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[cagess]

Philosophy: Relevant Logic and The Autonomy of Ethics

The Logical Autonomy of Ethics is Hume’s famous thesis (1978) that one cannot logically derive moral conclusions from non-moral premises. It is Hume’s view that there is some logical gap between facts on the one hand, and values on the other (Hume, ed. 2019). This is to be distinguished from the Semantic Autonomy of Ethics (Moore; Mares, 2010), which is the thesis that the meaning of moral claims cannot be identified with that of any non-moral claims; and the Ontological Autonomy of Ethics, which is the thesis that moral claims are true or not by virtue of their relation to a set of non-natural properties. Naturalism is the view that although there may be moral truths, there is no unique realm of moral facts or properties that they cannot be reduced to (Pigden, 1989, p.128). Naturalism being roughly the negation of the Ontological Autonomy thesis, it follows materially that the two doctrines are incompatible. It is the first thesis, the Logical Autonomy of Ethics that I will explore in this discussion, with particular reference to Prior’s argument.

It seems initially obvious that the Logical Autonomy thesis cannot be true —at least, not classically. Indeed, these “paradoxes of the material implication” are the entire motivation for various attempts to fix the conditional (Priest, 2001). In particular, I refer to the following arguments:

¬A ⊢A⊃B  and,  B ⊢A⊃B

For anything false in classical logic, its truth can imply anything at all; and anything true can be implied by anything at all. If we simply apply standard deontic operators (SDL) to these propositions, it is easy for anyone with a latent LaTeX fetish to arrive at counterexamples to the Logical Autonomy thesis. Supposing p is a purely descriptive statement, these are valid inferences:

¬p ⊢p⊃OBq and, q ⊢OBp⊃q.

This can also be shown with the principle of explosion, ex contradictione quodlibet:

A∧¬A ⊢B

In classical logic, all propositions —and their negations— are true, following any true contradiction. From explosion, the valid argument can be expressed as an enthymeme:

(p∧¬p),((p∧¬p)⊃q) ⊢OBp

Prior makes an argument in a similar vein, using instead the law of excluded middle. Suppose again that p is a completely descriptive statement, the following is a valid inference:

p∨OBp,¬p⊢OBp

It’s hard to say whether p∨OBp is a moral statement or not, it doesn’t seem purely moral, but I hesitate to claim it is entirely non-moral either. Here, a moral conclusion is derived from an at least possibly non-moral premise, which is worrying for the Logical Autonomy thesis.

In all these cases, there is something arbitrary is going on: whenever an inference is made from a purely descriptive claim to a purely moral claim, the inference is made vacuously. That is, the moral claim is true in virtue of the fact that any other conclusion in its stead would be true. Never mind that these inferences are valid, the conclusions aren’t truly moral ones any more than they are trivial ones. As Pigden (1989) puts it, “you can’t help feeling that Prior has taken himself in with a logical conjuring trick”. You cannot derive erinaceous conclusions from non-erinaceous premises, not because there is something unique about hedgehogs, but because logic doesn’t take us from old truths to new truths, but simply old truths to variations on old truths; you cannot get out what you haven’t put in. Prior’s argument from disjunctive syllogism isn’t any more about morality than it is about hedgehogs. In other words, while the inference is valid in classical logic, the argument does not satisfy the conditions for relevance. According to Pigden, a revision of the thesis is in order. Namely, that the Logical Autonomy of Ethics should more accurately be the claim that one can draw “no non-vacuous Ought-from-Is” (Pigden, 1989).

I find this exclusion of vacuous conclusions from what seems to be a valid inference to be slightly ad hoc. If it is ever possible to draw moral conclusions from non-moral premises, it would be the nature of such an inference to be necessarily vacuous simply because it would have to draw conclusions from unrelated premises. In the same way that it is not in virtue of the moral-ness of Prior’s conclusion that makes his argument classically valid, it’s not clear to me that it’s the non-vacuousness of an Ought-from-Is claim that makes an otherwise logically valid inference false. Rather, I would suggest that the inference is invalid altogether in virtue of it being vacuous —or non-relevant. That is, that vacuous conclusions are simply not valid conclusions.

Relevantism

The idea that arguments should be invalid if they are non-relevant is well-defended (Priest, 2001; Mares, 2010). Proponents of relevant logic suggest that the reason such vacuous inferences as ¬A ⊢A⊃B  and,  B ⊢A⊃B arise are due to a flaw in classical logic, particularly from problems with the material conditional. Contrary to what a two-dimensional truth-table might say, it simply does not seem plausible that a conditional is true anytime an antecedent is false or a consequent is true. They make the argument that this is not a good account of what a competent English-speaker means when she makes an if-then statement. A strict conditional was introduced to account for the material implication, however this gave rise to paradoxes as well:

⊨ A􏰞⥽(B ∨ ¬B) and, ⊨ (A ∧ ¬A)􏰞⥽B

Similarly, whether or not it is possible that A∧¬A, (there are at least some dialetheist out there) relevantists are skeptical that this would, if it were true, be enough to imply any trivial proposition is true. Therefore, relevant logics are paracomplete, rejecting the law of excluded middle (A∨¬A) as valid as well as; paraconsistent, rejecting the principle of explosion (A∧¬A ⊢B) as valid.

More pertinently, some relevant logics reject the disjunctive syllogism on which Prior’s argument rests. There is something I find implausible about disjunctive syllogism, A∨B, ¬A ⊢B. This is a flaw illustrated by Prior’s argument, that any conclusion moral or erinaceous can follow vacuously from a false disjunct. As Simons (2001)argues, there is something rather strange about the following disjunctions:

(1) Either there is dirt in the fuel line or it is raining in Tel-Aviv.

(2) Either there is dirt in the fuel line or there is something in the fuel line.

Both of these statements are classically valid, however, (1) is not related, in that as long as one disjunct is true, the other can be trivial; and (2) is not distinct because one disjunct is implied by the other. It seems implausible to me that this is a good account of disjunction. In classical logic, for any disjunction with one true disjunct, the other disjunct can be entirely trivial while still making the disjunction true.

Surely, some modal operators are in order if we want a proper account of disjunction. Such as it possibly being necessary that the second disjunct at least be possible; or that the true disjunct can be true, but not necessarily true, because this would result in vacuousness as well. More than a specific objection to vacuousness with specific regards to drawing moral conclusions from non-moral premises, such trivial arguments illustrate that we require drastic interventions for logic itself, not simply a fix for the Is-Ought problem. This has led relevantists to introduce the Relatedness and Distinctness conditions for a more relevant notion of disjunction.

Because Relevantists reject disjunctive syllogism, we can avoid Prior’s argument which is based on C.I. Lewis’s argument for explosion, one of the paradoxes of the strict conditional (Priest, 2001):

1. A∧¬A [assumption]

2. A [from 1, by E∧]

3. ¬A [from 1, by E∧]

4. A∨B [from 2, by I∨, or addition]

5. B [from 3, 4 by disjunctive syllogism]

Relevant logicians respond to Prior’s argument by differentiating two separate notions of disjunction, denoted by different connectives. The classical connective (∨) which is extensional and fission connective ⊕ which is intensional and does not allow for arbitrary formulae. I believe the Logical Autonomy of Ethics thesis survives the Prior objection, as his argument, while deductively sound in classical logic, only serves to raise issues about vacuousness and classical logic as a whole. If anything, Prior’s argument advances the merits of relevant logic over classical logic as not only a better account of implication, but as a better account of disjunction as well.

[cagess]

Philosophy: Truth Value Gaps and The Law of Excluded Middle

Russell was interested in finding a way to connect what we say to what we are talking about. He wanted to effect a connection between language and the world that respected our basic common- sense intuitions about what the world is like. Russell accepted Meinong’s view that words have meaning by denoting things. Fundamentally, he believed that words have meaning by denoting things; the semantic relation is a relation of denotation (Grayling, 2001).

This presents a problem because there are many words in our language do not denote spatiotemporal objects. And yet by virtue of the fact that they are meaningful, must nonetheless refer to something. When we speak about things like dragons and Sherlock Holmes, it is essential that we are able to reason cogently about these non-existent objects, if only to determine they don’t exist. By the denotative theory of meaning, these objects must have some sort of metaphysical being so that they can be the denotata of the words we use in language.

Meinong’s solution to this was to suppose that there are other ways by which an object can have being. According to Meinong (Grayling, 2001), we can use predicates to reason about things that don’t exist in the physical and concrete sense because these objects nonetheless “subsist”. When we speak of such things as the nonexistent present King of France, our propositions can have meaning because the referent of the proposition has some abstract kind of being. This is a view that Russell initially accepted, until it was pointed out to him that an infinite number of things can be brought into subsistence merely by conjecture. The idea that there exists some realm —Meinong’s Jungle— that holds every conceivable non-existent seemed implausible. As Russell admits, “this came to offend my vivid sense of reality”.

Russell gave up Meinong’s denotative theory, instead adopting the view that most words aren’t denoting expressions but rather concealed descriptions (Grayling, 1996). In fact, he was compelled by the idea that the only words that are denoting expressions are the demonstrative pronouns “this”, “that”, “these” and “those”. This is tautologically true because every time these words are used, they must, by definition, denote some object. This change allowed Russell to have an account of meaning based on denotation without being committed to what Quine called an “ontological slum” that the theory seemed to entail.

Russell was also keen to preserve bivalence; the view that propositions about the world are either true or false. If something is not true, it must be false, and if something is not false, then it is true. In classical logic, the law of excluded middle states that for any proposition p, p is either true or false, ⊢(p∨¬p). This is an axiom of classical logic, making it necessarily true without premises that all propositions are either true or false. It follows from this that a proposition is true if and only if its negation is false; and its negation is true if and only if the proposition is false. This allows us to use the double negation elimination axiom, ¬¬𝑝 ⊢𝑝. Russell, having come up with much of classical logic, is very committed to this view.

This is quite a claim, as Grayling (1996) points out, because there are other reasons for a proposition failing to be true. For example, a proposition might fail to be true because it is meaningless, or it might fail to be (only) true because it has more than one truth value. There now exist multivalent logics like First Degree Entailment (FDE) which is both paracomplete (allowing for failures of the law of excluded middle) and paraconsistent (allowing for failures of the law of noncontradiction and the principle of explosion). Some, like fuzzy logic, even allow for an infinite amount of possible truth values between truth and falsity (Priest, 2017).

Russell wanted to preserve bivalence because he was committed to classical logic, which is a two-valued logic. He wanted to do this because the predicate calculus which is based on classical bivalent logic was crucial in providing an analysis that is used to show how most words in our language (apart from “this”, “that”, “these”, and “those”) are not denoting expressions but concealed descriptions. He is burdens with responding to the following problem.

Suppose the proposition “The present King of France is bald”. Unless you believe that monsieur Macron is not a President but instead a King, you might otherwise be inclined to say that this proposition is false because there is no present King of France (Grayling, 1996). However, this causes a problem: if the proposition is false, then its negation is true by the double negation elimination axiom. Its negation, presumably, being that the present King of France is not bald. This is a problem for classical logic because we would like to say that the proposition if false for some other reason than the non-baldness of a present King of France. It seems there are two senses in which a proposition can be not true: either it is not true because its negation is true; or that it is not true for the reason that one of the premises does not apply to the situation.

This proposition poses a problem to the law of excluded middle. Namely, that if a proposition can be false for some reason other than its negation being true (as is the case with Russell’s vacuous falsity), then we must abandon the axiom of double negation elimination, ¬¬𝑝 ⊢𝑝. This in turn causes a contradiction with the law of excluded middle.

(p∨¬p) →(¬¬𝑝 →𝑝), ¬(¬¬𝑝 →𝑝)⊢ ¬(p∨¬p)

If the law of excluded middle is true, then double negation elimination rule is true. The double negation elimination rule is not true. Therefore, by contraposition, the law of excluded middle is not true.

Russell responds to this by saying that there is more than one way that a proposition can be not true; Russell believes that this proposition is not true, but vacuously so. And further by propositional logic, if it is not true, it is necessarily false. This must be represented with more specific logical machinery. He represents the proposition with the predicate calculus:

(∃x) (K(x) ∧ (y)(K(y) → x=y) ∧ B(x)).

That is, if we examine the proposition logically without the ambiguous English words, what we are truly saying is this:

(1) There is some x in existence (or indeed subsistence) that satisfies the conditions for being the present King of France

(2) and for anything whatever, y, that satisfies these conditions, it is identical to x.

(3) And further, that x possesses the further property of being bald.

This defines the proposition in Russell’s predicate calculus. The logical machinery in (2) accounts for the property of uniqueness suggested by the use of “the”. This is due to Leibniz’s law of the identity of indicernibles (Loemker, 1969: 308)—whatever shares the same properties shares an identity and as such, there is one and only one. Here, we assume that contained within the definition of a King of France, it is tautologically true that there cannot be more than one King of France and so (2) cannot fail in this case. Therefore, there are two ways in which the proposition can be false. Either it is false because (3) is false and the present King of France is not wise, or it is vacuously false because (1) is false and there is simply no King of France presently.

This overcomes the problem where a questioned is asked with a presupposition that is not fulfilled.

Grayling (1996) gives the common example “Have you stopped beating your wife?”. If I wish to say I have never beaten my wife, then I cannot respond “no” because this means it’s true that I haven’t stopped beating my wife, and I cannot say “yes” because this would mean that I once beat my wife and have since stopped. Russell responds to this by saying that if you look at the underlying structure of the question, there is more than one reason to answer “no”, either vacuously or non-vacuously.

Now that I have delineated Russell’s solution to the problem of definite descriptions, I would like to suggest that perhaps the problem does not lie with the substructures of the sentence, but rather with bivalence itself. Perhaps the proposition “The present King of France is bald” is neither true nor false. It might fail to be either because the proposition simply does not apply to what is the case. Of course, this requires us to abandon the law of excluded middle as well as its corollary, double negation elimination —at least, as a necessary logical law.

Of course it would make little sense to abandon an axiom of classical logic when a more classically compatible theory is available, strong reasons would have to be given to make the switch to weaker logics. The reason I am compelled to do so is not because a weaker logic provides a better solution to the specific problem of definite descriptions, but rather because adopting weaker logic is coherent with the solution to a number of other issues in philosophy (Priest, 2017).

Allowing the failure of the law of excluded middle also avoids a problem regarding facts about the future. Namely, if there currently exist facts about the future, then this seems to entail that hard determinism is true, which is, I assume, an unfavourable position to hold. Indeed, this is the motivation for Intuitionistic logic (Priest, 2017). The law of excluded middle is rejected so that propositions about the future can hold indeterminate truth values, without entailing determinism.

Another reason to adopt a weaker logic, such as relevant logic, is that it categorically avoids cases in which propositions can be vacuously true. Relevant logic ensures that conclusions in a valid argument are necessarily related to their premises (Priest, 2017). Rejecting the law of excluded middle as a logical law is crucial to the machinery necessary to the relevant account of the conditional.

The present King of France proposition causes tension between the law of excluded middle and the theory of denotation. Russell’s response to this problem was to abandon the idea that language has meaning only by denoting things, to adopt the view that words are concealed descriptions. To show this, Russell employs predicate calculus to show that a proposition can be false in more than one way if we examine the deeper substructure of the sentence, thereby preserving classical bivalence. Priest proposes that adopting a weaker logic may be more coherent with the solutions to various problems in recent analytic philosophy and should at least be considered.

[cagess]

What I learned today: Anaconda Choke

Oct 22 2020 Some adjustments from Steven today:

1. The palm of my support hand should face forward, pointing down. My choking arm should be deeper so that my gable grip is all the way through passed the arm. Bring the choking arm to the support arm, not the other way round.

2. I should be sprawled back on my toes, not on my knees. Kick my outer leg inwards to start the gator-roll.

3. Roll with the gable grip first, lock up the figure-four only after the roll.

[cagess]

What I learned today: Knee-cut

28 July 2020 It’s been well established that standing up is the best way to open a closed guard. However, when it comes to passing, a lower stance is better once the guard has been opened because it reduces the chances of getting swept.

For this reason, kneeling guard breaks are low-yield but low-risk. Benoit makes the argument that it is still worth trying at first. We can always pop up to our feet if it doesn’t work. When it does work, it puts us in prime passing position immediately without having to deal with the annoying De La Riva sweeps if we were trying to pass standing. Definitely going to reintroduce these old guard breaks to my game.

Sep 18 2020 Zack was telling me that my knee-cuts could be seen a mile away because:

1. My legs were too squared; remember stagger them with my cutting shin forward.

2. My stance is too tall, especially when I start to get tired; I either need to stay low or sit back for a leg-lock, but standing tall is not an option when passing.

Oct 24 2020 Benoit showed me a couple details about the knee-cut pass:

1. The staple leg and the posting leg come in at the same time. Previously, I’ve been doing it in two steps, which has left me off-balance for a good few seconds. Remember to move both legs at the same time.

2. I’ve been too quick to shoot for the underhook when passing. I have more success when I take the time to control the hip first before making the jump to fight for the underhook.

3. I can make my life a lot easier if I block the knee-shield before I even start passing. Controlling the hip with my hand, I can use my elbow to block the knee-shield from coming in. Another reason I shouldn’t fight for the underhook before first addressing the knee shield.

4. If I can’t get the underhook, grabbing the outer sleeve is not a good alternative. The nearside collar is better whenever available.

[cagess]

How to Exist: a letter to myself

Dear Cage,

1. I cannot promise you meaning in life, such propositions are palpably senseless (Wittgenstein, 1921). Of the mystical: the will to truth, the will to live, and the will to be kind; I will say simply: there are such wills. The imperatives that follow are to serve you, and no one else, in the hopes that you may only continue to exist.

2. How to exist (Sartre,1941; Camus, 1942).

2.1. Observe the essential properties of the self. These are the properties you have chosen to determine your identity, whatever they may be, and without which you cannot continue to exist as yourself.

2.2. Therefore, be authentic to those properties at all costs, they allow you to exist.

2.3. Authenticity is not something you hold, once attained. Living authentically is a constant endeavour not to violate your identity (Heidegger, 1927).

2.4. However painful, remain authentic in your relationships, at the cost of all losses. It is impossible to be with someone if you lose sight of yourself. In doing so, a person who loves you will not see you, and will not love you but someone else who shares your mere likeness.

3. Preserve your autonomy.

3.1. To exist, you must be authentic; to be authentic, you must have free-will.

3.1.1. To have free-will is to act, with the physical and mental capacity to have done otherwise.

3.2. Therefore, if you ever wish to be kind, you must seek the power to be unkind.

3.2.1. Kindness without the capacity for evil is merely weakness masquerading as virtue. Be formidable, then only is it virtuous to be kind (Peterson, 2018).

3.2.1.1. Therefore, have strength. Be prepared to fight, both physically and mentally, and have the courage to do so when you must. Then only is the choice to walk away truly yours.

3.2.1.2. Integrate your Jungian shadow, do not shy away from the monstrous parts of yourself. Dare “gaze into the abyss, and allow the abyss to gaze back into you” (Nietzsche, 1886; 146).

4. Seek truth (Nietzsche, 1886).

4.1. The will to truth allows you to exist. “If you believe the arsenic nourishes, you will exhibit a pathetic but praiseworthy tendency of dying before you reproduce your kind (Quine, 1969: 126)”.

4.2. Believe in what is evident. Deceive others if you must, but never yourself.

4.2.1. We avoid the things that threaten our identities (Manson, 2015).

4.2.2. Therefore, be precise; be accurate with yourself. To overestimate and to underestimate yourself are equal sins. Know the extent of your strengths and weaknesses.

4.2.3. Self-acceptance is overrated, if it would allow complacency where self-improvement is justified. Get good at the things that matter to you, and earn the love you owe yourself.

4.2.4. Therefore, allow yourself vanity. Take pride in the things you value about yourself. Avoid false humility. Instead, delight in your abilities, but know that always, there will be greater and lesser persons than yourself (Ehrmann, 1927). Do not resent the good fortune of others.

4.3. Appraise the world.

4.3.1. Know what you mean to others and what others mean to you.

4.3.2. Know when to accept advice. You will often receive advice from people trying to justify their own views and choices by suggesting you do the same. Trust your judgements above all.

4.3.3. Don’t accept criticism from those whose advice you would never ask for.

4.3.4. Take what is meant over what is said, this is the surest path to truth. When evaluating ideas, employ the principle of charity. The people with the best ideas may not be the most verbally articulate, you may have to make your interlocutors’ best arguments for them (Quine, 1873).

4.4. Understand what motivates people (Freud, 1923).

4.4.1. It is the nature of people to seek pleasure and avoid pain.

4.4.2. Understand what motivates others, and understand what motivates you. It is simplistic to believe that people are either good or bad. In reality, they are simply driven by their needs and desires. Learn what they desire and you will learn why they act the way they do. When you can understand behaviour, you can predict action.

5. Serve your needs and desires (Hobbes, 1651).

5.1. Feel no shame about pursuing your needs, however superficial they may seem.

5.1.1. Demand attention, if that is what you desire.

5.2. You are far more likely to regret missed chances than foolish actions. Reject the security of the familiar, and take the risks that are worth smiling back upon.

5.3. Know that you may have to hurt people in pursuit of things that are important (Nietzsche, 1883).

5.3.1. Be wicked if you must, but beware the effect this may have on the weak.

6. Do not shy from your emotions, to do so is to mutilate your identity; to do so is to cease existing.

6.1. In the face of adversity, let stoicism embolden you with the worst fate can offer (Epictetus, 135AD).

6.1.1. When you are anxious, it is common for those around you to offer reassurance that things will work out. Oppose this convention we find so much comfort in, it gives you false hope that ruins your chance for inner peace. While such hope can grant you transient comfort, it only sets you up for greater loss when confronted with the inevitable.

6.1.2. Admit to yourself that terrible adversity is a very possible, and often certain, eventuality. It is only when you stand in the wreckage of everything you love, that you realise you still live on.

6.1.3. You’re going to find that you haven’t lived up to my prescriptions, this is an inevitable consequence of pushing your limits. When you fail, it’s easy to let shame and humiliation erode your identity. I wrote this letter for this moment. Will yourself back into existence. True strength is not a repression of shame; walk amongst everything you are ashamed of. Have the courage to let it hurt you. Let it sink its teeth into you and sit in the pain. Then, stand up with your shoulders back, and keep walking (Peterson, 2018).

6.2. On matters of the heart,

6.2.1. Be neither naive nor grow too callous about love. Be cautious, but avoid your temptation to romanticise cynicism (Ehrmann, 1927). Protect yourself always, until you have someone worth protecting more.

6.2.2. Be willing to fight the ones you love; and be willing to leave when you must. This gives value to the commitments you make, every time you decide to stay.

6.2.3. Be desired, as far as you can be. Faithfulness is virtuous only if you remain able to do otherwise. Nonetheless, this is a virtue worth truly having, so be faithful (Peterson, 2018).

6.2.4. Remember those you lose and allow new persons to take their place.

6.2.5. Accept your heartbreaks with those you’ve given so much of your life to. Think of them fondly and speak of them fondly.

6.2.6. When you are ready to let go of someone you love, forgive all debts and transgressions, there is no enemy when the war is over.

7. And, when you have done all this, be kind.

Your most loyal and obedient servant, Cage