On the logical modeling of reality and human reason

Question

What is the system of logic which models reality and, furthermore, which models human reason?

Preface:

Of course, objective reality (that is, reality as it is before it's perceived) may operate under a logic which is not conceivable or understandable by humans, or even fit our understanding of what a "logic" is, but I'm simply concerned with the logic that underpins our perceived reality. Also, I think it's important to note that the logic which describes reality may be fundamentally different, and even incompatible, to that which describes human reason (although I will argue that that's not the case). Furthermore, for the sake of a roadmap, I want to say that while I outline the problem in the first 3 paragraphs, somewhere in the 4th paragraph is where I will start talking about and arguing my own ideas. I'm not horribly confident about the solutions I give, but I still want to offer my own thoughts on the problem and am eager to hear what people have to think about them and the problem as a whole.

Body:

Any pursuit of truth (i.e. an argument) is necessarily described by a system of logic which describes how truth may be derived and understood. This is true of philosophy, science, math, etc. But, if these pursuits of truth are to be valid for our reality, they must abide by the logic which describes our reality. Otherwise, the logic used is either incompatible with that of reality, or outside of it entirely, in which cases the argument's conclusion is either wrong or indeterminate, respectively.

For example, consider the argument: "water is wet implies hot dogs are tacos", "water is wet", therefore "hot dogs are tacos". This argument contains 3 assumptions, the two initial statements and that modus ponens is a valid rule of inference. If the negation of any of these 3 is true (either as axioms or provable statements), then the argument is false within our reality. If all 3 are true within the logic of reality, then the argument's conclusion is true. But, if any of the 3 assumptions is not axiomatically nor provably true within reality, then the argument's conclusion is indeterminate (conceptually similar to a Godel statement in math and computer science).

It follows then to ask: What is the system of logic which models reality? This system of logic, if an accurate model, would provide undeniable truth and validity to all argumentation which concerns reality. The problem is, how would this model be justified? If it is argued for, the argument itself must rely on a logic. This logic, if not equivalent to that which it is arguing for, will then provide a conclusion which is either wrong or indeterminate. So, for the argument to have any merit, the logic which underpins it must be identical to that which it is arguing models reality. This, however, is circular reasoning. It seems then that the logic which underpins reality cannot be logically determined. What does this mean then for philosophy and science? Is it all useless? How can physics, for example, determine the foundations from which all of reality is derived, if it seems that doing so is illogical? This leads me to my question about the logical modeling of human reason.

*This is where I begin to transition into talking about my own ideas concerning a solution to these issues.

You may say, for example, that if this is true then we can arbitrarily assert a logic to model reality, and this assertion, no matter how absurd, is equally valid as any other assertion. But, if you were to claim, say, that reality is described by a classical logic (laws of identity, excluded middle, and non-contradiction) and has the two axioms: "god is good" and "god is evil", then by the principle of explosion this becomes a trivialized logic in which every conceivable statement is a theorem. This however can be observed as not true, in that I am not on Mars right now so the statement "I am on Mars" must be false. The key realization here is that my observation is required, which leads to two things: one, our perception is necessary to have any information about reality, and two, the principles of induction are inherent to how humans process our perception. Reality can not be understood unless we take, axiomatically, at least a subset of our observations as true information, and the principles of induction as valid rules of inference. Therefore, an inductive logic (e.g. science) must be the logic which accurately models human reason. This lens of inductive reasoning is unavoidable in understanding reality as humans, and therefore, we must consider it a subset of the system of logic which models reality (to avoid the aforementioned problems). In a kind of poetic sense, this means that we model our own reality by virtue of perceiving it, and that this model is subjective to our individual perception.

From here, we may argue a logic to model reality by use of inference. First off, I would like to talk about Aristotle's formalism of classical logic which underlies all of western civilization. Aristotle proposed that, for any statement P, the following is true: "P is P", "P is either true or false, not anything else or in between", and "the statement 'P and not P' must be false". This is the foundation behind most civilized thought throughout history. The second statement (law of excluded middle) wasn't questioned and its negation formalized until the early 20th century. The third statement (law of noncontradiction) didn't have its negation formalized until the past ~3 decades. These formalisms have led to many-valued and paraconsistent logics. Please note that the ideas of these logics have been talked about for centuries (particularly many-valued logics in ancient China), but they weren't properly understood and formalized until the times listed above as far as I'm aware.

I want to propose that a classical logic is a very poor and inaccurate model of reality, and that a many-valued, perhaps even paraconsistent logic, is a much better one.

Firstly, there's a lot of justification in modern physics for a many-valued model. Quantum mechanics is the most successful and accurate theory of reality we have ever developed, but it is fundamentally probabilistic. That is, whether or not a particle is at a specific location, has a certain amount of momentum, or that it even exists, etc., can only be calculated as a probability. We can't know these things certainly, but only can calculate the probability that they are the case. For a long time, it was posited that there were "hidden variables", i.e. factors at play that we don't understand which determine these probabilities and are themselves certain. However, the Nobel prize in physics was recently awarded for Bell's theorem, which mathematically proves that hidden-variable theories are incompatible with quantum mechanics. The fact that these hidden-variable theories also don't stand up nearly as well to experimentation would justify that quantum mechanics is our most accurate theory of reality. This seems to justify using a probabilistic logic to model reality. That is, a logic where the truth value of a given statement is a number n, where n ranges from 0 to 1 and is the probability that the given statement is true. But, from the law of large numbers and observed properties of physics, these probabilities "cancel out" on a larger scale (physically, more mass/energy) such that the accuracy of this model could theoretically be approached asymptotically by that of a non-probabilistic logic (not necessarily classical), wherein the n for a statement gets infinitesimally close to 0 or 1, but never reaches it.

And, while I'm less confident about this, I think a paraconsistent logic would more accurately model reality than a non-contradictory or trivial logic. Paraconsistent logics allow for contradictions, and I feel contradictions are inherent to the human condition. Think absurdism in that we crave meaning but objective meaning can't be obtained, or sociologically in that we wish to self actualize but at the same time desire social connections which requires conformity which hinders actualization, or in game development in that the same company that created Fallout 76 also created Skyrim (possibly the most earth shattering contradiction of them all). These contradictions necessarily exist within the human condition, but we, as humans, must persist and reason how to make choices and live our lives anyways. This seems to suggest that paraconsistent reasoning is inherent to the logic of reality, or, more fundamentally, to the logic of human reason (which as aforementioned is a subset of the logic of reality). I'm only less confident about this argument because it's much more nuanced and philosophical than the quantum mechanics justification for probabilistic logic and feels less fundamental or necessary, although I do think it's right.

Therefore, I posit that the logic which most accurately models our reality is a probabilistic, paraconsistent logic.

The reason all of this is important, especially if you're to agree with me that classical logics are poor models, is that much of our pursuit of truth is built on classical logic. Mathematics is a classical logic for example, yet it's used to describe physics which seems to rely on a non-classical logic. Does this prompt the development of a "new math" which can be more logically compatible with physics? Furthermore, much of Western civilization is built on non-contradictory logic. How would it make sense, both systematically and culturally, to introduce paraconsistent logic so that our civilization is more logically compatible with the human condition? I believe the way we reason about things is often a much bigger, much more telling issue than the particular things we reason about. However, I'm quite worried that the ways we reason are largely non-standardized and incompatible with reality, which can lead to very fundamental problems in the ways we decide to lead our lives and our societies.

Afterword:

If you've managed to read all of this, I greatly appreciate your time. I know I wrote a lot, and I'm worried that I may have been overly wordy or unclear at points, although it's hard to tell since it's such a nuanced topic to begin with, but I am grateful if I've even only been marginally understood. These questions and their implications have been on my mind a lot recently and I've only now been able to really put a finger on it and put it into words, and I am very excited to hear what others have to say, as this is a topic I have not been able to find anything about online. I'm not sure if the concept of logically modeling reality and human reason is new, if it's equivalent to another idea and I'm just thinking about it differently, or if I simply haven't been looking hard enough to find anything about it. Either way, if anybody has any resources regarding this I would greatly appreciate them, and if you have any questions please don't hesitate to comment asking for clarifications. Also, I'm aware my format is kind of unorthodox, especially since aspects of a proposed answer are mixed in with my asking of the question (although I feel like this is often typical in philosophy), so if anybody has any suggestions on reformatting or anything of that nature, please let me know but I ask that you simply flag me with a suggestion or send me a notification rather than editing it yourself. Thank you!

Answer 1

What is the system of logic which models reality and, furthermore, which models human reason?

On a nominalist (SEP) reading, 'reality' is a linguistic entity that describes by way of representations, whatever is external to the human mind and body. In contrast 'logic' is a subsystem of language that deals with truth conditions. In the olden days, it was claimed there were Laws of Thought that were somehow objective and irrefutable, and all reasoning should conform to it. Immanuel Kant in his Introduction to Logic raises the quintessence of this view of logic, IMNSHO. These days, the notion that classical logic should be held as a normative standard is a bit outdated. The goal of many who are interested in logic is to model how humans reason, not necessarily try to discount all non-classical views as "defective logic". Computer scientists in the AI subfield have long abandoned any notion that classical logics are sufficient to describe what logic is and are very much interested in non-classical models such as those which model defeasible reasoning (SEP).

Of course, objective reality (that is, reality as it is before it's perceived) may operate under a logic which is not conceivable or understandable by humans, or even fit our understanding of what a "logic" is, but I'm simply concerned with the logic that underpins our perceived reality.

"Objective reality" is a metaphysically contentious term. That is, there are quarters in philosophy who reject it exists, and those who claim it exists but shy away from attempting to characterize it. There are also positions that fundamentally reject that some sort of material reality exists independent of our thinking. The dichotomies in question that are relevant are scientific realism versus instrumentalism and internalism versus externalism, among others. It is a metaphysical presupposition to suppose that there is a material reality populated by other minds (a popular one, of course), but it is not metaphysically necessary (SEP). Thus, there are often still metaphysical challenges to realism (SEP). What you presume is a core tenet of physicalism, and positions such as subjective idealism is just one position that questions that there's an objective reality independent of the mind.

Any pursuit of truth (i.e. an argument) is necessarily described by a system of logic which describes how truth may be derived and understood.

My bias is believe that logic is a little more complicated than this. There are multiple logics, and in the real-world, non-classical, that are used in modeling or representing reality, though to be fair, there are philosophers who maintain there is one right logic (SEP). That's a metalogical claim, and certainly a metaphilosophical presumption more than a universally accepted fact. I would suggest that it's best to see a formal logic as formal system that models truth-conditional semantics, and in different systems, formal logics are tools apply the power of logical consequence to particular linguistic frame. Instead of logic being an "essence" of reality, it's simply a grammar that allows one to move from one sentence to another consistently. Language expands reality by allowing us to integrate our perception, which is physically embodied with language resulting in conception. Thus, 'reality' is best characterized as a spectrum from our perceptions to our conceptions, with the good stuff being in the middle. Interestingly, some people believe that a language is the fundamental mechanism by which the mind processes meaning, which is held by those who advocate the Language of Thought hypothesis (SEP). Linguistics weighs in against this.

For example, consider the argument: "water is wet implies hot dogs are tacos"... then the argument is false within our reality...

What you are noticing is that there are theories of truth that correspond to taking in account the state of affairs of the external world. This is the correspondence theory of truth. It is the goal of language that is crafted with truth conditions to adequately describe and predict what happens outside of our bodies. The real philosophical discussion these days focuses around how do the words we use to describe reality get their meaning in the first place.

It follows then to ask: What is the system of logic which models reality?

This is wrong. Logic is an aspect of language, one that emphasizes truth conditions (be they correspondenent, coherent, deflationary, etc.), and most of what models reality (if you buy that language and grammar is a way of having representations that map onto different forms of intentionality) is not logical. Take the terms, 'Socrates', 'kitchen', and 'house'. These term represent things in the world, but aren't strictly logical in isolation. It is only subject to logic when governed by a language of relations. For instance, 'If Socrates is in the kitchen, he is in the house' expresses a logical truth about how space as our mind deals with it is composed, that is, the language also can be seen as expressing a generalized truth 'kitchens are contained by houses'. It's logically ambiguous 'Socrates isn't in the kitchen' whether the logical consequence is 'Socrates is in the house' or 'Socrates is outside the house'. But the meaning of 'Socrates', 'kitchen', and 'house' don't necessarily need to be expressed in logical terms. They might be conveyed through ostensive definition. Small children (whose first-order logical skills are somewhat lacking), understand the world in terms of associations that are pre-logical. This whole notion of how we construct meaning is relevant to notions of apriorticity and aposteriority and analytic and synthetic definitions with the modern consensus approaching that the terms are a little fuzzy, and are more oversimplifications of how thinking occurs. Today, I would consider them lies to children which work under many circumstances but break down on close inspection.

I want to propose that a classical logic is a very poor and inaccurate model of reality, and that a many-valued, perhaps even paraconsistent logic, is a much better one.

Propose away. I don't think professionals who deal in logic consider classical logics sufficient for modeling human thought and language, though I've never seen a survey. In Computer Science, MVLs are the norm now for implementing languages. Both Java and JavaScript, which are tremendously influential languages have truth values other true and false. And computer code is a the predominant formalism for modeling reality by virtue it's on tens of billions of computers. Here's Bumble's post on non-classical logics which I keep bookmarked and is worth reading.

Therefore, I posit that the logic which most accurately models our reality is a probabilistic, paraconsistent logic.

Yeah, deductive, classical logic doesn't handle the lion share of human reasoning remotely. Where we can shoehorn practical problems in it, we do, but IMNSHO, it's a pedagogical tool. I get the sense that people who buy into the idea that there are universal, classical Laws of Thought that are prescriptive have simply been reading non-contemporaneous philosophical and logical sources. Intro textbooks on logic and rhetoric, often start with Aristotelian syllogisms and Venn Diagrams of basic set theory.

You might have an interest in Montague grammar. It's a solid effort at combining the formalisms of natural language grammars into logical systems. While you won't find the term used a lot, "material logic" captures the idea that natural language has a system of logical consequence that goes beyond the logical formalisms like FOL, modal logic, etc. What you seem to be interested in is the philosophy of language, so I'd recommend a copy of Philosophy of Lnaguage (GB) by Szabo and Thomason (my copy is at my toes) and to consider exploring various other theories of semantics besides truth-conditional semantics. Logicians are rightfully obsessed with the truth conditions. But language as a form or representing the world is far richer than truth, and many philosophical questions go beyond those which analytic philosophy is preoccupied with. Model theory, set theory, and computability are fascinating topics, but they are not the end-all and be-all of philosophy but through a lack of imagination (and simply paying attention to other philosophical traditions).

If you've managed to read all of this, I greatly appreciate your time...

No worries. Stick around. Post. Participate. There's a lot of good contributions and well-educated contributors here, but (caveat emptor, there's also a fair amount chaff).

Answer 2

Reality, from a realist perspective, is just what exists, independently of us observing it. It doesn't operate under a logic, though it may be possible to describe it using the help of a logic. Fundamental physics does a pretty good job of representing how the universe works using equations. But scientific equations do not tell the universe what to do: they are human creations that we use to describe the universe. Similarly, logics are human creations that we use to represent structures and relationships.

When you ask about a logic of reality, we could perhaps understand this as asking, Is there a single logic that is adequate for the purposes of representing all of scientific knowledge? Maybe. Classical logic goes a long way, though as you say, we struggle to express quantum theory. Some have suggested using a quantum logic for this purpose, though it has not proved popular.

Systems of logic provide frameworks for representing propositions and the relations between them. They allow us to formalise propositions and arguments so that they can be more easily assessed as to whether the arguments are valid or invalid. Such systems do not necessarily represent how humans think, though they may serve a purpose in helping to justify the conclusion of an argument. The study of how humans think and reason lies within the realm of cognitive psychology rather than logic.

How human beings reason, draw inferences and update their beliefs has been studied extensively by cognitive psychologists for many decades. After all that work, there is no consensus among researchers on the subject. Some hold that people use mental rules akin to natural deduction rules. Others that people use mental models. Others that people make comparisons with paradigm cases. A popular view at present is that many people reason by performing something similar to Bayesian updating.

The fact that there is no consensus suggests that different people reason in different ways, so it may be futile to expect a one size fits all account of human reasoning. That said, there is a project to develop a logical model of a rational agent. It is described in a paper by Gabbay and Woods. I am pretty skeptical of such a project, but Dov Gabbay is one of the foremost logicians in the world, so I'm happy to cut him plenty of slack.

As you suggest, representing how humans reason may involve probabilistic and paraconsistent logics. Gabbay and Woods also mention non-monotonic logics, default logics, multi-dimensional logics and substructural logics. Such logics are commonly used for knowledge representation in artificial intelligence applications. The question of why there are so many logics and how they can coexist is an issue in the philosophy of logic.

Incidentally, as a matter of terminology, we do not say of an argument that it is false. If the conclusion does not follow from the premises the argument is invalid and if any of the premises are false the argument is unsound.

Dov Gabbay and John Woods, "The New Logic", Logic Journal of the IGPL, Vol. 9, No. 2, pp. 141-174 (2001).

Answer 3

On the "description of human reason" side of things, there's the defeasible-reasoning research program to consider. This is related to logics of belief revision and dialogical or dynamic epistemic logics. (One could also think through e.g. fuzzy logic in this connection.)

On the metaphysical side of things, analysis of logic's relationship with ontology (c.f. the matter of "logical truth") has included reflections such as:

One way to understand logic is as the study of the most general forms of thought or judgment... And one way to understand ontology is as the study of the most general features of what there is... Now, there is a striking similarity between the most general forms of thought and the most general features of what there is. Take one example. Many thoughts have a subject of which they predicate something. What there is contains individuals that have properties. It seems that there is a kind of a correspondence between thought and reality: the form of the thought corresponds to the structure of a fact in the world. And similarly for other forms and structures. Does this matching between thought and the world ask for a substantial philosophical explanation? Is it a deep philosophical puzzle?

To take the simplest example, the form of our subject-predicate thoughts corresponds perfectly to the structure of object-property facts. If there is an explanation of this correspondence to be given it seems it could go in one of three ways: either the form of thought explains the structure of reality (a form of idealism), or the other way round (a form of realism), or maybe there is a common explanation of why there is a correspondence between them, for example on a form of theism where God guarantees a match.

But the SEP article goes on to observe that, "Whether or not there is a substantial metaphysical puzzle about the correspondence of the form of thoughts and the structure of reality will itself depend on certain controversial philosophical topics. And if there is a puzzle here, it might be a trivial one, or it might be quite deep. And as usual in these parts of philosophy, how substantial a question is is itself a hard question."

Answer 4

Wow that's a long question!

Models of reality, are always going to be limited simplified subsets, usually gigantically so. You are mistaking the map for the territory.

Axioms and proofs, apply only within a specified system of abstractions. Proof is for math. Physics is about evidence. Axioms can never prove themselves, there must always be an implied system outside of what is axiomatised, that chooses the axioms. See the problems with a Foundationalist approach to knowedge summarised in Munchausen's Trilemma. Consider the alternative of a Coherentist approach, that we make an interconnected web of facts, which circle back to bear on each other.

We can understand 'true' as originating in when expectation matches what happens. Discussed in this answer: Why is a measured true value “TRUE”? Then the metaphor, the language-game of 'true vs false', is extended into all kinds of abstractions.

Implying reality must somehow have logic from which it arises, rather than logic arising or emerging from it, is very like the Mathematical-Platonist assumption that math must somehow be 'more real' than what it is abstracted from. See the problems with that discussed here: The Unreasonable Ineffectiveness of Mathematics in most sciences

I would describe logic as about drawing out what can be inferred from what has already been said, if being consistent by certain standards. That isn't truly modelling reality, but instead bringing consistency to our thinking.

I would look to intersubjectivity, as more fundamental to how we model reality, and underlying all language including logic and math: According to the major theories of concepts, where do meanings come from?