POLITICS AND PHILOSOPHY

Stephen Wolfram's Computational Foundations for the Second Law of Thermodynamics and Cosmonautical Philosophy
Some thoughts on mathematical structuralism
Attention Schema Theory and Illusionism
Information is Physical
Quining Qualia by Daniel Dennett
Eliminative Materialism by Paul and Patricia Churchland
"Relative State" Formulation of Quantum Mechanics by Hugh Everett
Misinterpreting Everett (The apparent difference between the possible and the actual is merely indexical)

Pandemic Response, Autumn 2020
What is the Purpose of the State?
Racism is Shallow Pattern-Matching
The Cultural and Ethnic Future of the UK
Altruism
Misunderstanding Contractarianism

The Problem of the Fourth: The Trinity and Leibniz's 'vinculum substantiale
Who or What is Satan?
Kenosis Theodicy

Evolutionary Psychology(6)

Land Management/Engineering/Miscellaneous:
Garden Soil (North London)
The Heliostat
Were food crops selected on the basis of their success in polycultural environments?
Constructing a dipole antenna
On Agriculture

Stephen Wolfram's Computational Foundations for the Second Law of Thermodynamics and Cosmonautical Philosophy

In Computational Foundations for the Second Law of Thermodynamics and Cosmonautical Philosophy Wolfram posits that the Second Law of Thermodynamics does not state that 'things becoming more random', but rather merely describes the effect of the world's computational irreducibility pushing up against the limited computational capabilities of observers (like humans). "At some level the Second Law is a story of the emergence of complexity. But it’s also a story of the emergence of simplicity. For the very statement that things go to a “completely random equilibrium” implies great simplification. Yes, if an observer could look at all the details they would see great complexity. But the point is that a computationally bounded observer necessarily can’t look at those details, and instead the features they identify have a certain simplicity"(italics mine).

When I first read this essay yesterday, I found it extremely exciting. I was already familiar with the idea that entropy is fundamentally subjective (a measure of an observer's ignorance about a system rather than a property of the system itself) via the work of Edwin Jaynes - as well as his subjective Bayesianism more generally, but I suppose I had never thought too deeply about what that implied for the second law itself. Returning to it today, however, I wonder how new the ideas really are. That the second law is hypothetically violated by the existence of of a non-computationally bound observer was already implicit in the solutions to Maxwell's Demon problem - and that's over 150 years old!

In any case it triggered a reconsideration of an idea I've always been very enthusiastic about, laid out in Toward an Ecological and Cosmonautical Philosophy by Joseph Kirby and influenced by the thought of Krafft Ehricke. Kirby and Ehricke make something of an idol of what they call 'negentropy'. They identify this with complex life in all its forms. Under Jaynes'/Wolfram's theory of subjective entropy, what can be said of 'negentropy'? Well, it must simply mean: 'increased computational power' of an observer or observers, perhaps increased to some absolute point at which we can no longer say any aspects of the universe are irreducible. Like this the cosmonautical philosophy gains a beautiful logical autonomy: imposing order in the universe by virtue of understanding it.

Wolfram potentially throws a spanner in the works here: "..So, yes, a future observer with vastly more advanced technology might successfully be able to sample lots of details of the future universe. But to do that, the observer will have to lose some of their own coherence, and ultimately we won’t even be able to identify that future observer as “coherently existing” at all." This claim probably bears some more looking into, but it seems plausible on its face. If 'reversing' entropy comes at the expense of losing internal coherence, should we still consider it a desirable goal? It rather deconstructs Azimov's 'last question', then immediately reconstructs it!

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Some thoughts on mathematical structuralism

"The fundamental tenet (though it's really more a rational-empirical conclusion) of structuralism realism is that "structure" is real, while entities are not. It comes in three distinct flavours:

Ante rem structuralism ("before the thing"), or abstract structuralism or abstractionism, has a similar ontology to Platonism. Structures are held to have a real but abstract and immaterial existence. As such, it faces the standard epistemological problem, as noted by Benacerraf, of explaining the interaction between such abstract structures and flesh-and-blood mathematicians.

In re structuralism ("in the thing"),or modal structuralism is the equivalent of Aristotelian realism (realism in truth value, but anti-realism about abstract objects in ontology). Structures are held to exist inasmuch as some concrete system exemplifies them. This incurs the usual issues that some perfectly legitimate structures might accidentally happen not to exist, and that a finite physical world might not be "big" enough to accommodate some otherwise legitimate structures. The Aristotelian realism of James Franklin is also an in re structuralism, arguing that structural properties such as symmetry are instantiated in the physical world and are perceivable. In reply to the problem of uninstantiated structures that are too big to fit into the physical world, Franklin replies that other sciences can also deal with uninstantiated universals; for example the science of color can deal with a shade of blue that happens not to occur on any real object.

Post rem structuralism ("after the thing"), or eliminative structuralism, is anti-realist about structures in a way that parallels nominalism. Like nominalism, the post rem approach denies the existence of abstract mathematical objects with properties other than their place in a relational structure. According to this view mathematical systems exist, and have structural features in common. If something is true of a structure, it will be true of all systems exemplifying the structure. However, it is merely instrumental to talk of structures being "held in common" between systems: they in fact have no independent existence."

I will say firstly that ante rem structuralism is clearly just Platonism in a wig. I will dismiss that out of hand because I'm strongly allergic to Platonism. The other suggestion made is that 'structure is something instantiated in the mind', but that endows the mind with all sorts of mystical properties... in other words, we are back to the hard problem of consciousness.

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Altruism

Altruism is favoured when: rB - C = 0

r = relatedness between altruist and recipient
B = fitness benefit to recipient
C = fitness cost to altruist

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Attention Schema Theory and Illusionism

Attention Schema Theory (AST) posits that the brain constructs an internal descriptive and predictive model of its own attention, and this model is what we know as 'consciousness'. Michael Graziano: "The purpose of the attention schema theory is to explain how an information-processing device, the brain, arrives at the claim that it possesses a non-physical, subjective awareness and assigns a high degree of certainty to that extraordinary claim."

This approach is interesting. Most literature on the hard problem asks how a brain might generate subjective experience, whereas the AST asks instead why a brain would make the claim that it has a subjective experience.

Just as with illusionism, I struggle with the implied recursiveness. My 'subjective experience' is a model monitoring my scope of attention, fundamentally a neurobiological process. I can think about my own subjective experience, and the 'I' that performs this metacognition is itself just a model. There is a seemingly infinite regress of witnesses in infinite cartesian theatres.

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Information is Physical:

Szilard's engine

A neat physical thought-experiment demonstrating how just the possession of information might in principle have thermodynamic consequences was established in 1929 by Szilard, in a refinement of the famous Maxwell's demon scenario. Consider Maxwell's set-up, but with only a single gas particle in a box. If the supernatural demon knows which half of the box the particle is in (equivalent to a single bit of information), it can close a shutter between the two halves of the box, close a piston unopposed into the empty half of the box, and then extract X joules of useful work if the shutter is opened again. The particle can then be left to isothermally expand back to its original equilibrium occupied volume. In just the right circumstances therefore, the possession of a single bit of Shannon information (a single bit of negentropy in Brillouin's term) really does correspond to a reduction in physical entropy, which theoretically can indeed be translated into useful physical work.

Landauer's principle

In fact one can generalise: any information that has a physical representation must somehow be embedded in the statistical mechanical properties of a physical system. Thus, Rolf Landauer argued in 1961, if one were to imagine starting with those properties in a thermalised state, there would be a real reduction in thermodynamic entropy if they were then re-set to a known state. This can only be achieved under information-preserving microscopically deterministic dynamics if the uncertainty is somehow dumped somewhere else — ie if the entropy of the environment (or the non information-bearing properties) is increased by at least an equivalent amount, as required by the second law, by gaining an appropriate quantity of heat. On the other hand, Landauer argued, there is no thermodynamic objection to a logically reversible operation potentially being achieved in a physically reversible way in the system. It is only logically irreversible operations — for example, the erasing of a bit to a known state, or the merging of two computation paths — which must be accompanied by a corresponding entropy increase.

Applied to the Maxwell's demon/Szilard engine scenario, this suggests that it might be possible to "read" the state of the particle into a computing apparatus with no entropy cost; but only if the apparatus has already been set into a known state, rather than being in a thermalised state of uncertainty. To set (or reset) the apparatus into this state will cost all the entropy that can be saved by knowing the state of Szilard's particle.

Negentropy

Shannon entropy has been related by physicist Léon Brillouin to a concept sometimes called negentropy. In his 1962 book Science and Information Theory, Brillouin described the Negentropy Principle of Information or NPI, the gist of which is that acquiring information about a system’s microstates is associated with a decrease in entropy (work is needed to extract information, erasure leads to increase in thermodynamic entropy). There is no violation of the second law of thermodynamics, according to Brillouin, since a reduction in any local system’s thermodynamic entropy results in an increase in thermodynamic entropy elsewhere.

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Pandemic Response

The NAP states that "aggression, defined as initiating or threatening any forceful interference (violating or breaching conduct) against an individual, their property,[note 1] or promises (contracts) for which the aggressor is liable and in which the individual is a counterparty, is inherently wrong". [Source]

It is both the case that:
1) knowingly transmitting a disease which can cause grievous bodily harm to or death of the victim violates the NAP, and that
2) forbidding those with Covid from public spaces violates their freedom

Market solutions?

Divide the population into roughly two groups who make different cost-benefit analyses regarding covid: 1) those who are concerned about contracting covid, either because they are high-risk themselves or because they live with someone who is, and who are willing to take reductions to their quality of life in order to avoid infection: 'the Worrieds', and 2) those who are entirely unconcerned with contracting covid, due to being low-risk or simply due to personal philosophy, and are not willing to take reductions to their quality of life: 'the Not-Worrieds'. Of course a large part or indeed the majority of the population exists somewhere between these two tribes, but I will not enumerate them all for brevity's sake. Retailers and essential service providers who wanted to court 'the Worrieds' could enforce social distancing etc as conditions of sale, similarly those who were not worried about contracting covid could take their custom elsewhere. An efficient market ought to be able to cater to these two (and many other) lifestyles. Indeed if the entire country was segmented into privately held property, then there would be little need for a government policy at all.

Response

However, we still have to engage with the world as it is. As desirable as it is for health to be a purely personal matter, there are hardly any aspect of our lives which are truly socially or economically 'personal' or 'private'. Yes health is a personal matter, but because we have socialised healthcare, the cost of 'personal' illness is in fact born by the general public.

- Some social distancing ought to be enforced in public spaces. This preserves 'the commons' for those who do not want to contract an illness whilst only mildly inconveniencing those who are indifferent.
- Social distancing ought not to be enforced in private spaces. There is no reason why members of the public cannot use their own discretion when deciding who to socialise with privately.
- School closures are unnecessary. "...individuals below 30 years of age infected fewer household members then all the other age groups" [Source] - The elderly/vulnerable ought to be advised to take precautions where possible. This could include support for the introduction of highly protective social 'bubbles' and recommendation of reduction of intergenerational physical contact
- Allow the market to deliver a vaccine

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What is the Purpose of the State?

The term ‘contractualism’ can be used to indicate the view that morality is based on contract or agreement. Derek Parfit argues that rule consequentialism, contractualism, and the best interpretation of Kant’s moral theory all coincide. The result is a triple theory, according to which “an act is wrong just when such acts are disallowed by some principle that is optimific, uniquely universally willable, and not reasonably rejectable” (Parfit 2011, volume 1, p. 413). As contractualism presents itself as an alternative to both consequentialism and Kant, this would be a very significant result.

The convergence argument explicitly deals with “what I believe to be the best version of Scanlonian contractualism” (Parfit 2011, volume 1, p. 412). Parfit defends two key ‘improvements’, by rejecting two restrictions that Scanlon places on the reasons that can be offered for rejecting a moral principle, namely:

“Individualist Restriction: In rejecting some moral principle, we must appeal to this principle’s implications only for ourselves and for other single people” (Parfit 2011, volume 2, p. 193). Or, in Scanlon’s own words: “the justifiability of a moral principle depends only on individuals’ reasons for objecting to that principle and alternatives to it” (Scanlon 1999, p. 229).

“Impersonalist Restriction: In rejecting some moral principle, we cannot appeal to claims about the impersonal goodness or badness of outcomes” (Parfit 2011, volume 2, p. 214). Or, in Scanlon’s own words: “impersonal values are not themselves grounds for reasonable rejection” (Scanlon 1999, p. 222).

Therefore, I argue that the purpose of the state is to enforce contracts between citizens. This necessitates that the state have a monopoly on violence.

Violence is essential for law and order

The truth that the law is only maintained by the tacit threat of violence is forgotten by most citizens who rarely breach any major law, and are willing to pay the fines imposed by the official discovery of their misdemeanours such as speeding. Even those who steal or murder generally accept the notion that public discovery will demand private penalty. However the reality is that without the threat, or actual use, of violence by law officers, the law would be ignored. People can only enjoy their property and liberty within a community because of the community’s readiness and ability to inflict violence upon lawbreakers.

Violence is the way an understanding asserts itself, so if authority recoils from violence, it recoils from imposing control. This failure to impose clear control allows any and every citizen to behave as they see fit, and obtains disorder with its inevitable eruptions of violence. So by pretending that violence solves nothing our community has changed from a peaceful community that controls its violence, into a community that is more dangerous to its citizens than to its enemies.

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Racism is shallow pattern-matching

Inter-national racism is likely rational

Some consider race to be a social construct, others biological — I consider it to be both: a reality due to the fact that human populations are ‘trained’ by local ecology, and an ideal since humans are capable of inventing synthetic identities based on abstracts.

Richard Lynn proposes that different traits evolve in different climates, colder environments being more cognitively demanding and therefore selecting for larger brains and greater intelligence [Kanazawa, Satoshi (1 July 2012). "The evolution of general intelligence". Personality and Individual Differences]. Simply put, individuals probably north western European, East Asian or other cold climate domestically selected, had the privilege of dying more often in the right proportions than any other demographic, which acted like a sieve or selective pressure. Tropical populations, on the other hand, experience year-round harvests, and eventually lose the ability to maintain civilisation under natural conditions due to lack of domestic selection. Any human population originally inhabiting there will not have developed the ability for novel thought to the same degree as temperate populations closer to the poles. The effect is lower average intelligence, rapidly diluted by the rapid growth and lack of selection for higher average intelligence. No amount of social engineering will patch the separation at the genetic level, the averages will remain unbridged unless there is selection (parallel/convergent evolution) to close this.

I originally assumed that racial mixing would have the ability to uplift the mean IQ of these tropical populations. However, several issues, such as hybrid depression and/or regression to the mean, have been brought to my attention (further reading: various publications by Richard Lynn, Charles Murray, Edward Dutton, Arthur Jensen). Regression to the mean for intelligence detracts from one group and benefits the other, but not both. The IQ of offspring will regress towards the mean IQ of the population group from which the parents come. This has been amply documented for a number of physical traits in humans and in other species. Eg. when individuals with high IQ scores mate, their children tend to show lower scores than their parents. The converse happens for low IQ parents; they have children with somewhat higher IQs. This is because the parents pass on some, but not all, of their exceptional genes to their offspring.

Inter-personal racism is likely irrational

It's important to note that for less intelligent Europeans, the fact that they regress to a higher mean does not mean they totally recover it. When less intelligent Europeans reproduce among themselves for generations without any genetic turnover from the congenital elites (as they do, due to assortative mating) — they are not able to resupply genes that failed to survive in the underclass subpopulation. Therefore, if a European thinks they ought to be able to discrimate against an African on the basis of Africans having on average lower IQs, oughtn't they to discrimate against less intelligent Europeans too? What rational preference can one give for an 85 IQ European over an 85 IQ African? Preference for arbitary traits like skin colour, and 'blood and soil nationalism' more generally, are clearly irrational. We quickly see that the emotional core of the racist's argument is not is not genuine concern for competence, but simply atavistic personal enmity. In-group preferences for the genetically similar can be (and have been) overcome by any person living in a sufficiently diverse society.

In any case, at the individual level, ethnic IQ differences can't really make any predictions that we couldn't more accurately obtain through listening to a person speak for five seconds. As mentioned above, our racial identities are synthetic - West Africans are more genetically distant from East Africans than White people are from Asians [Source]. It adds very little to our model of the world. I also can't help but notice the loudest adopters of hereditarianism are usually underperforming white people who oddly fail to live up to what they believe is their superior genetic potential - everyone needs someone to punch down to. For these people racism obviously serves some psychological function beyond mere in-group preference. As Martin Amis put it nicely: "Some white men needs to be able to step out of their trailer in the morning, see a Negro walk by, and spit at their lessors." Personally, I would adapt the English common law principle of 'presumption of innocence' to 'presumption of competence' (until proven otherwise, of course). This is a good faith means of interacting with the world. So, whilst gaps in achievement can be expected at the population level, this should not lead us to dehumanise the individuals we encounter socially.

The ethnic and cultural future of the United Kingdom

According to a US Bureau of Census projection [Source], white Americans will comprise below 50% of the US population by 2070. This is a source of much hysteria on the right. Yet they fail to note that in all historic examples heterogeneous states become vassal states serving the self interest of whichever ethnic group happens to have the highest average IQ. Minorites can rule.

I will make reference to two historical examples, Qatar and colonial India. Qatar has some of the most fascinating demographics on the planet, essentially importing millions of mainly male, mainly young, mainly South Asian workers, to do low-status jobs under the kafala (sponsorship) system. These migrant workers make up a whopping 88% of the total population, and have an M:F ratio of 3:1 (!). This strategy is excellent for several reasons:

1) Migrant workers produce and consume within the Qatari economy
2) Yet they do not collect pensions or benefits because they tend to work on short-term contracts, and never become true citizens
3) They are therefore disproportionately high-yielding and low-burden
4) Qatari citizens proper have some of the world's highest GDP per capita

I don't see why a similar system couldn't be adopted in the UK and other Western European countries. The UK has an increasingly lopsided ratio of productive (working age) to non-productive (65+) members of the economy, which will only get worse as this century progresses. African and South Asian immigration could meet this demand for workers, and likely will, emboldened by our lenient border enforcement and a series of climate crises. The UK government has for some time now been pursuing a strategy in which illegal immigration is publicly condemned, but tacitly accepted with the understanding that they will be replacing our own missing generations of young workers.

A census of India conducted by the British of 1901 gives the total population at 294 million, 170,000 of which are Europeans. This means that during the peak of empire Europeans comprised just 0.0006% of the total population - a mere handful of British controlling an enormous, unfamiliar land mass and climate, and a culturally heterogenous population. The British instituted a system of 'double government' during the East India Trading Company's rule (Pitt's India Act of 1784), with a governor-general in the capital, Calcutta, and a governor in a subordinate presidency (Madras or Bombay), and governors posted in other provinces. These governors oversaw infrastructure projects, the export of India's natural resources back to Britain, and the introduction of a complex bureaucratic state and British legal system, whilst Indian locals continued with subsistence agriculture.

I suspect that if (when?) white Europeans become racial minorities in the UK, they will probably continue to dominate government and other high-status roles, a similar fashion to the British Raj. This is simply because individuals belonging to less able groups will be competitively excluded by the niche Anglo population that excels in cosmopolitan, abstract, human resource management, media mastery, and mercantile profiteering. They might then function as a genteel bureaucratic class, likely living in safe, racially segregated communities, and enjoying a relatively high quality of life. British culture will likely be preserved to a great extent, although its geographical extent may be reduced.

The Future

The Qatari/Raj solution may see Western Europe through the next century or so (provided we avert climate crises and other catastrophic scenarios). As things stand, the TFR of the so called 'temperate' populations is significantly lower than that of the 'tropical' ones. Compare Europe's TFR of 2.1 to Africa's TFR of 4.1 (6.1 in sub-Saharan Africa). This means that over time the mean global IQ is gradually decreasing, as lower-intelligence populations outbreed higher-intelligence ones. There is a noted inverse relationship between fertility and intelligence.

Intelligence (capacity for symbolic thought, novel thought, inventiveness, ability to plan, co-operative behaviour, etc) is necessary if you want to build a functioning civilisation - intelligence is also necessary to maintain that civilisation. For example, we can all use smartphones, undergo MRI scans and use electricity produced by nuclear fission energy, but how many of us could recreate those technologies in isolation? Will we have a large enough pool of intelligent people from which to draw engineers and the desirable X number of doctors/100,000 people? Will violence and impulsivity correlated with low-IQ increase to a point where laws just stop being enforceable? Will we still have the capacity to innovate? I'm reminded in particular of the collapse of European colonies in the tropics after the Europeans pulled out, much of the infrastructure left to ruin unless the indigenous population’s intelligence was also similar or superior to them, or they were ‘crossbred’ with other high functioning populations (as in Singapore).

Despite these concerns, I remain unconvinced that the suffering entailed by a eugenics programme could possibly be justified (I will write about this elsewhere). Rejecting this option is a fairly honourable defeat. It may mean global capacity for innovation declines, and we encounter numerous climate, energy and demographic crises. It may mean waiting some indeterminate amount of time until random genetic mutations arise and create the conditions in which the mass production of the integrated circuit chip in the computer on which I am typing might be possible once again.

[This article is subject to revision pending confirmation of Richard Lynn's climate hypothesis]

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Misunderstanding Contractarianism

As mainstream contractarianism has it, per Hobbes, Rosseau, Gough and Rawls, the 'social contract' is made between the state and the citizen: "The people have made a contract with their ruler which determines their relations with him. They promise him obedience, while he promises his protection and good government..." (J. W. Gough, The Social Contract). I want to briefly point out the error in this conception of contract theory. I believe that the mistake originates from the fact that there are indeed two quite different types of contract which states enforce:

Particular contracts: Contracts made between two or more individuals or groups. For example, all forms of commercial exchange. These contracts do not usually implicate any third parties. In ideal cases, they are entered into by free agents, meaning that they are usally legitimate.
Unilateral contracts: Every citizen in the state is bound to every other citizen by these contracts. For example, those codified into a state's law, eg. it is illegal to murder, defraud etc. At present, unilateral contracts are not freely entered into by citizens. They are enforced by the full weight of the state's justice system yet are formed without explicit consent from participants, and cannot be exited, amended or opted out of - in this sense they must be described as coercive.

[For both types of contract, defection results in penalties such as fines or imprisonment meted out by the state. There is no gameplay without a referee with the power to disqualify - for this reason the state must have a monopoly on violence.]

It is with this second type of contract, 'unilateral contracts' or 'laws' that Gough's mistake is introduced. To take a very simple example: a law which forbid one citizen to murder another. Gough understands this law to be 'the state protecting the individual's right to life' in exchange for 'the citizen submitting to the state's authority'. But this is a strange obfuscation of what is really occuring. In reality, the state is merely enforcing the contract between citizens, according to which they will mutually refrain from murdering one another. So, the state is better described as a kind of impartial intercessorary body, or honest broker, which facilitates contracts between citizens but does not actually wnter into them itself. There is no 'contract with the state'.

It is also with this second type of contract that I find serious legitimacy issues. I will argue that 'unilateral contracts' ie. those contracts entered into 'tacitly', cannot be considered legitimate. Then, I will propose a simple policy which will allow us to retain the clear benefits of state-enforced laws, minus their current illegitimate character, and will take an eliminative stance towards the concepts of natural and legal rights.

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Stuck in the Middle with You

Pick a flavour of denial: one herd on the left denies intrinsic predicaments (human biodiversity, sex, race) and the other herd on the right denies extrinsic predicaments (peak energy-resources, global warming, pandemics).

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The Problem of the Fourth: The Trinity and Leibniz's 'vinculum substantiale'

The problem of the Trinity is primarily a mereological one. It is the same as the problem of composite substances - how should we reconcile a plurality of identities in one being? In this essay I will show that a unity of three divine persons produces what I call 'the problem of the fourth'. I will argue that God is not just the mere aggregate of the divine persons, but instead take the radical mereological position that a composite substance (the Godhead) is ontologically distinct from its constituent parts (the Trinity). I will then discuss the implications of this for Christian Trinitarianism, namely, that there are not three but four divine beings: the Father, the Son, the Holy Spirit and the Godhead.

This 'problem of the fourth' is an ancient one. An axiom attributed to alchemist Maria the Prophetess1 states that: "One becomes two, two becomes three, and out of the third comes the One as the fourth" is dated as early as the 3rd century. In spite of this, the precise qualitative difference between the mere aggregate of divine persons and the total unity of 'the Godhead' is often elided within conventional Trinitarian theology2. It is the existence and nature of this 'fourth' that I would like to explore. In part I, I will demonstrate using set theory that the whole is ontologically distinct from its constituent parts. In Part II, I will show how a Godhead of four divine objects can still satisfy conventional Trinitarian doctrine. In part III, I will introduce Leibniz's 'vinculum substantiale' in order to further elucidate the nature of this fourth. The doctrine of the Trinity describes a God comprised of three persons, each distinct from the others, yet sharing the same substance. I will give a brief account of Nicene Trinitarianism, quoting from the Catechism of the Catholic Church (1992). Three pertinent doctrines should be established in particular:

1) God is one of three persons ("The Trinity is One. We do not confess three Gods, but one God in three persons..."[Council of Constantinople II (553): DS 421.])3

2) the divine persons are consubstantial ("While they are called three persons in view of their relations, we believe in one nature or substance." [Council of Toledo XI (675): DS 528])4

3) the divine persons are really distinct from each other ("He is not the Father who is the Son, nor is the Son he who is the Father, nor is the Holy Spirit he who is the Father or the Son." [Council of Toledo XI (675): DS 530:26])5

I. God as superset

The Catholic Church does not explicitly recognise the totality of the Godhead as having unique being beyond the mere aggregate of Father, Son and Holy Spirit, but nor is this explicitly denied6. In much theological writing there is often some slippage between these ideas, of God as merely the aggregate of divine persons, God-as-unity, or here, God-as-container:

"... I give you but one divinity and power, existing one in three, and containing the three in a distinct way." (St. Gregory of Nazianzus, Oratio 40, 41: PG 36, 417. [italics mine])7

According to St. Gregory, God "contains" the three members of the Trinity "in a distinct way". This configuration subtly implies the ontological distinction between the members of the Trinity and their substantiative unity, the 'container' - or 'superset'.

In everyday life, too, we understand intuitively that a composite has existence beyond its constituent parts. Planks of wood stacked on a docking yard bear quite different properties from the ship that will be built out of those planks - for example, the latter floats, the former do not. A carbon atom may have certain distinctive properties, however, many carbon atoms in a certain spatial arrangement produce diamond, which again bears quite different properties altogether. Indeed, this may even approximate more closely how most lay Christians experience their faith - with the folk philosophy that 'the whole is more than the sum of its parts'. However, it still bears proving mathematically.

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. More broadly, it allows us to generalise the relations between objects to a very abstract level, including mereological relations. As the problem of the Trinity is of this very genre, I submit set theory as an under-explored and potentially fruitful way to go about Trinitology. I will use set theory to demonstrate that the whole is ontologically distinct from its constituent parts.

We may say that the three divine persons are proper subsets of the Godhead. As per the doctrine of real distinction, these subsets must be disjoint. The superset 'contains' the elements of its subset(s), but is still distinct from it. In this way, the Godhead should be understood as a superset, and the Father, the Son and the Holy Spirit can be understood as its proper subsets. Let the Godhead be represented by set {G}, the Father be represented by set {F}, the Son be represented by set {S}, and the Holy Spirit be represented by set {H}.

⊂ is used to denote 'proper subset of'

{F}⊂{G}

{S}⊂{G}

{H}⊂{G}

Set theory shows that the whole is ontologically distinct from its constituent parts. Here, there are not three but four sets, not three but four divine persons.

II. Identity of cardinality

Having established that there are four divine members of the Godhead, we can now test this configuration to see whether the Trinitarian doctrines described above are preserved under it. The Catechism of the Catholic Church states unambiguously in more than one place that: "The divine persons do not share the one divinity among themselves but each of them is God whole and entire." [Council of Toledo XI (675): DS 530:26. (italics mine)]8, and that: "Each person considered in himself is entirely God." [St. Gregory of Nazianzus, Oratio 40, 41: PG 36, 417. (italics mine)]9.

Here we approach the heart of the problem: if the Father is identical with God, and the Son is identical with God, and the Holy Spirit is identical with God, we must infer that Father, Son and Holy Spirit are also identical. Not only does this violate the doctrine of real distinction, it dissolves the Trinity conceptually: the law of identity of indiscernibles (‘Leibniz's Law’) states that there cannot be separate objects or entities that have all their properties in common10. Therefore, it would seem that the three members of the Trininty cannot be both identical and distinct, and are collapsed into one.

The divine persons, being substantial, are bearers-of-properties. Any two or more entities must be differentiated by their properties in order to be considered distinct11. Therefore, in order to satisfy both Leibniz's law and the Trinitarian doctrines, each of the three divine persons must bear at least one property that the others do not, whilst still participating in the Godhead. And yet if God is a unitive being, how can he not also bear the properties of the persons which he contains? Or put another way: how can identical beings bear different properties? Whilst on its face paradoxical, I submit that all three divine persons can be both really distinct from each other, and also identical with the Godhead - if we accept that their identity is one of cardinality.

'Cardinality' is used to define the number of elements in a set. According to the Catechism of the Catholic Church, God is infinite ("The Trinity is... the infinite co-naturality of three infinites." [St. Gregory of Nazianzus, Oratio 40, 41: PG 36, 417])12. Therefore, we can say that the cardinality of God is infinity (∞). Each divine person is also infinite13, and also has a cardinality of ∞. This seems to collapse the doctrine of real distinction. However, (as Georg Cantor demonstrated with his diaganol proof) some infinites are larger than others14. For example, the set of all real numbers contains three disjoint sets: the set of all prime numbers, the set of all even numbers, and the set of all irrational numbers. These four sets all have identical cardinality (∞). There are infinite prime numbers, infinite even numbers, and infinite irrational numbers15, and yet they are still subsets of (smaller than) the set of all real numbers. Similarly, the Father, Son, Holy Spirit and the Godhead are all identical in cardinality (∞), yet also retain their distinction, as the size of infinities varies among them. Therefore, the three members of the Trinity are all identical with, yet bear distinct properties from, the Godhead. The doctrines of both consubstantiality and the doctrine of real distinction is preserved.

III. Leibniz's 'vinculum substantiale'

Leibniz introduces the short, inscrutable phrase ‘vinculum substantiale’ ('substantial bond') during his correspondence with the Jesuit monk Bartholomew Des Bosses16 in 1713. It was used contextually to discuss transubstantiation, however, it carries implications for the problem of parts and composites more generally.

Throughout the Leibniz-Des Bosses correspondence, the 'vinculum substantiale' underwent several quite drastic modifications. It is described in one place as 'that which unites monads to form a composite substance', but in another is identified with the composite subject itself17. Brandon Look defines vinculum substantiale as: “some substance-like thing that exists apart from the monads in a composite; it is not a relation, a dominant monad, a substantial form or the entire composite substance.” (Notes on; Look, B. 2000, p. 205)18. I will use what I believe to be the ideologically mature form of the theory, which is taken from a letter dated 29th of May, 1716 (Leibniz 2007, p 375)19, the very last letter in the correspondence: 'If corporeal substance is something real over and above monads [...], we shall have to say that corporeal substance consists in a certain union, or rather in a real unifier superadded to monads...' (Leibniz 2007, p 225 [italics mine])

Broadly, then, the vinculum is what changes the mere aggregate into a genuine composite. It's important to note that Leibniz is quite explicit that this 'vinculum' exists substantially, and is not merely a form or property, when he describes it as being "superadded [to monads.]". We can modify this for our purposes: God is the real unifier superadded to the Father, Son and Holy Spirit. Using the vinculum, Leibniz hypostasises the unity of a composed substance. Likewise, the Godhead is the hypostatised unity of the Trinity. We can go so far as to say that this 'fourth' element of the Trinity - its substantiative unity - can be directly identified with the 'vinculum substantiale'.

At first glance, 'the fourth divine object' seems like an indigestible addition to conventional Trinitarian theology. However, Leibniz's vinculum does much to de-personify and deproblematize it, by firmly identifying the fourth subject as divine 'unifier' or 'vinculum', rather than divine 'person'. The problem can be accommodated by any Christian theology committed to Trinitarianism, with the reassurance that the difference made is only quantitive and not qualitative.

By Alice Lafferty

References:

[1] Haeffner, Mark. The Dictionary of Alchemy: From Maria Prophetissa to Isaac Newton. The Aquarian Press, London, 1991

[2] [3] [4] [5] The Catholic Church. Catechism of the Catholic Church. Vatican City : Libreria Editrice Vaticana, 1992.

[6] Catechism of the Catholic Church, 253-267: The Dogma of the Holy Trinity http://www.vatican.va/archive/ENG0015/_P17.HTM#1FT

[7] [8] [9] The Catholic Church. Catechism of the Catholic Church. Vatican City : Libreria Editrice Vaticana, 1992.

[10] [11] Philosophical Papers and Letters. By G. W. Leibniz. Translated and edited by Leroy E. Loemker. (University of Chicago Press: Cambridge University Press. Printed by Photopress, U.S.A. 1956. Two vols. Pp. x, 1228. Price 90s

[12] [13] The Catholic Church. Catechism of the Catholic Church. Vatican City : Libreria Editrice Vaticana, 1992.

[14] Simmons, Keith. Universality and the Liar: An Essay on Truth and the Diagonal Argument. Cambridge University Press, 1993

[15] Bagaria, Joan. "Set Theory", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Fall 2019 ed.), Metaphysics Research Lab, Stanford University, 2019.

[16] [17] Leibniz, G. W., Brandon C. Look, and Donald Rutherford. The Leibniz-Des Bosses Correspondence. Yale University Press, 2007.

[18] Look, Brandon. Leibniz and the Substance of the Vinculum Substantiale. Journal of the History of Philosophy, 2000 38 (2):203-220.

[19] Leibniz, G. W., Brandon C. Look, and Donald Rutherford. The Leibniz-Des Bosses Correspondence. Yale University Press, 2007.

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Who or what is Satan?

The temptation of Jesus (Matthew 4:1-11):

'8Again, the devil took Him to a very high mountain and showed him all the kingdoms of the world and their splendor. 9 "All this I will give you," he said, "if you will bow down and worship me."

10Jesus said to him, "Away from me, Satan! For it is written, "Worship the Lord your God and serve him only."

11Then the devil left him, and angels came and attended him.'

Augustine says that sin is a problem of 'improperly ordered love':

These are thy gifts; they are good, for thou in thy
goodness has made them.
Nothing in them is from us, save for sin when,
neglectful of order,
We fix our love on the creature, instead of on thee,
the Creator. (City of God, XV.22)

Similarly in Girard, Satan is the personification of mimetic desire. Satan "... is totally mimetic, which amounts to saying nonexistent as an individual self. THE DEVIL, OR SATAN, signifies rivalistic contagion."

In Dante's Hell, the Devil is not burning in a lake of fire, but suspended in a lake of ice [Dante canto XXXIV in the translation by Henry Wadsworth Longfellow]:

The Emperor of the kingdom dolorous
From his mid-breast forth issued from the ice;
And better with a giant I compare
Than do the giants with those arms of his;
Consider now how great must be that whole,
Which unto such a part conforms itself.
Were he as fair once, as he now is foul,
And lifted up his brow against his Maker,
Well may proceed from him all tribulation.
O, what a marvel it appeared to me,
When I beheld three faces on his head!
The one in front, and that vermilion was

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Kenosis Theodicy

The absence of a convincing solution to the problem of evil has always been the biggest obstacle to my faith, much bigger than even any of the numerous metaphysical issue with the Christian God. We can jettison omnipotence, omniscience, or perfect goodness, but that hardly leaves us with anything worshipful at all.

My theodicy is an adaptation of divine 'kenosis' (meaning 'emptying oneself of oneself'). We might say that the the universe is a space carved out of God and our world is defined by the total privation of divinity.

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Recognition

I've read and re-read this article perhaps five times over the last year. Every time I return to it, it hurts me more.

"Most theories of recognition assume that in order to develop a practical identity, persons fundamentally depend on the feedback of other subjects (and of society as a whole). Misrecognition thereby hinders or destroys persons’ successful relationship to their selves... thus, recognition constitutes a “vital human need” (Taylor 1992, 26)". Fichte goes as far as to say that consciousness itself is produced intersubjectively.

What of the more narrowly defined form of mutual recognition - romantic love? Surely there is nothing else like it for the achievement of mutual recognition.

Sergio Costa in Easy Loving: romanticism and consumerism in late modernity, 2004:

"Romantic love expresses itself in “a bond with the other that knows no more ardent desire than the yearning to lead one's own life in the body of the loved one”.
As an idealization, it promises the individual full recognition of the others’ singularities (dimensions, peculiarities and individual idiosyncrasies).
As a relationship model, it historically combines a fusion of sexual passion and emotional affection (i.e. marriage, love and family)."

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Gamete Value Inversion in Novel Technological Environments

In mammals, the female sex produces a finite number of large, non-motile gametes, and the male produces an almost infinite number of small, motile gametes. Parental investment after conception is also highly asymmetrical: the female gestates the infant for 9 months, undergoes labour which in ancestral conditions is extremeley dangerous, and lactates for up to 3 further years. Producing offpsring then, is very cheap for the male and very costly for the female. Large male die-off does not have a significant effect on the fertility rate of a group in the way that a large female die-off certainly would. Women are therefore the 'limiting factor' in sexual reproduction, and have gained a degree of social status by this fact.

8th March 2023: Kyushu University, Japan anounce the succesful production of a live mouse without the use of any genetic information from a female. Ova were created by deleting the Y chromosome of a male cell and duplicating the X chromosome. "Male skin cells were reprogrammed into a stem cell-like state to create so-called induced pluripotent stem (iPS) cells. The Y-chromosome of these cells was then deleted and replaced by an X chromosome “borrowed” from another cell to produce iPS cells with two identical X chromosomes". This organism has two fathers, and no mother.

This is of interest because it appears to turn on its head the historical value of male and female gametes. It is much easier to duplicate an X chromosome than it is to create a Y chromosome entirely from scratch. So, in these novel technological conditions, it is now the male gamete which is scarce and valuable, and the female gamete which can be produced in almost infinite numbers.

This, coupled with technology which offers men highly appealing virtual sexual experiences accessed with little to no effort, will upset the dating market and compound the existentially threatening female status crash.

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Are complaints about sexual objectification covert attempts to surpress sexual competition?

When I see a sexualised image of an attractive woman, I might feel a somewhat negative emotion. The negative emotion is particularly strong if one or more attractive men are directing attention to the woman in question. I have always cognitively interpreted this emotion as 'disapproval of/indignation at the objectifying male gaze'.

And yet I noticed recently that looking at sexualised images of women who I believe are less conventionally attractive that me is not attended by this negative emotion. If I am indignant at the objectification of women because of the harm it causes them, why isn't this feeling triggered when the woman is unattractive? I wonder now if condemning the sexualisation of other women and insisting that they are harmed by it is not just a strategy to surpress sexual competition. Viewing sexualised images of female models causes women to engage in indirect aggression - I would suggest that the negative emotion is real, but may in at least some cases just be anxiety/aggression triggered by confronting a more attractive (more successful) sexual competitor. Less attractive women do not trigger this aggression because they are not threatening competitors.

Might go as far as to say that the entire elaborate theoretical infrastructure of 'sexual objectification' may have been devised post hoc in order to obscure female intrasexual competition, and secondarily to discharge anxiety without betraying its real cause. Not 'I hate the male gaze' but 'I hate that the male gaze lands on those more attractive than me'. As others have noted, people rarely complain about sexual objectification until after they are no longer subject to it.

Not that being sexually objectified is particularly pleasant - yet it still seems preferable to being sexually invisible. Also useful to note that I'm probably >99th percentile neurotic, and therefore very sensitive to status competition in general. So plausibly this is just a 'me' thing.

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Normative male sexuality

Female sexual attractiveness to men likely peaks at around 13 years of age. Female reproductive value begins to decline immediately after menarche.

"For male raters, there was significantly and strikingly greater attractiveness for the early adolescence female photos... preference for peak residual reproductive value was apparent."