Ok.

When I was the only one who had brought up or defended the idea of truth-preservation in the entire thread? — Leontiskos

You weren't the only one to bring this up:

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. — neomac

I was dipping back into the Routledge handbook of metaphysics and it made me think of something. For folks who don't like thinking of logic in terms of naturalism, or logic as "out there," "in the world, sans mind," do you embrace realism towards propositions, states of affairs, facts, and events?

It seems like a fairly popular position in contemporary metaphysics to allow that these sorts of abstract entities, particularly propositions, do indeed exist. That is, there is a real set of all possible propositions that can be true or false, and likewise a real set of all possible states of affairs that can obtain or not obtain. Only some of these states of affairs are actualized; only some propositions are made true by the actual facts in the world. However, they all exist as abstract entities.

I am curious about this because objections against such abstract entities that I am familiar with tend to be made on naturalist grounds. Something like: how can a human being, a natural system, "grasp" an abstract entity like a proposition or state of affairs that exists outside space-time? How can language, which develops in space-time, come to accurately reflect these abstract entities?

But it seems to me that if these abstract entities are accepted, a second path opens up to seeing logic "out there," in the world, outside of minds or formal systems. Realist metaphysicians tend to assert that there are relationships between propositions and states of affairs, such that they map to one another. There is a relation between "I throw the rock at the window," being true and "the window breaks," being true, for example.

My point would be that, just as metaphysicians accept that there are isomorphisms between the set of all propositions, all facts, and all states of affairs, there seems to be other isomorphisms between how members of these sets relate to one another. And this set of relations would seem to be what people are talking about when they refer to "the logic of the world," or things like "the logic of natural selection, the logic of thermodynamics, etc.," i.e. a sort of "logos," external to mind and systems, but inherit to the way the world evolves.

These relations could be put in the form of broad propositions about how broad sets of these abstract entities relate to one another, i.e., propositions about "rules" that obtain for describing how one state of the universe will evolve into future states.

So, on the one hand I see a bridge between all three "types" of logic laid out in the initial definitions that comes from naturalism. Humans are natural systems and our minds formed by nature and our systems are formed by our minds. Thus there seems to be a way in which our minds and representational systems should map to things present in the world and be shaped by any patterns therein.

But on the other hand, if we are less inclined to naturalism and embrace abstract entities, then an abstract sort of logos seems to go hand in hand with the existence of entities like propositions, states of affairs, etc.

I suppose a thoroughgoing nominalism that takes logic to be solely a property of mind doesn't have this problem. But to my mind such ontological commitments seem to threaten a fall into radical skepticism and solipsism. On the other hand, from the standpoint of the "formalist," it seems possible to embrace a sort of epistemic nihilism and deflationary theory of truth that avoids having to assume that logic is ever anything more than a set of "games" we play, but this seems to have follow on consequences for epistemology as a whole and also lend itself to a sort of extreme skepticism.

It seems to me that a general difficulty here is that the third account of 'logic' that you give has not yet been shown to be coherent. It seems to piggyback on the Stoic or Christian idea, but "disenchanted," as you say. It is not the anima mundi of the Stoics nor the divine Word of the Christians, but it attempts to inherit and "naturalize" that concept. But again, is this really coherent? Do naturalists really speak this way when they are being rigorous and are not engaging in loose and poetic metaphor?

The crux is that there is an age-old connection between Logos and mind or spirit, and its not clear that one can take one and leave the other. What is in fact occurring, I aver, is that an entirely new concept is being introduced under an already-established word. This results in a sort of equivocation, where a new concept gets disguised in the garb of an old word, and an attempt is made to pass it off under the old concept. Those promoting such a thing perhaps do not understand how radical is their break with the traditional and established meaning.

Do naturalists really speak this way when they are being rigorous and are not engaging in loose and poetic metaphor?

Yes? We speak of the "law like behavior," of the universe and it is considered perfectly legitimate to rule out a scientific explanation if it suggests that nature is somehow preforming a contradiction. Work in quantum foundations for instance is largely about how to explain puzzling phenomena in a manner that is consistent and doesn't admit contradictions.

When there are references to the "logic of natural selection," vis-á-vis evolutionary game theory we mean to say that logic of our simplified models "maps onto" nature, that there are isomorphisms there, not that the logic is something "we create in order in our mind to make an orderless process out in the world comprehendible." In the physicalist, naturalist view, our ability to "make sense," is after all, the product of nature, in no way suis generis. This is why biology admits both "functional," and "adaptive," explanations as distinct types of causal explanations in its field.

I've read enough biology and philosophy of biology to feel fairly confident in saying that talk about the logic of selection is about morphism between our model and how nature is in-and-of-itself. Physics is less clear on this. QBism for example punts on such an assertion, but many theories in quantum foundations are saying that our mathematical formalism is mapping to nature, that nature embodies this formalism.

The concept of Logos is problematic not only for its spiritual connotations and connotations of intentionality (the idea that nature is not teleological is a bit of a dogma in naturalism today) but even moreso because it implies that any order in nature is enforced externally, say by eternal "laws of nature," that exist outside nature. This isn't popular due to Hume's "problem of induction" and Kripke's essentialist response. We generally now think that nature has the properties of order that it does because of what nature is, or because of what natural entities are. That is, the "logic" of state progression in nature is intrinsic, not extrinsic. But this in no way means that the order doesn't exist outside the mind, it simply means that such an order is inherit to nature because of what nature is.

Any ability we have to recognize such patterns and develop logical systems is itself the result of natural causal interactions. Further, while logical systems have "contrived, mental sources," writ large natural language, and the logical explanations it allows, is an evolved capability in hominids that appears to have likely predated homo sapiens. Further, language itself, and maybe even the sciences arguably appear to advance due to the same sorts of dynamical processes that lead to biological evolution. This isn't particularly surprising given how the same mathematics can describe such a wide range of phenomena in complexity studies; the world seems to display a sort of multiscale fractal recurrence in causal patterns.

The concept of Logos is problematic not only for its spiritual connotations and connotations of intentionality (the idea that nature is not teleological is a bit of a dogma in naturalism today) but even moreso because it implies that any order in nature is enforced externally, say by eternal "laws of nature," that exist outside nature. This isn't popular due to Hume's "problem of induction" and Kripke's essentialist response. We generally now think that nature has the properties of order that it does because of what nature is, or because of what natural entities are. That is, the "logic" of state progression in nature is intrinsic, not extrinsic. But this in no way means that the order doesn't exist outside the mind, it simply means that such an order is inherit to nature because of what nature is. — Count Timothy von Icarus

Okay, I think that's accurate.

I think the Logos idea has to do with the whole, whereas the idea that you've been focusing on has to do with subsets of the whole, "isomorphisms between how members of these sets relate to one another" (). Then there is the other question of the <isomorphisms between mind and reality>.

So let's look at how Merriam-Webster defines logic:

• 1a
  
  • (1): a science that deals with the principles and criteria of validity of inference and demonstration : the science of the formal principles of reasoning
    
    • a professor of logic
  • (2): a branch or variety of logic
    
    • modal logic
    • boolean logic
  • (3): a branch of semiotics
    
    • especially: Syntactics
  • (4): the formal principles of a branch of knowledge
    
    • the logic of grammar
• 1b
  
  • (1): a particular mode of reasoning viewed as valid or faulty
    
    • She spent a long time explaining the situation, but he failed to see her logic.
  • (2): Relevance, Propriety
    
    • could not understand the logic of such an action
• 1c: Interrelation or sequence of facts or events when seen as inevitable or predictable
  
  • By the logic of events, anarchy leads to dictatorship.
• 1d: the arrangement of circuit elements (as in a computer) needed for computation
  
  • also: the circuits themselves
• 2: something that forces a decision apart from or in opposition to reason
  
  • the logic of war

Now let's subdivide your third definition:

3. Logic is a principle at work in the world, its overall order. Stoic Logos, although perhaps disenchanted. — Count Timothy von Icarus

• 3(a). Logic is a principle at work in the world, its overall order. Stoic Logos, although perhaps disenchanted.
• 3(b). Logic is a principle at work in the world, in the order of subsets of the whole. "The logic of natural selection."

Interestingly, there is no correlate in Merriam-Webster (MW) for 3(a). I think this is right. Logos and logike are two different things. 3(b) maps to MW-1c. I think the idea about isomorphisms between mind and reality is implicitly related to MW-1a(1), MW-1a(4), and MW-1b(1). This idea is implicit in science and phusis, especially Aristotle's "form or source of motion" vis-a-vis phusis. To speak about the "logic" of natural selection is to speak about the nature (phusis) of natural selection.

The other central question is the question of what exactly you are asking or aiming to do in the OP. Apparently you are trying to understand how the various different usages relate to one another, no? We must inevitably ask what methodology is being presupposed in responding to this inquiry. But I will leave this for another post.

I was dipping back into the Routledge handbook of metaphysics and it made me think of something. For folks who don't like thinking of logic in terms of naturalism, or logic as "out there," "in the world, sans mind," do you embrace realism towards propositions, states of affairs, facts, and events? — Count Timothy von Icarus

It seems you are suggesting 3 alternatives: naturalism, platonism, or nominalism. But I don't think these alternatives are the only ones available. I think that Wittgenstein offered a distinctive philosophical approach which is reducible to none of such alternatives.

I suppose a thoroughgoing nominalism that takes logic to be solely a property of mind doesn't have this problem. But to my mind such ontological commitments seem to threaten a fall into radical skepticism and solipsism. — Count Timothy von Icarus

Then the link between nominalism and radical skepticism or solipsism should worry naturalists too. Quine was both naturalist and nominalist. Wilfrid Sellars too.

So, on the one hand I see a bridge between all three "types" of logic laid out in the initial definitions that comes from naturalism. Humans are natural systems and our minds formed by nature and our systems are formed by our minds. Thus there seems to be a way in which our minds and representational systems should map to things present in the world and be shaped by any patterns therein. — Count Timothy von Icarus

Take a deduction like Premise1: "If Trump won the 59th presidential elections, the earth is flat", Premise2: "Trump won the 59th presidential elections", Conclusion: "the earth is flat", how do you figure such mapping?

Logic is not a formal system, a formal system is a logic.

Logic are necessary conclusions, when we say that something is "logical" we say that it follows from the information we have available, while non the less expressing that information in a way that were different from the way that information occurred to us initially by application of dualistic concepts (non of which are abstracted from experience) in our major premise such as "all/some".

It is impossible to know that something follows (as a conclusion) from the information available without also knowing at the same time that something else would not or that it did not have to before we concluded so.

In other words, logic are the reversed order of subject -> predicate, constituting the ongoing falsification of the predicate by the plurality of subjects experienceable or thinkable in existence. One posits a predicate, a fireman, it may be preceded by an experience or from imagination, and it is then either affirmed or denied by the pattern that is recognised in the subject a moment later.


Everything is possible until it is necessary, and both these concepts are contingent on the concept of negation, and negation contingent on the disjunction of plurality of experience, as in derived a posteriori. Logic precedes that of which there is formal systems, or of which there are the field of "Logic" the same way physics precedes everything ever thought in the field of physics.

Inductive systems are no different, they are wholly downstream of deductive ones, the only change is that predication takes an extra step or that the subject becomes our own ideas (the realists imagines that the precise opposite happens), which is to say that whether someone is a fireman or not is not known by him merely wearing the uniform, but whether we have reason to believe it is known, which in turn is another way of saying that all we have is knowledge, the propositions we have imagined for ourself by means of that knowledge are exactly that: fictions of our imagination, we create the non-knowledge by allowing (though really perpetuating) propositions to refer to something that does not correspond to experience, this is the invention of "truth" and though it seems to be irrelevant to the precise topic discussed I ended up here because it follows directly from analysis of logic.

Everything is possible until it is necessary, and both these concepts are contingent on the concept of negation, and negation contingent on the disjunction of plurality of experience, as in derived a posteriori. Logic precedes that of which there is formal systems, or of which there are the field of "Logic" the same way physics precedes everything ever thought in the field of physics — Julian August

This take on logic sounds more compatible with Analytic than with recent Continental approaches. Re your analogy of logic to physics, for many continental philosophers there is the field of formal logic, and there are the more general presuppositions grounding this formal field, which limit it to subject-object propositions generating necessary relations of truth or falsity, negation or affirmation. But there are more fundamental logics which are not propositional in nature.

Logic is a wreath of pretty flowers which smell bad.


(Can’t believe it took three pages for someone to say that.)

Hey @joshs thank you for the good response, let me reply back here with how I understand (or don't) your notion of a non-propostional logic!

It is hard for me to imagine away the behaviour of my own which characterises my whole life and appears to characterise everyone I have ever come in contact with, yet this is that I am asked to do by people who says that my thoughts can be empty of truth value.

Thoughts could hardly do anything besides appear a) in a way they did in my past or b) appear in a way they never before did to me, and in either of these cases, say a bus in the former case and a bus with unicorn-wheels in the latter case, I would as a thinking subject know that I am distinguished from these thoughts and that they thereby fail to predicate me.

In other terms: nothing human appear to ever happen in absence of instantiations of the concept of negation, regardless of whether external objects of phenomena were present, what would it even mean to say that a logic could be composed of modalities and quantifiers to the exclusion of truth-values if all examples of either are involved in the process of negating the self with which they come conjoined?

Formal logic and Symbolic logic are not able to deal with the real world phenomenon and states very well. They are OK for dispositional propositional truths findings, and as "tools for understanding the world" - (www.marxists.org), but for real world applications, Dialectic Logic seems a better system.

https://www.marxists.org/reference/archive/hegel/txt/system2.htm

Without revealing too much of my own framework, this is my description of logic:

Hilbert said, "Mathematics is the art of giving the same name to different things." This applies to all of logic, as does its opposite. For logic is also the art of giving different names to the same things, and in a sense, these two actions are the same.

For my definition of logic, you'll have to wait for my magnum opus, if it ever comes.

Without revealing too much of my own framework, this is my description of logic:

Hilbert said, "Mathematics is the art of giving the same name to different things." This applies to all of logic, as does its opposite. For logic is also the art of giving different names to the same things, and in a sense, these two actions are the same.

For my definition of logic, you'll have to wait for my magnum opus, if it ever comes. — Ø implies everything

Is this a riddle?

It is no more of a riddle than anything else is.

Science is rigor, or the body of knowledge rigorously obtained. Logic is a subset of science that describes relationships that always replicate. Math is a subset of logic that deals exclusively with relationships of quantity.

Of course, sometimes when we talk about logic we want to refer to the logic of the external world, not just thought. For example, we can talk about an organelle being shaped by "the logic of natural selection." In this case, "the logic of natural selection," might be described by numerous formal systems, but it is not the formal description itself we are talking about, but rather the way the series of causal events that appears to conform to the more general logic. That is, the formal system is itself merely an encoding of the principle we want to refer to. — Count Timothy von Icarus

Above point tells us Logic is not just simple symbolic formula manipulation.
Some people (not the OP) seem to think Logic is just a bit of formulas which has no content, and it cannot describe the reality. I feel it is too narrow and restrictive view of Logic. Logic is the way how the world and universe works, and how our reasoning and intuition works to discern right from wrong, the valid from invalid etc.

For instance it is a logical phenomena that it is likely to rain under the low pressure and high humidity in the sky. It is a logical statement describing a phenomena in nature.  

I am conscious of myself, therefore I exist.  Being conscious means, by necessity, having the conscious being.  This is a simple psychological logic based on the deductive reasoning describing how the self existence is deduced and proved.

If Age >= 20, then the client is an adult.
Writeln "OK, you are allowed to buy the ticket"
Do Issue Ticket
Print Ticket.
End.

This is a simple computational logic in computer programming algorithm snippet showing how the applied logic can work describing adult (set age >=20), and then picking out adult members in the business clientele.

Formal logic and Symbolic logic are not able to deal with the real world phenomenon and states very well. — Corvus

They are at the very heart of the development of digital computers, such as the one you're reading right now.

Hilbert said, "Mathematics is the art of giving the same name to different things." — Ø implies everything

Seems you're conflating Hilbert with Poincare.

Formal logic and Symbolic logic are not able to deal with the real world phenomenon and states very well.
— Corvus

They are at the very heart of the development of digital computers, such as the one you're reading right now. — TonesInDeepFreeze

What Corvus should have said is that they are not very good at cognizing in the way living systems do, as Hubert Dreyfus famously showed 60 years ago with his ‘What Computers Can’t Do’ and his more recent update ‘What Computers still can’t do’. Of course they are a part of the real world. Specifically, as technological
implementations they function as appendages to human ecological systems , the way a nest belongs to the bird’s ecology and the web belongs to the spider’s built niche. While an animal species are stick within a single ecological niche, humans continually construct new ones. As we evolve culturally, so will our built niche, which may involve the replacement of symbolic logic with different technological languages.

Without comment on the specifics, I think that's a pretty good perspective.

Above point tells us Logic is not just simple symbolic formula manipulation.

I'm a bit more cautious about that. It seems like the die is already cast on logic generally referring to formal systems in philosophy. I was searching around for a good term to refer to the idea of "what we use logic to describe in nature," but I haven't thought of a catchy one.

"Logos" has a nice ring, but it's quite pregnant with mystical and theological connotations, and I don't necessarily want to imply all of those.

They are at the very heart of the development of digital computers, such as the one you're reading right now. — TonesInDeepFreeze

Sure, logic must be the working engines of all the computers and even AI agents suppose. But there would also some custom logics they set up, and embed into the programs in the devices depending on what they are used for. It wouldn't be just the plain classic symbolic logics only in use.

Above point tells us Logic is not just simple symbolic formula manipulation.

I'm a bit more cautious about that. It seems like the die is already cast on logic generally referring to formal systems in philosophy. I was searching around for a good term to refer to the idea of "what we use logic to describe in nature," but I haven't thought of a catchy one. — Count Timothy von Icarus

Yeah, that was written sometime ago, when I knew little about logic. Since then I have read a few different logic textbooks, which totally changed my ideas and views on logic.

What Corvus should have said is that they are not very good at cognizing in the way living systems do, as Hubert Dreyfus famously showed 60 years ago with his ‘What Computers Can’t Do’ and his more recent update ‘What Computers still can’t do’. Of course they are a part of the real world. — Joshs

The traditional classic logic wouldn't be able to deal with the dynamic and unpredictable nature of the real world. From quite some time ago, various types of non classic logics seem to have been implemented, and used such as Temporal Logic, Description Logic, Fuzzy Logic, Epistemic Logic, Many-Valued Logic, Probability Logic, Topological Logic, Assertion Logic, Deontic Logic ... etc to deal with the dynamics of the real world.

What is logic? IMO, it's semantics. "And", "or", if...then....else" and "not" have precise meanings, as clarified in truth tables. We apply logic applies to propositions, also semantic representations.

The world does not depend on logic. Our understanding of the world (which is semantical) is improved through valid logic. If we were omniscient, logic would be pointless.

It wouldn't be just the plain classic symbolic logics only in use. — Corvus

Right.

various types of non classic logics seem to have been implemented, and used such as Temporal Logic, Description Logic, Fuzzy Logic, Epistemic Logic, Many-Valued Logic, Probability Logic, Topological Logic, Assertion Logic, Deontic Logic — Corvus

Ordinarily, 'classical logic' refers to any of the equivalent formulations of predicate logic, in first or higher orders, with the ordinary features such as excluded middle, non-contradiction and explosion.

Advancements have been added to classical and non-classical logic, such as modal logic, temporal logic, etc. And some advancements may be incompatible with classical logic, such as multi-valued logic, relevance logic, paraconsistent logic, etc.

It is of course granted that predicate logic is not adequate for all forms of inference. However, that does not vitiate that predicate logic (and even just sentential logic) is useful.

Note also that I replied to a claim about formal, symbolic logics. And such things as temporal logic, deontic logic, fuzzy logic, etc. are given as formal, symbolic logics, even if they may also be studies informally. So their uses does not vitiate the point that formal, symbolic logic is useful, since they are themselves formal, symbolic logics. And usually an intellectual prerequisite for study of those advanced logics is an understanding of plain vanilla predicate logic. Moreover, as far as I've seen, set theory may be a meta-theory in which those advanced logic are studied, which is to say that in set theory we may formulate those other logics and prove theorems about them.

Classical logic is useful, even just in its sentential component, which is the Boolean logic used in ordinary computing, and further as classical logic is the logic for the ordinary mathematics for the sciences and for the study of recursive functions and the theory or computability that are at the very heart of the invention and development of the digital computer. And, while predicate logic cannot account for all forms of inference, predicate logic is usually prerequisite for study of the more advanced logics.

Math is a subset of logic that deals exclusively with relationships of quantity. — Kaiser Basileus

Whether or not mathematics is a subset of logic, it is decidedly not the case that mathematics is only about quantity.

Classical logic is useful, even just in its sentential component, which is the Boolean logic used in ordinary computing, and further as classical logic is the logic for the ordinary mathematics for the sciences and for the study of recursive functions and the theory or computability that are at the very heart of the invention and development of the digital computer. And, while predicate logic cannot account for all forms of inference, predicate logic is usually prerequisite for study of the more advanced logics. — TonesInDeepFreeze

Good point. Yes, I agree with that. Classic logic is very useful in checking out logical validity and soundness in the spoken languages and written documents. It is also the foundation of all the other non-classic logic too. One must learn classic logic first in order to understand all the non-classical logics.