving a ton of physical interactions, all of which occur over time-- simple as that. — Count Timothy von Icarus

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.

It’s not the world that satisfies such rules, but our representations of the world. While we can represent and logically process representations of state of affairs that do not map into reality and do not correspond to facts, are there real states of affairs that we can not represent ? But how can we answer such question without possibly representing such state of affairs? What are we picking with the notion “state of affairs“ for whatever goes beyond our means of representation (so including the notion of "state of affairs" itself)?


Not everything can be put into words. I'm not sure if it makes sense to posit things that can be known in any way though. — Count Timothy von Icarus

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.

Anyhow, would you agree that the world has an influence on how we represent it? — Count Timothy von Icarus

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.