Subjective and objective philosophy

By subjective philosophy, I mean philosophy which sees itself as basically engaged in a project of thinking about people and their experiences. In other words, subjective philosophy self-consciously reflects and portrays the self-perceived nature of people, and inevitably the self-perceived nature of the philosophers themselves.

By objective philosophy, I mean philosophy which sees itself as basically engaged in a project of describing how the world really is, and (optionally) how people really are.

In the term subjectivism, I mean to include all schools of philosophical thought which are biased towards subjective philosophy.

In the term objectivism, I mean to include all schools of philosophical thought which are biased towards objective philosophy.

Philosophy can be both objective and subjective. The two categories are not mutually exclusive. Furthermore, I’m not saying that all philosophy falls into at least one of the two categories; maybe there’s philosophy which is neither objective nor subjective.

Metaphysical naturalism, a.k.a. scientific materialism, is an objectivist school of philosophical thought which is popular among the academically schooled humans of Earth in 2017. Metaphysical naturalism purports that the things that really exist are the things which figure in the theories of natural science. These theories are either the theories of the natural science of today, or the theories of some hypothetical completed natural science.

Ayn Rand is a prime example of an objectivist philosopher. She originally coined the term Objectivism. I don’t think that Ayn Rand meant the term “Objectivism” in the same sense I define the term “objectivism.”

Existentialism is a school of largely subjective philosophical thought which is popular among the academically schooled humans of Earth in 2017. Existentialists are often concerned with examining how humans look at themselves, their lives, others, and the world. This includes how our environments and our choices affect our concepts of self, life, others, and world. Existentialists commonly believe that life has no inherent meaning but humans can choose what their lives mean to them.

Postmodernism is a school of subjectivist philosophical thought which is popular among the academically schooled humans of Earth in 2017. Postmodernist philosophers (not all of them, I assume) seek to explain human ideas by explaining how those ideas arise in the context of humans’ psychologies and social lives, and considering what purposes the ideas serve for the humans who hold them. This type of project has sought to undermine the claim to objectivity of ideas in fields such as science and history. For example, see Michel Foucault in The Archaeology of Knowledge.

One can find simpler examples of subjective philosophy throughout culture. For example, consider the idea that it is wrong to say things which make people feel uncomfortable. This is a subjective ethical principle, because it bases ethical judgments on people’s subjective feelings of discomfort.

Immanuel Kant is an interesting example to look at. Kant (e.g., in his Critique of Pure Reason) is a skeptic about objective reality. Kant doesn’t think humans can ascertain how things in themselves are. He says that’s because our contact with objective reality is always mediated by perceptions, which are mental constructs.

Kant’s skepticism about objective reality is interestingly combined with what can appear to be a rather naive objectivism when it comes to his own psychological theories. The Critique of Pure Reason is mostly a treatise on psychology, describing the structure and features of the human mind. The theory is quite detailed. It looks to me Kant thinks his theory is objectively true for all humans and perhaps for all minds. For example, Kant writes:

For there is no other function or faculty existing in the understanding besides those enumerated in that table.

Source: Critique of Pure Reason. Translated by J.M.D. Meiklejohn (1784). Published by Barnes & Noble, Inc. (2004). Part II, §6, p. 37.

My reading of Kant is that he thought of his psychological theories as objective and true for all humans. Let me know if you have evidence against that reading.

Ludwig Wittgenstein’s Tractatus Logico-Philosophicus is an example of a text with major subjective and objective concerns. In it Wittgenstein is concerned with describing how language depicts the world: an investigation of how subjects relate to objects by studying the objective intermediary of language. Wittgenstein is also concerned in the Tractatus with demonstrating the distinction between that which can and can’t be expressed. In the Tractatus, that which can’t be expressed includes “the mystical,” which is of course subjective. Quoting Wittgenstein in the Tractatus:

6.51. Scepticism is not irrefutable, but palpably senseless, if it would doubt where a question cannot be asked. For doubt can only exist where there is a question; a question only where there is an answer, and this only where something can be said.

6.52 We feel that even if all possible scientific questions be answered, the problems of life have still not been touched at all. Of course there is then no question left, and just this is the answer.

6.521 The solution of the problem of life is seen in the vanishing of this problem.

(Is not this the reason why men to whom after long doubting the sense of life became clear, could not then say wherein this sense consisted?)

6.522 There is indeed the inexpressible. This shows itself; it is the mystical.

Objectivist and subjectivist philosophers have had a lot of division. For example, see Ayn Rand’s attack on subjectivism in the final chapter of Introduction to Objectivist Epistemology. There she writes:

The crass skepticism and epistemological cynicism of Kant’s influence have been seeping from the universities to the arts, the sciences, the industries, the legislatures, saturating our culture, decomposing language and thought.

In the history of philosophy — with some very rare exceptions — epistemological theories have consisted of attempts to escape one or the other of the two fundamental questions which cannot be escaped. Men have been taught either that knowledge is impossible (skepticism) or that it is available without effort (mysticism). These two positions appear to be antagonists, but are, in fact, two variants on the same theme, two sides of the same fraudulent coin: the attempt to escape the responsibility of rational cognition and the absolutism of reality — the attempt to assert the primacy of consciousness over existence.

To speak in generalizations, objectivism (in my sense, not the Randian sense) and subjectivism have the following dynamics.

  • Objectivism accuses subjectivism of arrogance, narcissism, or romantic weak-mindedness, for placing the self at the center of philosophy.
  • Objectivism holds itself superior for its focus on reality and its practical successes.
  • Subjectivism rasies skeptical challenges to objectivism. Subjectivism accuses objectivism of arrogance, for claiming too much insight into the real world.
  • Subjectivism accuses objectivism of being unconscious of the self’s degree of influence on philosophy.

These generalizations of course do not apply at all times or to all subjectivist or objectivist philosophies.

To put it simply, objectivism looks down on subjectivism for its self-conscious indulgence of humanness, whereas subjectivism accuses objectivism of being unconscious of its own indulgence of humanness.

“Objectivism vs. subjectivism” is not a war to be won by one side. There is no single issue at stake in the dynamics between objectivism and subjectivism. I can’t envision what a comprehensive answer to the “objectivism vs. subjectivism” question would be. I don’t think there’s just one question.

My philosophy has often been about bringing together objective and subjective philosophical threads in some coherent way. For example, I have for about seven years been concerned with the problem of reconciling rationality and mysticism. I have shared thoughts about this problem in my books Eh na? and Winning Arguments, and in my posts on neosocratic.net.

Rationality is first and foremost an objective philosophical paradigm, whereas mystical philosophy is a highly subjective philosophical paradigm. It is hard to make rationality and mysticism play nicely together. I would like to be able to point you to a nice overview of how I make them work together in my thinking, but it doesn’t exist yet. Stay tuned.

Objectivism was the prevailing philosophical mentality in my formal education. My professors were mostly just concerned with describing reality as it actually is independent of human sentiment and opinion. Even when studying humans, as in my Psychology courses at Arizona State University, my professors focused on objective studies, facts, and figures, most of the time studiously neglecting anything subjective.

This struck me as a backwards way to approach studying ourselves. To me it’s clear that much more can be learned about humans by thinking and talking, as opposed to studying human behavior in artificially limited experimental circumstances which are usually designed to demonstrate a pre-determined conclusion via statistical methods that are often flawed. Of course there are highly informative experiments in psychology, but in my opinion they are the exceptions, not the rule.

I think my experience with the Arizona State University Psychology Department exemplifies the extreme degree of intellectual aversion to the subjective which is prevalent in much of academia.

It has been personally challenging for me to publicly advocate unpopular subjective philosophical ideas, as I have done and am preparing to do further. A lot of my challenges have been caused by cognitive dissonance from the clash between subjective thinking and the ways of thinking I developed from my objectivist academic education.

I am interested in subjective philosophy centrally because I believe that it is very beneficial for us to exercise judgment in how we think about ourselves, how we think about others, and how we think about ourselves in relation to each other and the world, I think a great deal of human potential can be unlocked by thinking about these topics in more constructive ways. We humans are relying on numerous failing patterns of thought, feeling, and mentation, particularly in the areas of self and other. It is important to consider that we can choose how we think around these topics, and that the choices we make have effects on our personal and social realities.

In short, some of the most important philosophical issues are deeply personal and subjective in nature. I think it’s essential for philosophy as a whole to embrace the mysteries of subjectivity deeply and completely as possible. Equally, I think it’s essential for philosophy as a whole to embrace the mysteries of objective reality deeply and completely as possible.

Mystical philosophy is an especially problematic form of subjective philosophy. It can be accused of asserting the primacy of consciousness over existence, as Ayn Rand did. More sharply, one can accuse mysticism of asserting the primary of mystical consciousness over other forms of consciousness and existence, when it comes to discerning truth. Basically, mystical philosophy can be viewed as being supremacist, in a bad way, putting some forms of consciousness over others. That thought has been a source of a lot of cognitive dissonance for me. Here’s what I say about it.

Truth can be perceived and talked about. Generally, conscious perception of a truth precedes talking about it.

It is undeniable that some forms of consciousness are more likely than others to be correlates of true perceptions of a given kind of truth.

For example, the consciousness of a sober, sane, awake adult human will yield perceptions of their immediate physical surroundings which are reliably true. Humans make errors in perception, but our sensory perceptions are typically accurate to reality.

On the other hand, schizophrenic psychosis frequently involves hallucinations and delusions: highly convincing perceptions of phenomena that are not real. (If the phenomena are real, then the diagnosis of hallucination or delusion is mistaken.)

Unlike the consciousness of a sober, sane, awake adult human, the consciousness of a schizophrenic is not a reliable correlate of true perceptions.

To give another example, the consciousness of a professional mathematician is a far better tool for discerning mathematical truths than the consciousness of somebody with no training in math.

It is not necessarily an attractive reality that some forms of consciousness are better than others as correlates of true perceptions. It is, however, a reality.

Whereas I think the examples of the schizophrenic and the mathematician will arouse little controversy, there is much more basis for controversy about whether mystical consciousness is a usual correlate of true perceptions. This is a matter of opinion. People are free to reject the point of view that mysticism is a source of truth, and I’m not aware of any general way to talk people out of the point of view that mystical consciousness is a variety of true perception.

Nonetheless, I believe that mystical philosophy has the potential to help people to unlock their inner potentials. I believe I have witnessed how mysticism has helped to bring depth and energy to my consciousness. I have attempted to demonstrate this energy and depth in my philosophy (to what success, the reader to judge). I feel an urgency from a service to others perspective to create new and useful mystical philosophy to share with others.

To balance these conflicting concerns, I think it’s useful to say that anybody who isn’t interested in mystical philosophy should ignore it. I also think it’s useful to say that the recognition of truth in mystical philosophy is rooted in subjective perception. Therefore if an idea in mystical philosophy doesn’t resonate with you, let it be, leave it behind.

I think this idea can be extended to subjective philosophy in general. The standards of evaluation are generally subjective. People’s perceptions of subjective philosophy are informed by their personal biases. Depending on people’s biases they will resonate differently with different subjective philosophies. A philosophy that is healthy food for one person might be harmful food for another.

With objective ideas, there is the hope that expert consensus can cause true ideas to spread throughout the population. This dynamic makes most participants passive consumers of truth, with the responsibility for discerning truth resting with experts.

Especially with subjective philosophy, in my opinion there is the need for the responsibility for discerning and finding truth to rest more with each individual. Everybody will resonate differently with different ideas, and there are a lot of different ideas to choose from, so that we only have time for a small fraction of them. We can derive many different kinds of value from ideas, we all want different things, and there is room for all of us to make our choices.

The most informed and intellectually responsible people about a topic think for themselves about the topic. The idea of thinking for oneself can be opposed to the idea of trusting experts and authorities. Trusting experts is generally a better tactic when one is relatively uninformed and appropriate experts exist. On some subjects, such as various philosophical subjects, one may contend there are no experts. Where there are no experts, intellectual responsibility necessarily devolves to each of us.

I think that mysticism is one of the areas where there are no experts. Or, more modestly, unthinkingly trusting experts won’t take you on a very informative journey with mysticism, because a non-expert in mysticism has no real hope (in my opinion) of discerning who might be an expert in mysticism vs. who is a mere performer or a mere academic without deep experiential understanding of mysticism.

I think the same goes for subjective philosophy more generally. There are no experts on it. Or, more modestly, expertise in subjective philosophy is in the eye of the beholder. It’s an open playing field. The game is whatever you want it to be.

Are philosophers arrogant?

Is it inherently arrogant to be a philosopher? I think maybe so. I think arrogance is a tendency philosophers should push back against in themselves, but I suspect it is inherent in the activity of philosophy anyway.

Maybe it’s inherently arrogant to think you can say something true, new, and useful about topics which have confounded humans and remained mysterious for all of recorded history.

Let’s analyze more carefully. For starters, what do I mean by “philosopher,” and what do I mean by “arrogant?”

In the past, people (e.g. Isaac Newton) did not draw clear distinctions between philosophy, science, and magic; these concepts were somewhat rolled together into one.

Historically, “philosophy” encompassed any body of knowledge.

In the 19th century, the growth of modern research universities led academic philosophy and other disciplines to professionalize and specialize.

Wikipedia

With the rise of the modern university system, there was a shift in the meaning of “philosophy.” The term went from referring to intellectual studies in general, to referring to a specific area of study, the area studied by philosophy departments in universities.

Basically, it seems to me that the department of philosophy in a university is the department which studies all the questions which aren’t the kind of question addressed by any other department.

Academic philosophers don’t answer questions of physics, biology, history, etc. Academic philosophers study a “miscellaneous” category of questions, which includes most of humanity’s deepest and most intractable intellectual mysteries. The category includes many questions which people have asked for all of recorded history without arriving at any agreed upon answers.

For this post I’ll assume that philosophers are people who ask and try to answer big questions, which can’t be answered by any established methodology in academia, and which relate to perennial intellectual mysteries. Is it inherently arrogant to engage in such activity?

What do I mean by “arrogant?” Here are some dictionary definitions I looked up:

  1. having or revealing an exaggerated sense of one’s own importance or abilities.” (Google)
  2. “exaggerating or disposed to exaggerate one’s own worth or importance often by an overbearing manner” (Merriam-Webster)
  3. “Someone who is arrogant behaves in a proud, unpleasant way toward other people because they believe that they are more important than others.” (Collins Dictionary)

Do philosophers necessarily meet any of these definitions?

I’ll set up a case which tries to maximize the likelihood of not meeting these definitions. Let’s consider a philosopher who says something like this:

I am interested in big questions which have confounded humans as long as we can remember. I don’t believe that I myself can answer these questions definitively, but I believe that humanity as a whole can deepen our understanding around these questions. I believe that I can build on the work of past philosophers, and perhaps help out future philosophers, towards furthering humanity’s progress around these questions.

This philosopher’s assumptions could be questioned. Maybe philosophy does not progress in the way the philosopher says it does. Maybe philosophers across history wander from opinion to opinion in an overall aimless way, always arrogantly viewing the opinions of the day as the pinnacle of human understanding.

Though the premise can be doubted, I would say it’s not arrogant to believe that humanity deepens its philosophical understanding over time, because this is a belief about humanity, not about oneself in particular.

Is it arrogant to believe that one can potentially help with humanity’s philosophical progress? If you accept the premise that many people have already done so, I would say not. It may be arrogant to think you can help with humanity’s philosophical progress if you’ve put no effort into training yourself as a philosopher (such as by studying what philosophers have said in the past). But somebody who has trained as a philosopher is not necessarily arrogant to suppose they may be in a position to contribute to humanity’s philosophical progress.

It might seem, then, that the statements above could be the statements of a non-arrogant philosopher. Of course a philosopher could say these things and still be arrogant. Yet there seems to be nothing inherently arrogant about this philosopher’s expressed attitude towards philosophy.

Let’s examine further, though. Maybe philosophers are necessarily arrogant whenever they stake claims. The complexities in philosophy are such that it is fundamentally hard to tell when a claim is justified. Perhaps, then, making any kind of general statement in philosophy is always hazarding a guess, and always implies the arrogance of jumping to a conclusion. Yet a philosopher who never staked any claims would arguably not be much of a philosopher. Perhaps for this reason doing philosophy is inherently arrogant.

It would be arrogant of me to assert positively that there can never exist a non-arrogant philosopher. I believe it would be arrogant of me to deny that I myself am an arrogant philosopher. I am not familiar with any philosophers who I am satisfied to call non-arrogant. I am inclined to accept the generalization, “philosophers are arrogant.”

I believe that arrogance is an important tendency for philosophers to push back against in ourselves. Jumping to conclusions is a good way to be wrong. Much of the challenge and reward of philosophy is found in unpacking the subtle moving pieces of our thoughts, teasing apart distinctions, and uncovering fallacies which we have unconsciously passed over.

The principal antidote for intellectual arrogance is intellectual humility. Intellectual humility, in my opinion, requires acknowledging that my perspective has deficiencies I’m not yet aware of, and others’ perspectives basically always have at least some merit.

For me, intellectual humility entails that if I am going to make positive assertions, then first I must take apart my thoughts and rigorously look for defects, and I must hear others’ points of view on the questions I’m asking. These steps are important counter-measures against the negative consequences of intellectual arrogance.

Yet, even if I take these counter-measures, it doesn’t obviate my worry that I am arrogant or can be viewed as arrogant in virtue of doing philosophy. I do still suspect that arrogance is the perennial condition of a human philosopher. Maybe the time we have in life is too limited to think issues through to the extent that our philosophical statements can be considered so cautious that it is not arrogant to hazard making them.

I see great value in doing philosophy. I think it is very important for the future of humanity. Because I love philosophy more than I love having a squeaky clean public image, I am willing to expose myself to ridicule by publicly exhibiting arrogance for the sake of philosophy. Those who don’t like what I’m doing are entitled to ridicule me for it. I’m writing, with the hazard of attracting ridicule, for the sake of people who may find what I’m doing helps them with their projects and problems.

Still, you might ask, if doing philosophy is arrogant, and arrogance is wrong, then how can it be a good idea to do philosophy? As far as I can see, this question only arises if you assume a perfectionist attitude about morals. A perfectionist attitude about morals would say that behavior must be free of moral flaws in order to be moral. This is not a realistic perspective on morals.

So, maybe the activity of philosophy has embedded in it an inherent moral flaw, arrogance. If so, that does not mean that philosophy is not a morally good activity to engage in. It means that philosophy is a morally imperfect activity. In a world where moral imperfection is ubiquitous, if not universal, this is hardly much of an argument against philosophy, at least if you think that philosophy has enough positive value to counter-balance its moral imperfections.

Paradoxes and the rules of logic

Consider the statement “this statement is false.” Is it true or false? Some reflection will show that if it’s true, then it’s false, and if it’s false, then it’s true. What should we make of that? Is it both true and false? Or else what’s going on?

This is a classic logical problem known as the “liar paradox.” The liar paradox, and paradoxes like it, have been subject to immense philosophical attention stretching back thousands of years.

In this post I’m going to present a solution to this classic problem. In a nutshell, I say, ignore it, like almost everybody does. The length of the post is spent in making this solution rigorous and explaining the basis of my opinion that this is the best way of solving the liar paradox and similar paradoxes, for most purposes.

The workings of the solution lead to a picture of logic which is potentially surprising and new to people. In this picture, the rules of logic have exceptions, the rules of logic are subject to legitimate subjective differences of opinion, and the rules of logic are not completely rigorous and formal, but are made up as we go along to at least some extent. In the course of the work I hope to convey a deeper explanation of this picture.

I’m not trying to provide a full picture of how the practice of logic should work under the assumption that the rules of logic are not completely rigorous and formal. I’m providing a solution to paradoxes which exploits that assumption. I hope for other work which builds out a bigger picture of how logic can work when it’s not completely rigorous and formal. I have sketched only a little fragment of what I imagine to be a big space of potentially interesting problems and solutions.

 

The problem

In this post, by “paradox” I will mean, “an argument which proceeds from apparently true premises to a contradictory conclusion.” A contradictory conclusion is a statement of the form (P and (not P)), asserting that a statement P is both true and false.

Here is an example of a paradox: the liar paradox. Consider the statement “this statement is false.” I’ll refer to this statement as L. If L is true, then L is false. If L is false, then L is true. L is either true or false. Therefore L is true and L is false, or in other words, (L and (not L)) is true. The preceding argument, which I call the liar paradox, has a contradictory conclusion, so it is a paradox.

Other examples of paradoxes include Russell’s paradox and the Sorites paradox. In this post I will focus mainly on the liar paradox as a chosen example of a paradox.

This post explains a general method of solving paradoxes.

What does it mean to solve a paradox? Every paradox presents a problem: it appears to imply that something false is true, which is impossible, at least on a traditional understanding of logic. Nothing impossible can occur, but paradoxes appear to be cases where something impossible occurs. In that sense, paradoxes are intellectual, theoretical problems. To solve a paradox is to solve this problem, for example by pointing out which of the paradox’s premises are not true, or by explaining why its conclusion does not follow from its premises.

 

This theory, this post, and their history

I don’t claim the theory I’m giving is fundamentally new. I think it is basically a technical extrapolation of the common way of responding to paradoxes like the liar paradox, according to which these paradoxes can safely be ignored.

I didn’t base this theory on anybody else’s work.

I first described this post’s method of solving paradoxes in my book Winning Arguments. This post aims to describe the method in a quicker and more surveyable way, putting together thoughts that are scattered throughout a wide span of text in Winning Arguments.

This post is aimed at a general philosophical audience. It is not very technical and it doesn’t engage deeply with the scholarly literature on paradoxes. There are over 2,000 scholarly works about the liar paradox cited on PhilPapers. This post talks about one solution to the liar paradox, which is in competition with a huge number of solutions discussed in the weighty corpus of paradox research. I have kept the comparison with competing solutions brief and superficial, relative to the extent of the literature.

I studied the topic of paradoxes in the University of Connecticut Philosophy PhD program, where I learned about paradoxes among lovely and intelligent philosophers including, for example, world paradox experts Jc Beall and David Ripley. I published research related to paradoxes in two of the top journals related to the topic: the Journal of Philosophical Logic and the Review of Symbolic Logic.

The solution to paradoxes which I’m describing in this post is something I began conceiving around 2011, during my undergraduate studies at Arizona State University. I have been developing the idea since then. By the time I left UConn in 2015, I had all the pieces of the theory conceived. It took me until 2017 to put the pieces together, to believe the resulting theory, and to put it down in writing.

This post does not provide my full theory of paradoxes. It only provides the first piece of the theory. This piece of theory is called the ad hoc method of rejecting incorrigible paradoxes, or the ad hoc method, for short.

The ad hoc method deals only with the technical aspect of solving paradoxes. The other part of the theory, to come in a later post, deals with the more philosophical question of why paradoxes happen and how we can explain them.

 

Summary of the ad hoc method of rejecting incorrigible paradoxes

Some arguments have apparently true premises and contradictory conclusions, but some of their premises, though apparently true, are false. An appropriate method of solving such paradoxes is to identify which of the premises are false.

In contrast, this post is mainly concerned with incorrigible paradoxes. An incorrigible paradox, by definition, is an argument which leads from true premises to a contradictory conclusion via correct rules of deductive logical inference.

The notion of an incorrigible paradox is implicitly relative to: (a) some language in which arguments can be formulated, (b) some opinion about what rules of deductive logical inference are correct, and (c) some opinion about what statements are true. You will get different, sometimes irreconciliable notions of what constitutes an incorrigible paradox by starting from different choices of (a), (b), and (c).

If a paradox is not incorrigible, then either it has at least one false premise, or its conclusion does not follow logically from its premises, and solving the paradox is a matter of finding a false premise or using logical methods to demonstrate that the conclusion doesn’t follow from the premises.

If a paradox is incorrigible, then the ad hoc method of rejecting incorrigible paradoxes recommends rejecting the conclusion of the paradox and all further inferences from it, understanding this rejection to be an ad hoc modification/exception to the rules of logic one employs.

 

Assumptions

The notion of an incorrigible paradox is implicitly relative to some language, some opinion about what rules of logical inference are correct, and some opinion about what statements are true.

In this post, I’m going to choose English as the language in which arguments can be formulated.

I’m going to assume that the rules of classical logic, as described for example by the system LK, are correct rules of deductive logical inference.

I’m going to assume a lot of common sense about what’s true. I will assume that the following statements, which I construe as premises of the liar paradox, are true:

  1. The statement L = “This statement is false” is an English statement.
  2. If L is true, then L is false.
  3. If L is false, then L is true.

From these premises it follows by the rules of classical logic that L is true and L is false, and that (L and (not L)) is true.

The rules of classical logic are always described relative to some formal language, such as the language of first-order logic used in the system LK. In this post I’m assuming the rules of classical logic can be construed as rules governing use of the English language.

Since English isn’t based on a set of precise rules that cover all cases, it is practically impossible to give a precise description of the rules of classical logic as they apply to English.

When logicians apply the rules of classical logic to English, they generally rely on a precise understanding of the rules of classical logic as understood through some formal description such as the system LK, and on a more artistic understanding of how to translate between English and a formal language such as first-order logic. This mapping between English and the formal language yields an imprecise method for applying the rules of classical logic to English. This imprecise method is precise enough to be unproblematic for typical purposes, and for our purposes.

According to the assumptions of this post, an incorrigible paradox is an English-language argument whose premises are true and whose conclusion follows from the premises by the rules of classical logic. By assumptions, the liar paradox is an example of an incorrigible paradox.

The solution to paradoxes of this post will work for basically any choice of language, rules of logic, and concept of truth. The assumptions of this post, as described in this section, are primarily for the purpose of making the discussion concrete. If you dislike the assumptions chosen in this section, you can still use the solution to paradoxes I’m describing, replacing English with your language of choice, replacing classical logic with your logic of choice, and using your choice of assumptions about what statements are true.

 

The ad hoc method of rejecting incorrigible paradoxes

To solve any paradox by the method this theory prescribes, you start by determining whether or not the paradox is incorrigible. This requires answering two questions: whether the premises are true, and whether the conclusion follows logically from the premises. Answering whether the conclusion of an argument follows from the premises by the rules of classical logic is basically a routine process if you are familiar with appropriate techniques. Answering whether the premises are true is in general more complex, and I don’t provide any general method for doing that.

If you show that a paradox is not incorrigible, then you’ve solved the paradox. Either you’ve shown that its premises or not all true, or you’ve shown that the conclusion doesn’t follow logically from the premises. Either way, you’ve shown that there is no problem.

If your analysis concludes that a paradox is incorrigible, then the next step of the method is to reject the conclusion of the argument. One makes the stipulation that the paradoxical argument is to be rejected, even though its premises are true and its logical inferences are valid. This is an ad hoc modification/exception to the rules of logic which one employs.

One ends up having not only positive rules of logic, according to which certain inferences are correct, but also negative rules of logic, which supersede the positive rules by stating that inferences which are valid in general are invalid in some particular cases (the cases of incorrigible paradoxes).

This method leaves the rules of logic one employs perpetually incomplete. If you employ this method, then the rules of logic you follow are unlike (for example) the rules of the system LK in that you lack a precise and complete description of the rules of logic you follow. If you employ this method, then you have the expectation that if you encounter new incorrigible paradoxes in the future, then you will need to extend the rules of logic you employ, by adopting new negative rules to block the new incorrigible paradoxes.

In classical logic, it is possible to infer any statement from a contradiction. If you can infer a statement of the form (P and (not P)) from a given set of premises, then you can infer any statement whatsoever from those premises. This is called the principle of explosion.

Because of the principle of explosion, the ad hoc method of rejecting incorrigible paradoxes also involves rejecting any variants on a paradoxical argument which can (in other variations) be used to prove any statement. For every argument whose conclusion is a contradiction, there are many variations with conclusions including all statements. All such variants are rejected, in the method.

People may arrive at differing results by this method. Differences on what constitutes an incorrigible paradox may arise from different opinions on what rules of logic are correct, different opinions on what statements are true, and different judgments about what constitutes a variation on an incorrigible paradox, among other possible sources of differences. Different judgments about what constitutes a variation on an incorrigible paradox may arise because I don’t offer any general method for making such judgments; rather, I assume there to be some ineliminable element of artistry involved in making such judgments. This assumption is justified later.

These sources of potential variability in people’s results from this method may be viewed as a consideration against the use of this method. Of course, people arrive at different results in reasoning due to all kinds of causes. I view the mentioned consideration against this method as a valid one, to be weighed against other considerations (and of course I believe this method has considerations in its favor that outweigh the considerations against, for general purposes).

According to the ad hoc method of rejecting incorrigible paradoxes, one augments the rules of logic one follows on an ad hoc basis by adding negative rules which exclude the inferences to the conclusions of incorrigible paradoxes. One does this as needed. One also rejects all variations on incorrigible paradoxes which can be used (in further variations) to prove arbitrary statements. I don’t provide strict rules on how to draw the line between such variations on incorrigible paradoxes, and other arguments; I assume there is an ineliminable element of artistry in drawing the line. In other words, I assume that the technique of drawing the line can’t be made completely formal.

Some appropriate questions:

  1. How does the ad hoc method of rejecting incorrigible paradoxes compare to other ways of solving paradoxes? Why use this method over competing methods?
  2. What’s the reason for the assumption that there is an ineliminable element of artistry in identifying variations on incorrigible paradoxes which can be used (in further variations) to prove arbitrary statements?
  3. What are the risks involved in using the ad hoc method of rejecting incorrigible paradoxes?
  4. Is there any intuitive picture that explains why this method is correct?

Subsequent sections will speak to these questions. Here is a summary of the subsequent sections.

 

Non-classical logic and its successes and limitations with paradoxes reviews some of the successes and limitations of some competing approaches to solving paradoxes, which are based on restricting the rules of classical logic in some formally defined way, in the form of a so-called non-classical logic. This section looks (in a very high level way) at the pros and cons of approaches using non-classical logic, as compared to the ad hoc method of rejecting incorrigible paradoxes. This section speaks to questions 1, 2, and 3.

Implications for reasoning talks at a high level about how this approach to paradoxes works in the context of everyday practical reasoning. This section speaks to question 3.

Implications for math talks at a high level about how this approach to paradoxes works in the context of math. This section speaks to question 3.

I will speak to question 4 in a subsequent post.

 

Non-classical logic and its successes and limitations with paradoxes

Classical logic is the prevailing perspective on logic. Classical logic is a system of rules of inference, which exists in many variants, and which is used, taught, and studied far more often than any other paradigm of rules of logic.

A non-classical logic is any system of rules for logical reasoning which is not a form of classical logic. Non-classical logics are a huge and diverse category. PhilPapers cites over 6,000 works on non-classical logics.

An early and important type of non-classical logic is intuitionistic logic. Roughly, this is the logic you get by removing from classical logic the principle that every statement is either true or false.

Another important type of non-classical logic is relevance logic. Systems of logic known as relevance logics aim to disallow inferences known as “paradoxes of relevance,” such as the inference (valid in classical logic) from the premise “the sky is blue” to the conclusion “if the sky is red then the sky is blue.”

Neither intuitionistic logic, nor most relevance logics, solve the liar paradox and similar paradoxes.

I’ll focus on two categories of non-classical logics which get traction in solving paradoxes such as the liar paradox. These are paraconsistent/paracomplete logics, and substructural logics.

As far as I’m aware, these are the best studied categories of paradox-solving logics, with no competing categories of comparable prominence in the academic literature. Each of these categories includes many different formal systems of logic, and the literature around each of them is extensive and technical. I’ll only provide a very high-level survey of what is going on in these subfields of logic, without going into technical details about any of the systems.

For a more detailed survey of the topic of non-classical logics, I would recommend Graham Priest’s An Introduction to Non-Classical Logic. That book does not discuss substructural logics. For an entry point into the field of substructural logics, I would recommend Greg Restall’s article in the Stanford Encyclopedia of Philosophy. Now I’ll proceed to my nutshell survey of these fields.

A paraconsistent logic is a system of logic in which some statements can be both true and false, without every statement being true, and without every statement being false.

An example of a paraconsistent logic is LP, the Logic of Paradox. LP is a system of logic in which there are three possible “truth values:” true, false, and paradoxical (meaning both true and false). Every statement is either true, false, or paradoxical.

LP provides simple rules for determining the truth value of any statement as a function of the truth values of the sub-statements that make it up, provided one knows the truth values of the smallest sub-statements. For example, a sentence of the form “A or B” is has the following truth value:

  • “True,” if A is true and B is true.
  • “False,” if at least one of A or B is false and neither is paradoxical.
  • “Paradoxical,” if at least one of A or B is paradoxical.

Notice that these three possibilities cover all the possibilities, so that the truth value of “A or B” is always determined by the truth value of A, the truth value of B, and the given rules.

LP is similar in design to classical logic, but in LP, you can let some statements be both true and false, without all statements being so. LP allows this by having rules that are less restrictive than those of classical logic; they let you infer less from the same premises, so that in particular the principle of explosion is not valid in LP.

A major problem with LP is that its rules are too weak to allow the development of math in the usual manner of proving theorems from a limited set of axioms. I have proven facts about LP which illustrate this general phenomenon. That LP is too weak to allow the development of math in the usual manner is such a broad and imprecise statement that I doubt it can be stated completely and precisely, much less proven.

LP is an example of a paraconsistent logic, meaning it allows for true contradictions without every statement being true.

Moving on to another type of non-classical logic: a paracomplete logic is a logic in which some statements can be neither true nor false.

K3, or Kleene 3-valued logic, is an example of a paracomplete logic. In K3, there are three possible truth values: true, false, and neither. K3 has simple rules, exactly parallel to LP’s, for determining the truth value of any statement from the truth value of the statements making it up, provided one is given the truth values of the smallest statements.

Kripke’s “Outline of a theory of truth” is an example of applying K3 to solve paradoxes like the liar paradox. Kripke’s solution works as far as it goes, but it doesn’t go as far as giving an operational explanation of how to reason in the presence of paradoxes, and it’s not clear how to extend it to work for paradoxes of set theory such as Russell’s paradox.

In any case, K3 is an example of a paracomplete logic, one which allows for statements which are neither true nor false.

Some logics are both paraconsistent and paracomplete. FDE, or First-Degree Entailment, is a simple example. It has four truth values: true, false, both, and neither. It works like a fusion of LP and K3.

Substructural logics are another class of non-classical logics, usually defined in the form of a sequent calculus. A sequent calculus is a manner of defining a system of rules of logical inference. It is based on patterns called “sequents.”

A sequent is a pattern of the form “A1,…,An entails B1,…,Bm,” where A1,…,An is a sequence of zero or more statements, and B1,…,Bm is another sequence of zero or more statements.  Usually the word “entails” is written as a turnstile. A basic way of reading the sequent “A1,…,An entails B1,…,Bm” is as saying “if A1,…,An are all true, then at least one of B1,…,Bm is true.”

A sequent calculus tells you how to produce all sequents that are “valid,” by repeatedly applying a small set of rules. The system LK is an example of a sequent calculus, one which defines the rules of classical logic.

The system LK tells you what arguments are valid according to classical logic, if you can translate the arguments into the language of first-order logic. Take an argument to consist of one or premises A1,…,An, and a single conclusion B, with the claim being that the premises are true and B follows from them. Suppose A1,…,An and B are written in the language of first-order logic. Then the argument in question is valid according to classical logic, meaning its conclusion follows logically from its premises, if and only if “A1,…,An entails B” is a valid sequent in the sense that it can be produced according to the rules of the system LK.

Sequent calculi have rules known as “structural rules.” In the system LK, there are the following structural rules:

  • Weakening: If you add statements to the premise or conclusion side of a valid sequent, then you get another valid sequent.
  • Contraction: If a statement occurs repeatedly on the premise side or conclusion side of a valid sequent, then you can drop extra occurrences and still have a valid sequent.
  • Permutation: You can change the order of the premises and conclusions in a valid sequent, and get a valid sequent.

There is also the rule of cut, which is not always classified as a structural rule. It is harder to summarize, but you can look at it in Wikipedia’s presentation of LK.

Substructural logics are logics which relax/weaken some of the structural rules of a sequent calculus, with the system LK being a prototypical starting point.

One reason some people are interested in substructural logics is that some people see them as a promising avenue for solving paradoxes.

One example of an approach to paradoxes based on substructural logic is an approach advanced by Dave Ripley and others, articulated for example in Ripley’s paper Paradoxes and failures of cut. This approach starts with an LK-like sequent calculus, and removes the rule of cut.

This approach avoids the problem seen in the case of LP, that the weakening of logic makes too many things unprovable, so you can’t get things like math off the ground. It avoids the problem because the rule of cut is not necessary for the completeness of the system LK. One can remove the rule of cut from the system LK and exactly the same sequents are valid (derivable) in the resulting system. This is Gentzen’s cut elimination theorem. The catch is that sequent derivations not using the cut rule may need to be much longer than derivations of the same sequent using the cut rule.

The interesting observation is that by starting with this cut-free sequent calculus, one can add a concept of truth which gives rise to the liar paradox, without causing the system to explode the way that classical logic does. Ripley’s theory shows how to reason in the presence of the liar paradox, in a way that works and is operationally understandable.

Ripley has also applied his approach to other types of paradox, including paradoxes of vagueness and paradoxes of set theory. Perhaps it can be deemed a generally successful approach to paradoxes. In my opinion, the only part of Ripley’s approach that is not evidently successful is the approach to the paradoxes of set theory. It remains to be seen how capable Ripley’s set theory is of proving the usual theorems of math. Many failures and difficulties have been encountered in this area. Similarities between Ripley’s set theory and LP set theory may be a warning sign of limitations similar to those found in LP set theory. However, as far as I’m aware, it remains to be seen either way whether or not this set theory can be used effectively as a foundation for math. Resolving this uncertainty would shed light on how generally Ripley’s cut-free approach can be applied to solve paradoxes. Does it work on all the hardest paradoxes, or does it fail to apply to some of the hardest paradoxes?

I have discussed only a small and biased selection of approaches to solving paradoxes using non-classical logic. I have discussed each approach only to a superficial extent. We have only skimmed the surface of this subject. I, personally, have not read most of the academic literature on paradoxes. I am limited by the desire to keep this post’s length reasonable and this section not overly laborious or time-consuming for the reader.

Now I will make some general comments on how the ad hoc method of rejecting incorrigible paradoxes compares to approaches to solving paradoxes based on non-classical logic.

I am not aware of any approach to paradoxes based on non-classical logic which solves all of the hardest paradoxes, including the liar paradox, the Russell paradox, etc., which approach is uniform across such paradoxes, and which approach results in a method that is practically usable. I do not rule out the possibility that such an approach can be constructed. However, my own suspicion is that it won’t happen. My own suspicion is that the paradoxes are an intellectual trick of God which no finite system can completely contain or address. I have no proof of that opinion. My opinion is that the opinion can’t be proven, it can’t be proven that it can’t be proven, and so forth.

All currently existing non-classical logic solutions to paradoxes that I’m aware of, insofar as they are successful, are successful in a limited area. On the other hand, the method I’ve proposed can be applied uniformly to all paradoxes. I’m not aware of a non-classical logic approach to paradoxes which can claim the same.

All non-classical logic approaches to paradoxes involve the complexity inherent in non-classical logic. Learning how to apply the full formal rules of classical logic, as expressed e.g. through the system LK, is a lot to ask of people. Non-classical logics provide more stuff to learn, and they are usually more complex and/or less intuitive and/or harder to apply than classical logic. In most non-classical logic solutions to paradoxes I have seen, there is no clear idea of how to operationalize and apply the ideas. In the cases I’ve seen and can recall, when there is an idea of how to operationalize the solution in principle, there is still not a fleshed out idea of how to do it practically.

In contrast, the method I’ve proposed is easy to apply. Indeed, I think the ad hoc method of rejecting incorrigible paradoxes is the method which most people instinctively apply when presented with the liar paradox. The method is so easy to execute that it doesn’t even need to be taught.

Considering these things, I think it’s fair to say that from a practical perspective, the method I’ve proposed has distinctive advantages over non-classical logic approaches to paradoxes. I think most people will probably be sympathetic to my assessment that at least at this time, the method I’ve proposed is more suitable for most practical purposes, compared to non-classical logic approaches.

Where the non-classical logic approaches are better than the ad hoc method of rejecting incorrigible paradoxes is mainly in the theoretical qualities of exactness, formality, and certainty. The non-classical logic approaches provide systems of rules that are not ad hoc, but in principle handle all cases, in their domains of applicability. Meta-logical theorems can provide assurances that certain undesired outcomes will not result from applying the rules.

On the other hand, the method I’ve proposed is inherently inexact, and there is the possibility that applying it will fail to protect one from falsehoods that can be inferred from paradoxes, if one somehow unintentionally invokes a paradox in one’s reasoning. This is an area where non-classical logic approaches have the advantages.

In summary, the ad hoc method of rejecting incorrigible paradoxes has the advantages that it is easy to learn and apply and it works uniformly across all cases, whereas the non-classical logic approaches have the advantages of exactness, formality, and certainty.

The question becomes, which considerations are more important? This depends what is important to you.

If your interest in paradoxes is theoretical, and an exact solution to the problems is simply what you want, then you’ll deem that more important than ease of learning and having a general, easily usable solution on the table.

If you’re interested in this topic for some extrinsic reason, e.g. because you want to understand how to reason in general for all purposes, then you will likely favor the ad hoc approach I’ve presented, because you can apply it today to all your paradoxes. Naturally, it’s up to you how you approach these problems, and how much time you spend thinking about them. I would not discourage you from taking whatever approach to paradoxes seems to you to suit your goals.

In my view, the approaches to paradoxes based on non-classical logic have had such tough going because they are going against a general principle, one I call the law of no perfect system.

In general, the law of no perfect system is that there is no perfect system for doing anything. Whatever your problem is, if it’s above a certain level of complexity, then there is no finite and exact set of rules which solves the problem optimally in all cases.

As applied to this case, there is no perfect set of rules for logic which has everything it can correctly have and nothing else, defined formally and finitely.

Gödel’s first incompleteness theorem can be construed as the law of no perfect system as applied to axioms for math. It implies that there is no set of axioms for math, which can be listed by a computer program, which prove everything true and nothing false about math.

The law of no perfect system, as a general rule of thumb, tells you that it is proper for rules to have exceptions. Because no system of rules is able to handle everything, each particular situation should be considered as a particular situation where exceptions to rules might properly apply.

I think the general law of no perfect system is fairly common sense, but as applied to logic, it goes against the grain of the academic literature. I’m not aware of other defenses, besides the present one, of the law of no perfect system as applied to logic. Please let me know of any you’re aware of.

 

Implications for reasoning

What does the ad hoc method of rejecting incorrigible paradoxes have to tell us about general reasoning for practical purposes?

As far as I can tell, the theory has virtually no implications in this area. For practical purposes, people already reason as if they were following the ad hoc method of rejecting incorrigible paradoxes.

By using the ad hoc method, one accepts the possibility that one will be led from truth to falsehood by following the rules of logic, by stumbling across some unseen paradox. I’m not aware of cases like this, but it is a theoretical possibility that this will happen to somebody and that it will matter for their purposes.

One accepts a certain level of risk and uncertainty around one’s use of logic by using the ad hoc method. To put it in perspective, most people carry a much higher level of risk and uncertainty around their use of logic, because they probably haven’t learned any set of rules for logic, and they probably don’t subscribe to any theory about how to solve paradoxes.

 

Implications for math

The ad hoc method of rejecting incorrigible paradoxes, or for short the ad hoc method, has some practical implications for some theoretical math.

Using the ad hoc method has consequences for set theory. The method lets you do math using naive set theory, in which every set you can describe exists, avoiding the need to use a set theory like ZFC whose paradox-avoiding mechanisms introduce complications and limitations.

Using the ad hoc method has consequences for category theory. Category theory has conventionally used paradox-avoiding mechanisms of varying levels of complexity in rigorous presentations. The ad hoc method tells us that there is no need to do this. Paradoxes arise naturally from category theory, but they can be handled by the usual ad hoc method, without a need for paradox-avoiding restrictions. Category theory’s paradox avoiding restrictions usually limit what categories you can talk about, preventing you from talking about sensible categories such as the category of all sets, the category of all groups, or the category of all categories. It’s nice to do away with the paradox avoiding restrictions.

Using the ad hoc method has consequences for type theory. For example, the original impredicative formulation of intuitionistic type theory gave rise to a paradox, Girard’s paradox. Subsequent systems introduced paradox avoiding restrictions which reduced the expressive flexibility of the systems. As in other cases, these paradox avoiding restrictions can be done away with if one is comfortable with the ad hoc method of rejecting incorrigible paradoxes.

This method can even be applied to dependent type theory as applied to software development. People already use logical methods in this context which bear some resemblance-like relation to the ad hoc method of rejecting incorrigible paradoxes.

For example, Idris is a computer programming language based on dependent type theory. In Idris, you can prove theorems in your code, and in particular you can apply this capability to prove that your software has desired properties. In Idris, you can prove any statement. Yet, this is unlikely to happen by accident. Arguably, Idris’ ability to prove any statement is an outcome of overall-desirable design tradeoffs. Normally you wouldn’t use that ability, and the fact that it’s there does not prevent you from drawing confidence from the proofs which you write and Idris verifies. From such a proof, formulated in a normal fashion free of prove-anything back-doors, you can draw practical certainty that the statement proven is true.

Although it can prove any statement, Idris contains paradox avoiding restrictions (a hierarchy of nested type universes). As far as I can see, those paradox avoiding restrictions are not necessary. They’re not necessary to keep the system from proving arbitrary statements, because Idris developers have built the capability to prove any statement into the system anyway. Probably there is approximately nothing to lose from dropping the paradox avoiding restrictions and including the axiom Type : Type which allows paradoxes to be proven. This modification would (arguably) make the system simpler and nicer to use.

Please comment if you’re aware of paradox theories similar to the one laid out here, and to share any paradox research that you think I might find interesting.

God, sovereign, free

Audio of this text available on YouTube and on VidMe.

Here I am going to explain what I see as the most important philosophical departure between Christianity, in most forms I’m aware of it, and the Law of One philosophy as I believe and practice it.

The Law of One states that all is one, and that all things are the one infinite creator, i.e. God. I am further articulating my understanding of this philosophy in Winning Arguments. Other articulations of this philosophy which I appreciate can be found in the Ra material (where I learned the Law of One philosophy), and in the ascension glossary created by Lisa Renee.

I would like to compare the Law of One to the mystery/doctrine of the Holy Trinity in Christianity. According to the Holy Trinity doctrine/mystery, God is three persons in one: God the Father, God the Son Jesus Christ, and God the Holy Spirit. It is a central paradox of Trinitarian Christianity that three distinct beings can at the same time be one being, namely God.

The Law of One entails the doctrine/mystery of the Holy Trinity. The Law of One, which states that all is one, implies that everything conceivable exists and that all things are God.[1] Therefore the Law of One implies that God, Jesus Christ, and the Holy Spirit exist and are the same being. It goes further by extending this identity to everything. The mystery/doctrine of three distinct and identical forms of God is subsumed by the mystery/doctrine of infinite, all-encompassing distinct and identical forms of God.

The Law of One importantly negates the distinction, important to most forms of Christianity, between forms of God and forms that are below God. Christianity acknowledges three forms of God, and an incredible multiplicity of forms below God. According to the Law of One, all forms are forms of God. This mystery/doctrine implies that even the most profane thing is holy.

Of course, the Law of One is paradoxical. The Trinity is paradoxical too, in the same way. Both mysteries/doctrines say that some distinct things are identical. Both mysteries/doctrines contain a logical contradiction, which by the rules of classical logic, allows one to infer that every statement is both true and false. In short, both doctrines have an incompatibility with classical logic, because it is incompatible with classical logic to say that multiple distinct things are perfectly identical.

One may argue that the Law of One’s contradictions are more problematic, because they extend to everything, rather than just three things. A Christian might retort that while the paradoxes of the Trinity apply only to three things, those are the most important things that exist, meaning that the paradoxes of the Trinity are not much less important for extending to fewer things. However, the Law of One’s contradictions might be thought to create more practical problems, since they extend to the world of practical things as well as spiritual things.

I go into this topic much more in Winning Arguments. In the section titled Paradoxes, I have a practical solution to logical paradoxes, based on defining, defending, and justifying the practice that people already employ of rejecting proofs of logical contradictions on an ad hoc basis.

In the section of Winning Arguments titled The Law of One, I am working on a philosophical, theological, and metaphysical route to solving paradoxes, to complement and supplement the practical approach in the section titled Paradoxes.

The hope is to provide an intuitively satisfying solution to the paradoxes which makes a world with paradoxes make sense, as closely as I can attain to such a goal. It’s my opinion that perfectly comprehending the paradoxical mysteries/doctrines of the Law of One and the Trinity is beyond the intelligence of humans. I am merely working to do my personal best at the problem.

I have articulated the abstract difference of opinion between the doctrine/mystery of the Trinity and the doctrine/mystery of the Law of One. I think there are a lot of more concrete differences of opinion that can flow from this key difference of opinion between the Law of One philosophy as I believe and practice it, and most forms of Christianity I’m aware of.

For me the most important of these concrete differences have to do with the attitude towards the self and the attitude towards God.

Most forms of Christianity I’m aware of encourage the worship of God in the form of Jesus Christ as envisioned by the practitioner (often in the likely inaccurate[2] form of a white male). They encourage a sense of the dependence of the self on God and the powerlessness of the self relative to God.

These attitudes, in my opinion, are basically accurate. I think that we as humans are dependent on God and relatively powerless compared to God. These are facts about the world as I see it. Here I am understanding God as the infinite intelligence which is the unity of all things. But I think there is an important truth missing from the previous paragraph, namely that each of us is God. Being God, each of us is potentially as powerful as any part/form of God. The judgment that we and all others are God has many implications for our relationships to ourselves, to others, and to God.

How does believing that I am God affect my relationship to myself? It creates a moral imperative to hold myself in very high regard. This is balanced by the belief that others are God, which creates an analogous moral imperative to hold others in very high regard. There is an imperative not to resonate with disrespect of oneself by the self or others, and an imperative to afford others the same respect one feels entitled to. All of these attitudes, of course, are quite popular, independently of the Law of One.

For me, years of looking into the meaning of respecting oneself and respecting others have felt very informative in exploring the mystery of how to behave morally in the world. This journey goes on for me, as I think it does for us all.

These attitudes toward the self and others come into conflict with various forms of Christianity.

They come into conflict with authoritarian attitudes towards doctrine, where individuals are told to understand God’s truth through the word of authority as opposed to their own intellectual, moral, intuitive, and spiritual discernment.

They come into conflict with forms of Christianity which have the effect of hobbling people with the psychological slavery of guilt and self-hatred. The Law of One teaches what I would call “master mentality,” which can be contrasted with “slave mentality.”

Master mentality. I like all others, am the master of my choices. No others can tell me what choices to make unless I consent to be ruled by them in this way. All of my allegiances are chosen by me based on my personal discernment that they are good from my perspective.

Slave mentality. Some others are my only proper masters, or God, who is a person separate from me, is my only proper master. I cannot trust myself to steer my life for myself. I should submit unquestioningly to some authority in order to lead an upright life.

Slave mentality is a point of view that is hard to reconcile with the understanding of oneself as God. To be God is to be sovereign and free. To be God is to be ruled by no higher master than oneself. Since I regard those with slave mentality as God, I am of the opinion that they are choosing their slave mentality; but I think most people with slave mentality don’t see themselves as having any proper choice in the matter.

I think slave mentality is usually rooted in fear. For example: believing the doctrine of one’s church for fear of being ostracized from one’s church; following or not challenging a dominant political ideology for fear of being ostractized or attacked by its supporters; shying away from master mentality because one fears the potential of one’s power or what one would do with a mind liberated in that particular fashion; etc.

I am not saying that slave mentality is wrong for everybody. The people who choose it have reasons for their choices. I am saying that believing “I am God” naturally leads to master mentality, and that slave mentality is hard to reconcile with believing “I am God.”

I am not saying that master mentality is always a good thing. Clearly many people who have regarded themselves as masters of themselves have gone on to do very evil things on that basis. In my view, master mentality is, generally speaking, a good thing in the context of a philosophy aimed at service to others, and built on a recognition of the weighty moral responsibility entailed in holding oneself God, sovereign, and free.

Trinitarianism does not necessarily lead to slave mentality. I think one can believe that God is three persons in one, the Father, the Son, and the Holy Spirit, and that these are the only forms of God in existence, while also seeing oneself as master of oneself.

However, I do think that Christianity as I’ve observed it, and I would say most institutions of Western culture, trend towards encouragement of slave mentality and discouragement of master mentality. I attribute this, in the case of Christianity, in part to the observation that Christianity as we have it today in the West is almost all derived from the Catholic church, even if by way of the Protestant traditions, and that the Catholic church, as an organized system of social and political control, has always had a lot to gain from inculcating slave mentality in people.

More generally, all organized systems of social and political control benefit from inculcating slave mentality in the general public. Why? A population infected with slave mentality is much easier to control. In contrast, a population infected with master mentality is much harder to control. Slave mentality keeps master mentality safely at bay. I think that we can see the inculcation of slave mentality by those in control basically anywhere we look in history.

As such, I am inclined to see slave mentality in general as a kind of mental parasite, whose purpose is not to help its host, but whose usual purpose is to help some force in the social universe which is getting power over the host by manipulating their mentality.

These are some of the reasons why I am getting over my own fear of adopting master mentality, which is rooted in fear of myself stoked throughout my life by those who wish to inculcate a slave mentality in me. I don’t have time for that.

[1] The Law of One implies that all conceivable things exist because it implies that every statement is true. One way of reaching this conclusion is as follows. Assume the Law of One is true, let A be any statement, and let B be any true statement. According to the Law of One, all is God. Therefore, A is God, and B is God. Therefore, by the transitive property of equality, A is B. Since B is true and A is B, A is true.

[2] Jesus is said to have lived in the Middle East, where most people today have brown skin.

OOP explained with category theory

This is a short post intended to describe a category theoretic formalization of the concept of stateful objects, as employed in object oriented programming and in some styles of functional programming, and as a general concept.

Here is my thesis. A stateful object is a concrete monoid.

What is a concrete monoid? There are many ways to describe them, and I will choose a simple description which lacks dependencies on other concepts from category theory.

Definition. A concrete monoid M = (S, T) consists of the following data:

  • A set S of black box objects, which we can think of as possible states of the stateful object.
  • A set T of functions f : S -> S mapping states to states. These are the elements of M when M is considered as a monoid. They are the arrows of M when M is considered as a one-element category. When we think of M as a stateful object, the elements of T are the possible actions that can be performed on M. Each maps any given possible state of M to a new state; this describes how each action affects the state of M.

End Definition.

In OO terms, the elements of T can be thought of as method calls, with each set of distinct arguments to a method yielding a distinct element of T. So for example if M has a method “foo” which takes an integer and a boolean, then foo(3, true), foo(5, false), foo(-3, true), and so forth are each distinct elements of T.

Suppose now that we have multiple stateful objects. Suppose they might interact. How can we model their interaction?

I think that it’s appropriate to apply different models depending on the nature of the interaction between some stateful objects, and to apply the simplest model that describes the case at hand.

Let’s consider a simple case. Let S = (SS, ST) be a stateful object representing a server (e.g. a Web server). Let C = (CS,CT) be a stateful object representing a client (e.g. a Web browser). Let’s idealize away for the moment the intermediate layers between S and C, pretending that S and C are two stateful objects that interact directly with each other, by rubbing up against each other as it were. Their only method of interaction is the prototypical client-server interaction where C makes a request to S, and S provides a response to C.

We can describe this interaction by the following data:

  • A function req : CS -> Maybe Request. This function tells us what request the client will make in a given state, or it tells us that the client isn’t going to make a request in the current state.
  • A function res : Request -> Pair ST CT. This function tells us what response the server will make to a given request. The response is represented by giving an element of ST which describes how the state of the server is affected by processing the request, and an element of CT which describes how the state of the client is affected by processing the response.

Given this data, a complete interaction between the client and server can be inferred from given initial states of the client and server. Let cs be an element of CS, representing the initial state of the client in the interaction we want to model. Let ss be an element of SS, representing the initial state of the server. req(cs) tells us what request, if any, the client will issue. If req(cs) = Nothing, then no request is issued and no interaction occurs.

Suppose on the other hand that req(cs) = r is some Request object. In this case the client issues the request r to the server, and the server processes it to receive a response. The server’s response is described by a pair (st,ct) = res(r). st : SS -> SS is an element of ST: i.e., a transformation on the server state. ct : CS -> CS is an element of CT: i.e., a transformation on the client state. As a result of this interaction, the client C advances to state ct(cs), and the server S advances to the state st(ss).

I leave further extrapolating these ideas as an exercise to the reader. Your feedback is welcomed!

I am not sure whether these ideas are new or not. Please comment if you know of prior articulations of this set of ideas or similar ones.

What is a Neo-Socratic?

This blog is called Neo-Socratic. Why? What’s in the name? To answer this, I will start with some background on the term “Socratic.”

Ancient Greece is generally considered to be the birth place of Western philosophy. The Greek root φιλοσοφία (philosophia) of the English term “philosophy” literally means “love of wisdom.”

As far as I know, the term philosophia was coined by Socrates to refer to an approach to intellectual inquiry and rhetoric that Socrates first demonstrated to the people of Athens. Socrates, in my opinion, has the best claim of anybody to being the father of Western philosophy. Socrates was the progenitor of the Socratic line of philosophers, including most importantly Socrates, Socrates’ student Plato, and Plato’s student Aristotle. As far as I understand, the Socratic line of philosophers were the first, seminal practitioners of the discipline of philosophy as the Western scholarly world knows it today. No other school of philosophers have been more influential in the development of Western scholarly thought.

We know the thought of Socrates mainly through the writings of Plato and Xenophon, which contain retellings of many philosophical debates which Socrates allegedly participated in. It is widely suspected that Plato made up some of the debates he wrote about, using Socrates as a mouthpiece for his own views. There is less suspicion that Xenophon did this, because Plato was a philosopher, whereas Xenophon was a historian. Both writers were friends of Socrates, and the view of Socrates which both writers present is fairly rosy.

Socrates’ approach to philosophy was a first draft which subsequent approaches have improved upon in numerous ways. However, I regard Socrates’ philosophy as continuing to be a fresh and valuable wellspring which offers bold challenges even to modern thought. By reading Socrates I am taken to a place of ignorance where I feel called to re-examine fundamental assumptions.

I would describe Socrates’ project as primarily destructive in nature. Socrates developed the Socratic method of using questions to uncover incoherencies in people’s beliefs and deficiencies in people’s ability to articulate their own assumptions. This slash and burn rhetorical technique has the effect of creating room for new intellectual growth.

Socrates was largely not a systematic theorizer. We can contrast Socrates with Aristotle, who wrote extensive and complex theoretical dissertations which have provided foundations for much subsequent Western thought. Aristotle carried out a positive project of attempting to discover and articulate many true propositions through the method of reason or philosophy, following the way initially paved by Socrates.

Socrates did, however, do some “positive” work of arguing in favor of certain perspectives, as well as his “negative” work of destroying misconceptions.

Socrates’ biggest area of philosophical concern seems to have been the area of morals or ethics. Socrates was very concerned with the question of how one should live. Many of the debates he engages in are ethical debates wherein he attempts to persuade his colleagues that some behavior they regard as ethical is unethical, or that some behavior they regard as non-advantageous is advantageous.

I think we can most easily get a sense of Socrates’ moral views by examining what has been reported to us about his life and his behavior.

Socrates lived a life of poverty. His primary activity was philosophy, and he did not charge money for his philosophical engagements with people. As such he was largely without income. He lived primarily off of charity.

Socrates claimed to be very happy with his life. He derived fulfillment and the gratitude and admiration of others from his philosophical activity. He lived in a relative state of physical deprivation, frequently being exposed to the elements and living off of simple food in modest quantities. According to him, being used to this way of living, it did not bother him and he enjoyed a subjective sense of comfort in life.

Socrates did not charge for his philosophical activity, he explains, because if he did then he would not get to choose who to do philosophy with, and he would need to do philosophy with wealthy people who might not be his favorite people.

Emulating these details of how Socrates lived is not part of my conception of what it is to be a neo-Socratic. Let me explain my conception of what it is to be a neo-Socratic.

Neo-Socratic. A philosopher, a seeker of the truth, who does not obediently follow tradition or popular opinion, but who aims to follow only reason and intuition. Who seeks to reveal falsehood and incoherence for what it is. Who seeks accurate moral discernment, between right and wrong, good and bad, advantageous and disadvantageous, etc. Who seeks to actually live a moral life and to be a moral example to others.

With this conception I aim to describe, as well as I can in a few sentence fragments and with my limited wisdom, what is most centrally good and valuable about the Socratic philosophical spirit.

Many philosophers, of course, meet this definition without calling themselves neo-Socratic. The term “neo-Socratic” is not a widely used term. I’m not aware of any philosophers besides me who are alive today and call themselves neo-Socratics. Regardless, I believe that the Socratic spirit is alive and quite well today in many, many philosophers. Perhaps, even, this is more so today than it has ever been in the past.