[logic] is the study of the most general features of thoughts or judgments, or the form of thoughts or judgments. Logic thus understood will for example be concerned with the occurrence of subject and predicate structure that many judgments exhibit, and with other such general features of judgments. It will mostly be concerned with thoughts, and not directly with linguistic representations, though, of course, a proponent of this conception can claim that there is a very close connection between them.
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
But this brings up the question, "does the absence of a 'one true logic' necessitate deflating logic into formalism? — Count Timothy von Icarus
Or can we meaningfully speak of things like the logic of cause? — Count Timothy von Icarus
And if we can meaningfully speak of things, what is the relationship between the formalism and the referents? — Count Timothy von Icarus
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
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).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
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.
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.
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.)
Formalism helps us discriminate better different ways allowing us to meaningfully speak of things according to various sets of “logic” rules.
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.
3. Logic refers to rules that make the world intelligible to us.
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
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
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
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 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
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.
Does rule following entail intentionality? — Count Timothy von Icarus
Interesting, I'm not familiar with the term "causative rules." — Count Timothy von Icarus
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
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
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
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’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? — unenlightened
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.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
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.
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.
But I’m interested in what others have to say about it. — Quixodian
A necessity for one thing to happen because another has happened does not exist. There is only logical necessity. — Wittgenstein
.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
Good points, and we have the problem, per Tarski, of being able to define truth from within a system. — Count Timothy von Icarus
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
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
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
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
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
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
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.
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.
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.
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?
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.
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)?
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.
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
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
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
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
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
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
But most philosophers are naturalists, so it doesn't seem too outlandish. — Count Timothy von Icarus
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
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
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
Anyhow, would you agree that the world has an influence on how we represent it? — Count Timothy von Icarus
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