Review of "A Universe from Nothing" by Lawrence M. Krauss

universe

Some five years ago, the consensus concerning this short and polemical book across several online literary venues was this: it's a good book of popular science and a bad book of philosophy.

This assessment is correct. This really is a pretty damn good of popular science. It succeeds brilliantly despite the heavy constraints that are imposed in any attempt to enable informing the current status of physical cosmology to the general public - as I shall explain in greater detail.

It also has barely nothing to contribute to the metaphysical issues behind concepts of nothingness. In that, the book is guilty of false advertisement - perhaps as part of an editor's ploy. It delivers neither the title nor the subtitle. What this book truly consists of is a dense expository history of over a century of physical cosmology in clear ordinary language.

The Intellectual Fraud Behind Popular Cosmology

The very motivation behind the literary industry of popular cosmology and theoretical physics is an unspoken socially acceptable intellectual fraud - albeit a relatively harmless one. It is an intellectual fraud in a way popular science books on many other scientific topics (such as evolutionary biology) are not. And that is because the type of knowledge that must be acquired to truly apprehend what is going on in theoretical physics and cosmology is knowledge of a tacit character that simply can not be acquired by reading books. This may even trick otherwise intelligent and educated persons into the false belief that they truly understand these advanced topics when in fact, they do not.

Let me assume that you, the reader, under reasonable standards, is a scientifically literate adult living in an urban and industrial society. Do you understand Natural Selection? More than likely you do. To put it in the bold words of philosopher Daniel Dennett, you can explain Natural Selection in a minute. Natural selection really is a simple idea - although one with tremendously complex consequences and, as an epistemic tradeoff, much prone to caricature.

But do you understand General Relativity? More than likely, you do not. And it doesn't matter how much Brian Greene and Stephen Hawking you've read and how many visually breathtaking documentaries filled with lively metaphors of basketballs deforming pillows you've seen and entertained in your imagination - and it doesn't really matter how wonderful you take your imagination to be. Not even ingenious uses of spandex will do.

To truly grasp General Relativity, one must master a myriad of mathematics and physics. This includes the much more accessible topic of Special Relativity. But it also includes the tools of tensor calculus and differential geometry (and just for this you'll generally require multivariable calculus and some solid understanding of linear algebra). Depth and differences in research traditions across physics will demand additional mathematics such as topology and analysis. This means that even if you are a person of above-average general intelligence, it will take years to master this content, in the form of undergraduate and most likely graduate-level courses in physics and mathematics.

Depending on the level of your intelligence (and moxie) this will probably mean that one can only develop the required geometrical and physical intuition to truly understand General Relativity through a mostly solitary mental journey of laborious homework, amidst pages of scribbled exercises and piles and piles of mistakes. It is much more cognitive demanding than grasping a simple algorithm such as Natural Selection. If you can do it, you'll be a part of a selected intellectual elite that has a special understanding of the cosmos.

If you lack this know how, you are not qualified to understand and much less to criticize General Relativity. It really is that simple. Tough luck for physics crackpots.

Think you understand String Theory? That is even more unlikely. For General Relativity just is one of the behemoths you need to master to understand these families of theories. The obsession of contemporary cosmology with n-dimensional manifolds starts with Kaluza-Klein Theory right after the development of General Relativity (for a popular historical overview, I recommend [1]). To understand String Theory, you need to be intimately acquainted with the formalisms of Lagrangian and Hamiltonian Classical Mechanics, the mysteries of Quantum Field Theory, some Group Theory and more.

And that's why popular cosmology is a fraud. Humans, in general, are superb storytellers but terrible mathematicians [2].

Succeeding in an Impossible Task

Given these hard facts, how should an intelligent and scientifically literate dilettante that is humble and intellectually honest behave? One can muster here a distinction between belief and acceptance ([3], Chapter 4). As a whole, the literature concerning this distinction states that while "belief" is an involuntary and irresistible act, "acceptance" is a willful deliberation or commitment. If the belief in counter-intuitive empirical statements is the consequence of deep understanding, i.e., the through and through acquisition of the tacit knowledge required to engage with the relevant alongside an honest evaluation of the evidence, then dilettantes with mere procedural knowledge of General Relativity cannot believe it. But they may accept it.

You are epistemically warranted to accept the conclusions of high-caliber cosmologists and theoretical physicists. Their authority is a proxy for the reasons and evidence over which their claims are justified. Let them do the thinking.

Good Science

Given this pessimistic panorama, I was pleasantly surprised with the output of Krauss. His prose is at least as good as the best popular cosmology I've read, from Victor Stenger and Michio Kaku. Krauss joins the ranks of talented popularizers of science that are also first-rate scientists.

Krauss is truly talented in this overbearing task of condensing material comprising a full century of understanding of physics.

As someone who has devoured a fair share of popular cosmology and theoretical physics since teenage years, this book still managed to deliver novelty in both concept and presentation. It displays a never-ending succession of instances of how our common sensical intuitions are broken down when we confront the structure of empty space. For instance, Krauss is an avowed realist on the existence of virtual particles; they truly are there and are not merely heuristic computational devices (for a classic alternative interpretation, see [4]). Here's one of the bolder sections:

“[C]onsider the [nonzero energy] electric field emanating from a charged object. It is definitely real. You can feel the static electric force on your hair or watch a balloon stick to a wall. However, the quantum theory of electromagnetism suggests that the static field is due to the emission, by the charged particles involved in producing the field, of virtual photons that have essentially zero total energy. These virtual particles, because they have zero energy, can propagate across the universe without disappearing, and the field due to the superposition of many of them is so real it can be felt.”

I have never seen a more striking display of the contrast between the concreteness of the everyday experience of our Umwelt and what we way find at scales very far away from our notional world.

“Here is a snapshot of how things actually look. It is not a real photograph of course, but rather an artistic rendering of the mathematics governing the dynamics of quarks and the fields that bind them. The odd shapes and different shadings reflect the strength of the fields interacting with one another and with the quarks inside the proton as virtual particles spontaneously pop in and out of existence.”

In the book you only see a slice of an existing animation; I found the entire thing through the wonderful blog Back Reaction by theoretical physicist Sabine Hossenfelder. This animation is known as the "Quantum Chromodynamics Lava Lamp", and it is the output of the research of theoretical physicist Derek B. Leinweber. Here it is:

This simulation displays the action density of the quark and gluon field fluctuations of "empty" space. It was featured in the lecture of the 2004 Nobel Prize of Physics.

“The proton is intermittently full of these virtual particles and, in fact, when we try to estimate how much they might contribute to the mass of the proton, we find that the quarks themselves provide very little of the total mass and that the fields created by these particles contribute most of the energy that goes into the proton’s rest energy and, hence, its rest mass. The same is true for the neutron, and since you are made of protons and neutrons, the same is true for you!”

Simply amazing - for the non-instrumentalist on virtual particles, at least.

Right on Philosophy

Of the many diatribes that Lawrence Krauss (and after him, other physicists such as Freeman Dyson) delivered against academic philosophy, one lesson is absolutely correct; most of what passes as "philosophy of science" is of little cognitive value.

One cannot do philosophy of science without understanding science. It is insane that there are philosophers of physics can't calculate a simple derivative. I've recently read Sir Anthony Kenny's History of Modern Philosophy and he makes the same exact point in his chapter delineating the development of physics from natural philosophy: "such a discipline [contemporary philosophy of physics] can only be pursued by those with more knowledge of the modern science of physics" ([5], p.180).

There are excellent philosophers of physics around who truly know what they are doing - researchers such as Bas Van Fraassen, Décio Krause, James Ladyman, Mario Bunge, Newton da Costa, Steven French and Otávio Bueno.

Philosophical folklore disguised as adamant historical tradition tells us that engraved at the door of Plato's Academy, it read "Let no one ignorant of geometry enter!". It's a good story, but it is probably false. Nevertheless, the spirit is absolutely right on; "Let no philosopher ignorant of science do philosophy of science!".

Bad Philosophy

I agree with the general sentiment; Krauss really adds nothing to the perennial problems of nothingness and ex nihilo existence as they have been formulated throughout most of the history of Western philosophy. For instance, he writes:

I suspect that, at the times of Plato and Aquinas, when they pondered why there was something rather than nothing, empty space with nothing in it was probably a good approximation of what they were thinking about.

I know very little about the metaphysics of Plato and Aquinas but I know enough to know their conceptions of "nothingness" are more abstract than empty space. Krauss' suspicion is false.

However... I do know a thing or two about my Greek intellectual great-great grandfathers, Leucippus and Democritus. Under their framework, Krauss' suspicion is spot on. For the early atomists, "Nothingness" (or Nonbeing) was identified with "The Void"; the ontological correspondent to "The Full" of Eleatic philosophy were the atoms. So here we have at least one veritable philosophical tradition that shares this conception of nothingness ([6], Chapter 6).

Something from Nothing?

But what would a reasonable addition to this philosophical problem look like? I hold that the epistemic space of solutions to philosophical problems falls into four cases; there are problems solvable through empirical methods, problems solvable through a priori methods (and if strong forms of empiricism are correct, this category gets subsumed by the later), there are pseudo-problems and there might be unsolvable mysteries and antinomies. Concerning this issue, my unrelenting scientism acquires a logical positivist flavor. It is my opinion that most problems stemming from issues of nothingness are pseudo-problems; they superficially look like answerable questions that mandate unique non-arbitrary answers but they are not. One of my favorite papers that explicitly follow this line of reasoning is Stephen Maitzen's "Stop Asking Why There's Anything" [7]. I submit that Maitzen's remarks may be generalized to surrounding questions involving things and non-things.

[1] M. Kaku, Hyperspace: a scientific odyssey through parallel universes, time warps, and the tenth dimension, OUP Oxford, 1995.
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[2] A. Rosenberg, The atheist's guide to reality: enjoying life without illusions, W. W. Norton & Company, 2011.
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[3] N. C. A. da Costa and S. French, Science and partial truth: a unitary approach to models and scientific reasoning, Oxford, 2003.
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[4] M. Bunge, "Virtual processes and virtual particles: real or fictitious?," International journal of theoretical physics, vol. 3, iss. 6, pp. 507-508, 1970.
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[5] A. Kenny, The rise of modern philosophy, Oxford University Press, 2006.
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[6] C. C. W. Taylor, From the beginning to plato: routledge history of philosophy volume 1, Routledge, 2003.
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[7] S. Maitzen, "Stop asking why there's anything," Erkenntnis, vol. 77, iss. 1, pp. 51-63, 2012.
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#GoogleGate explained

Peter Paul Rubens (authorship contested), Battaglia delle Amazzoni (1615)

When I read software engineer's James Damore's "manifesto", aptly titled Google's Ideological Echo Chamber, I fail to see many things. I'm sincerely flabbergasted, given my worldview, at not being able to find a single instance of "sexism", "biological determinism", "misogyny" or any other colorful expletive used by progressive radical egalitarians as a smear word. That's how different conceptual schemes can be once we exclude those who are being intellectually dishonest and have either not read the document or are deliberately misrepresenting it.

What I do see are the reasoned, balanced words of an intelligent young man who desires to simultaneously achieve both goals of truth and social justice at his workplace, with the best interests of his company in mind. I see a truly morally courageous individual who stood off against injustice as he saw it against a very different moral community from his own, which apparently happens to be having enormous influence in one of the most powerful companies on the planet. I can almost feel at times that he seemed to be walking on eggshells and wasn't as vocal as he could be.

How is this possible? How come the same document activates so wildly different semantic frames in different people? And who's right? Have I become so blind by my own cognitive biases to the point I'm missing that much bigotry and hatred?

I have a cluster of hypotheses to explain this mess. They are not novel; they are the coalescence of several different theoretical and empirical results. I'll briefly summarize on this post some of the arguments brought forth in my recent paper on political correctness.

First, we must assume that there exists a plurality of mutually inconsistent accounts of practical reason that human beings may enact. There is no "true and only" rationality; there are rationalities that fit different forms of life, infusing them with different aims and standards of success. Even on the same form of life, such as philosophical activity, we find competing and conflicting accounts of rationality [1].

But let us consider what is generally understood prototypically as "rationality", the like we expect to be expressed by bona fide philosophical and scientific cognition; this is a rationality of objectivity, guided by epistemic values such as empirical adequacy, internal consistency, predictive accuracy and explanatory power. With some exceptions such as constructive empiricists (that have some really nice arguments) and postmodern sociologists (that have some really underwhelming arguments), this type of reasoning deals fundamentally with a discourse that is truth-apt and truth stands as the supreme epistemic goal of this kind of rational inquiry.

But this is not the sort of rationality that is responsible for the crucifixion of James Damore. This is not the rationality being enacted by the so-called "social justice warriors."

Which rationality is it then? It all starts with this hypothesis: human beings are suckers for tribes [2],[3]. It's part of who we are. We relish ourselves into organizing (and re-organizing, and merging, and dissolving...) gangs, crews, bands, factions, congregations and the like; these are fractally expressed as families, political affiliations, religions, football teams, nationalities, army units and so on. Belonging to a social group is a fundamental source of well being for humans. No wonder then, given the importance it has on our lives, that a huge part of practical reason will be devoted to this setting.

Here enters the theory of identity-protective cognition [4], a realization of the expressivist account of rationality by philosopher Elizabeth Anderson [5].

The goal of this type of reasoning is not truth. It is securing the integrity of the group one belongs by defending its core beliefs and values with one's cognitive, affective and behavioral resources. This is manifested in many ways. Confirmation bias will rule that which reinforces the group's beliefs and values, and contrarian opinions can be easily interpreted as insults to the group's intellectual tradition. Adherents can become gratuitously aggressive against someone who disagrees with them in order to suppress dissenting thoughts. These are some of the aspects that make echo chambers and ideological uniformity so dangerous.

Progressive radical egalitarians have their own species of identity-protective cognition; here we have a rationality that aims at social justice and whose standards of success are non-epistemic values of political correctness such as inclusiveness, diversity, empathy and political uniformity.

The worldview of progressive radical egalitarians, I claim, has certain core beliefs which must be defended at all costs. I also hold it has an implicit underlying ethical principle which I've named the Generalized Difference Principle (GDP). This principle is inspired by a usage by philosopher of biology Neven Sesardić ([6], p.224) of the famous heuristic devised by political philosopher John Rawls in his monumental defense of liberal democracy [7].

According to the GDP, if you utter the statement that a population x fares statistically better than a population y with respect to a given mental trait M where both x and y are of the same social genus \cal G, where this leverage of x in comparison to y is partly genetic in origin and finally, where x is taken to be the dominant or oppressive group and y the marginalized or oppressed group, then your assertion exemplifies a class of immoral acts associated with \cal G.

To speak it more plainly: if men are stated to be the oppressors of women, then if you claim, for instance, that men have on average a greater interest to pursue STEM careers than women due to natural inclinations, then you are sexist. In the semantics of progressive radical egalitarian worldview, there exists a strong conflation of facts and values. "Sexism" isn't just outright discrimination; factual statements can be sexist as well (and "racist", "ableist", "homophobic", etc).

Violations of the GDP are taken to be grievous because they necessarily violate one of the core beliefs of PC adherents; a thesis I call anthropological mental egalitarianism, the denial of between-group differences in cognition, affect and behavior that is traceable to genetic factors and socioeconomically significant.

Violations of the GDP are evil. And for that, James Domare needed to be punished by the moral community hegemonic to Google.

James Damore has been "Summered"; he dared to mention the contemporary behavioral genetics and differential psychology behind sex differences in cognition, affect and behavior which is established by existing empirical evidence to be partly genetic in origin (see, for instance, [8], [9], [10], [11])

Progressive radical egalitarians are mental environmentalists. They hold that the between-group variation of socioeconomically valuable psychological traits to be exclusively environmental in origin.

Even if the means and medians of arbitrary psychological traits in men and women were the same (and we have empirical evidence suggesting they are not), this would still not be enough. One of the most important facts about our species is how different the phenotypical distributions for arbitrary traits are among the sexes. For instance, as a group, women display significantly lesser intra-sexual variability for arbitrary mental traits [12]. There are more men in both tails of the cognitive-affective-behavioral spectrum; for example, concerning general intelligence, there are both more cognitively impaired and delayed men as well as more intellectually gifted men. Why is that? My favorite hypothesis is powerful but deeply counter-intuitive; overwhelmingly, your ancestors have been female.

For the contemporary defenders of social justice, sex differences in cognition, affect and behavior need to be a hundred percent environmental in origin due to core beliefs of their worldview. It would not fare well for with the theory of social oppression under which if groups are economically unequal, it is because some privileged group is oppressing another marginalized group. If mental environmentalism is false, however, in the complete absence of discrimination, there could still be economic inequality due to natural talent - inequality would not simply be an artifact of "social construction."

For those who are interested, I refer to Section 4 of my paper where I explain these concepts in detail.

Are we to infer the executioners of James Damore who are deeply offended and angered by his words merely stupid and irrational people? Not at all. They are enacting perfectly the rationality of identity-protective cognition. They have very successfully attempted to preserve the mandatory narrative script of social oppression theory by purging the one who dissented against anthropological mental egalitarianism into unemployment and social ostracism.

[1] A. C. MacIntyre and A. C. Macintyre, Whose justice? which rationality?, Duckworth London, 1988.
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[2] P. J. Richerson and R. Boyd, "The evolution of subjective commitment to groups: a tribal instincts hypothesis," Evolution and the capacity for commitment, vol. 3, pp. 186-220, 2001.
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[3] M. Van Vugt and J. H. Park, "The tribal instinct hypothesis," The psychology of prosocial behavior: group processes, intergroup relations, and helping, 2009.
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[4] D. M. Kahan, D. Braman, J. Gastil, P. Slovic, and C. K. Mertz, "Culture and identity-protective cognition: explaining the white-male effect in risk perception," Journal of empirical legal studies, vol. 4, iss. 3, pp. 465-505, 2007.
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[5] E. Anderson, Value in ethics and economics, Harvard University Press, 1995.
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[6] N. Sesardic, Making sense of heritability, Cambridge University Press, 2005.
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[7] J. Rawls, Political liberalism, Columbia University Press, 1993.
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[8] Sex differences in the brain: from genes to behavior, J. B. Becker, K. J. Berkley, N. Geary, E. Hampson, J. P. Herman, and E. Young, Eds., Oxford University Press, 2007.
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[9] D. P. Schmitt, A. Realo, M. Voracek, and J. Allik, "Why can't a man be more like a woman? sex differences in big five personality traits across 55 cultures.," Journal of personality and social psychology, vol. 94, iss. 1, p. 168, 2008.
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[10] T. C. Ngun, N. Ghahramani, F. J. Sánchez, S. Bocklandt, and E. Vilain, "The genetics of sex differences in brain and behavior," Frontiers in neuroendocrinology, vol. 32, iss. 2, pp. 227-246, 2011.
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[11] A. N. V. Ruigrok, G. Salimi-Khorshidi, M. Lai, S. Baron-Cohen, M. V. Lombardo, R. J. Tait, and J. Suckling, "A meta-analysis of sex differences in human brain structure," Neuroscience & biobehavioral reviews, vol. 39, pp. 34-50, 2014.
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[12] A. Lehre, K. P. Lehre, P. Laake, and N. C. Danbolt, "Greater intrasex phenotype variability in males than in females is a fundamental aspect of the gender differences in humans," Developmental psychobiology, vol. 51, iss. 2, pp. 198-206, 2009.
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Can numbers be racist?

It appears to be the case - at least according to historian Sarah E. Bond, an expert in Classical Studies. In her essay Why We Need to Start Seeing the Classical World in Color, Professor Bond claims that the cephalic index is racist.

But what is the cephalic index? Every metazoan from a lineage that endured cephalization (that is, every animal with a head) potentially exhibits a cephalic index. The cephalic index is defined as the ratio of the width of a head times a hundred divided by the length of the same head.

Heads evolved at least four times in our planet (taken from Berkeley's excellent Understanding Evolution)

From the point of view of orthodox dimensional analysis, the cephalic index [CI] is a dimensionless quantity expressed through the formula [CI]=\frac{a L}{L} where:

  • The coefficient a is a real number conventionally fixed as 100
  • L is the base or fundamental quantity "length"
  • As it is commonly taught, the operation of division is said to "cancel out" the dimension "length" (L) of the numerator with another of its instance in the denominator and thus we say that the cephalic index is "dimensionless".

    The numerical value of dimensionless quantities remains invariant under different representation standards (for instance, using inches instead of centimeters to calculate a certain cephalic index). Dimensionless quantities are typically simply identified with real numbers. These numbers are deemed to be "pure", that is, unitless, devoid of dimensional content. So claiming that the cephalic index is racist is claiming that pure numbers can be racist.

    But I digress; if we were to only acknowledge established orthodoxy, the world would become boring really fast. The fact of the matter is that there appears to be something really troubling going on conceptually with the readied identification of dimensionless quantities with real numbers (see for instance Chapter 10 of [1] and Chapter 5 of [2]). Cephalic indexes in some ways are like angles; both are features defined as the ratio of two lengths. But despite being prototypically "dimensionless", angles are similar to quantities such as times, lengths, masses and resistances in that they can be extensively measured. And we also liberally assign units such as radians and degrees to angles. No wonder Krantz et al. aptly named angles "the bastard quantity of dimensional analysis". This leads to quirky characterizations; for instance, the late dimensional analysis theorist Ain Sonin [3] took angles to be dimensionless quantities that were also derived from the base quantity of length. Some modern treatments of dimensional analysis frown upon tradition and openly include the dimension of angle \alpha side by side with other base quantities [4].

    Similar vexations happen with a large number of quantities sporting obvious empirical significance which are expressed logarithmically and thus, by default, dimensionless. This standard narrative of dimensionless quantities and pure numbers is troublesome when one investigates the formal semantics of these features under measurement theory.

    But back to our original issue; even if the cephalic index is not a "pure" number, this hardly improves the case that it is "racist". Everything with a head exhibits a cephalic index and the cephalic index has reliably tracked real patterns in the behavior and cognition of metazoans hundreds of millions of years before the first human being displayed enmity towards conspecifics.

    [1] D. Luce, D. Krantz, P. Suppes, and A. Tversky, Foundations of measurement, vol. i: additive and polynomial representations, New York Academic Press, 1971.
    [Bibtex]
    @book{Suppes1971a,
    author = {Luce, Duncan and Krantz, David and Suppes, Patrick and Tversky, Amos},
    citeulike-article-id = {13531614},
    posted-at = {2015-03-02 22:50:45},
    priority = {2},
    publisher = {New York Academic Press},
    title = {Foundations of Measurement, Vol. I: Additive and polynomial representations},
    year = {1971}
    }
    [2] L. Narens, Theories of meaningfulness, Lawrence Erlbaum Associates, 2002.
    [Bibtex]
    @book{Narens2002a,
    author = {Narens, Louis},
    citeulike-article-id = {13531638},
    posted-at = {2015-03-02 22:50:46},
    priority = {2},
    publisher = {Lawrence Erlbaum Associates},
    series = {Scientific Psychology Series},
    title = {Theories of Meaningfulness},
    year = {2002}
    }
    [3] A. A. Sonin, "The physical basis of dimensional analysis," Massachusetts Institute of Technology 2001.
    [Bibtex]
    @techreport{Sonin2001a,
    author = {Sonin, Ain A.},
    citeulike-article-id = {13531648},
    institution = {Massachusetts Institute of Technology},
    posted-at = {2015-03-02 22:50:46},
    priority = {2},
    title = {The Physical Basis of Dimensional Analysis},
    year = {2001}
    }
    [4] J. C. Gibbings, Dimensional analysis, Springer Science & Business Media, 2011.
    [Bibtex]
    @book{Gibbings2011a,
    author = {Gibbings, John C.},
    citeulike-article-id = {14387318},
    posted-at = {2017-07-03 19:35:45},
    priority = {2},
    publisher = {Springer Science \& Business Media},
    title = {Dimensional analysis},
    year = {2011}
    }

    A Tale Of Two Sciences

    Wildebeest in the savannah

    Here is the tale of two researchers - an ethologist and a critical race theorist.

    The ethologist is studying certain classes of sociobiological phenomena, displays of interspecific aggression in the savannah ecosystem of the African continent.

    He posits that wildebeests cannot be agonistic towards lions because wildebeests lie in a lower trophic level than lions.

    At the same time, the critical race theorist is also studying certain classes of sociobiological phenomena; displays of intraspecific aggression in the anthropogenic biomes of the North American continent.

    He posits that human populations of Amerindian, African, East Eurasian and Oceanic descent cannot be racist towards a certain population of West Eurasian descent because they lie in a lower level of "institutional power" than these very West Eurasians.

    The researchers then show their results to their colleagues.

    The normative biologist receives scorn and ridicule for his spurious ad hoc reasoning and is never to be seen again in his faculty.

    The normative sociologist not only receives praise and respect for his insight but his statement enters public discourse and becomes common sense.

    Why?

    Moral Carryover

    powerlifting
    Image taken from Syatt Fitness

    The rational toolkit of the reflexive radical naturalist should be open, display content-wise heterogeneity (consisting of both prescriptions represented linguistically and nonverbal habits) and embrace a dose of pragmatism as a meta-epistemic value. It is unlikely that robust and psychologically realistic rationality can be characterized by an elegant set of principles - a neat list of behavioral or cognitive prescriptions, a naturalistic counterpart to the Ten Commandments. For reality is messy.

    Several heuristics, rules of thumb and regulatory principles appear to have robust cross-domain applicability over different normative fields. One of my favorites is the Pareto Principle which thrives in areas as diverse as management science, economics, software engineering and personal development. The statistical distribution behind the Pareto Principle is so widespread that I believe this regularity hints at a thermodynamical foundation for these phenomena.

    Another interesting concept found in sports science, particularly as it relates to strength training, is "carryover".

    'Carryover' in this context is informally used to name a property of motor patterns to readily "transfer" increases in performance onto other distinct motor patterns (with some shared structure) when trained. 'Carryover' also names the very gains or increases of performance enabled in this process.

    Very briefly, "carryover" is the n-ary property of a given motor pattern {x}_{1} to enhance the performance of one or more different motor patterns {x}_{2},...,{x}_{n} through the realization of x_{1}. For instance, heavy unilateral dumbbell rows by increasing grip strength are said to deliver carryover to deadlifts, i.e., to enhance your global performance in deadlifts. Thus carryover is a relation of causation found in a given network of motor patterns.

    I believe this concept has a natural application in practical ethics. Assume an agent-based account; what behavioral patterns are most conducive to the global enhancement of moral character? To answer this, we will need some theoretical understanding of moral character and virtues.

    A Network Of Virtues

    One of the chief ideas discussed in virtue-based accounts which is of relevance here is the thesis of the unity of virtues. This has been framed in many ways with varying restraint by different authors since the revival of virtue ethics over the last decades.

    One such way, which allegedly can be read quite directly from the dialogues of Socrates, is through logical entailment, by the thesis of the mutual entailment of virtues [1].

    Take 'C' and 'J' as the Socratic virtues of courage and justice and 'x' as an arbitrary moral agent. Consider 'Cx' the proposition "x is courageous" and 'Jx' the proposition "x is just". The thesis of mutual entailment states that both \forall x (Jx \to Cx) and \forall x (Cx \to Jx) are theorems in our formal system. This viewpoint of the unity of virtues can be summed by the saying "if you have one, you have them all". This is a quite strong constraint that is nowadays rejected by most virtue ethicists.

    For moral carryover, we need something weaker. We need to secure a relational causal structure. This can be represented as a connected graph, in a graph-theoretical sense. All but one of the vertices is a virtue to be exercised, each path is a causal relation. One central node will be the agent's character. We may call this bland virtue causal holism.

    Feedback is typically modeled in terms of systems of differential equations. But the procedures of calculus assume that we are dealing with quantitative data, and I find it highly doubtful that the psychological traits that embody traits like honesty or courage have this structure.

    For now, I will simply have to assume that there exists an appropriate conception of ordinal feedback to model how a network of virtues may evolve through habitual repetition - I can think of some simple qualitative methods from the time I used to work with Soft OR, many years ago. Given this sketchy graph-theoretical framework, the question thus is this; which individual node would contribute the greatest feedback, i.e., deliver the greatest moral carryover, to global character?

    A potential interesting proposal comes from the work of moral and political philosopher Alasdair MacIntyre. Under a conventional reading of MacIntyre, there is something special about honesty, courage and justice, three of the four Socratic virtues. It is as if the very grammar, in a Wittgensteinian sense, of many human social activities presuppose something like honesty, courage and justice for its proper functioning.

    These virtues are thus prime candidates for moral carryover. I will develop this argument in greater detail in the next section.

    Practices In the Philosophy of Alasdair MacIntyre

    In order to advance, I will have to say something about what constitutes a practice, a central term of art from the philosophy of MacIntyre. For this task, I have learned quite a bit from the scholarship of Christopher Stephen Lutz [2].

    Practices are a class of human behaviors. Practices are goal-oriented social activities with standards of performance and execution that are external from the agent enacting the practice. One could even risk a comparison with John Searle's theory of social institutions. It would seem that that under the terms of the former, practices just are human social institutions; they are intentional, collective, functional, agentive and status-conferring. Searlean social facts would the truthmakers of statements about practices. MacIntyre, however, explicitly distinguishes practices from institutions [3]; practices require institutions. Institutions are the social enforcers of the rules of the practice - one of the reasons they exist is to police practitioners, to make sure they are playing by the rules. Institutions set up the events where the abilities of the practitioners are put to test. Institutions are also the gatherers and backers of the external goods of the practices (as I will elaborate more later). While consortiums, federations and companies are paramount examples of institutions, these need to be seen as sophisticated developments of what institutions may become - an institution can exist more loosely as an embodied network of agreements, without formal treasury, committees or special buildings. What practices demand is at least a tacit endorsement of this social structure that is implied by them.

    Now for an example; take the behaviors involved in barbell strength training. The behavior you may enact by casually and aimlessly lifting heavy stuff from the floor (or from the rack, etc) is not a practice in MacIntyre's sense, for it is lacking the appropriate teleology that frames some behavior into standards of excellence. But the sport of powerlifting is a practice, or better, a family of closely related practices which are organized and promoted in our world by different organizations at the regional, national and international levels.

    Professional sports are prototypical examples of human activities with strict standards of performance and benchmarks of excellence, both of which are carefully regulated and recorded by organized international federations. For instance, a valid bench press movement for the International Powerlifting Federation requires the athlete to have his feet flat on the floor. In the International Powerlifting League, the athlete may bench from his heels up. These different constraints promote different standards of what counts as a good bench press movement.

    For an example of a benchmark of excellence, as of the day I'm writing, the male open bench press record in the 93kg category for the bench press (in a single lift competition) in the IPF is 318,5kg. This sets the current maximal standard for all equipped male benchers in this weight category for this federation.

    Practices and their standards are dynamic and evolve through history inside traditions. Records get broken, more impressive masterpieces get crafted, other neighboring practices indirectly enhance the performance of the practitioners (such as the relationship between sports nutrition and professional sports) and the rules may change. Some practices, like the game of chess, one of MacIntyre's favorite examples, are very robust and have been largely invariant rule-wise across time (chess has remained largely changeless since the first half of the XIX century). It is usual for current practitioners that are conscious of its history of their practice to emulate the feats of the best experts while pursuing excellence of achievement.

    Practices, being behaviors, are processes - and processes produce something [4]. Practices reliably produce certain goods. In MacIntyre's framework, there are goods which are external to the practices and goods which are internal to the practices. These categories are quite intuitive and I am fond of them because they can't be neatly fitted into traditional distinctions between the "subjective" and the "objective".

    For instance, the external goods of powerlifting involve the pleasures coming from the victories of competitive athletic achievements, the wealth in prizes and sponsorships and the increases in social status due to public recognition.

    The internal goods of a practice consist of getting good at the practice, i.e., the development of the abilities and skills that are conducive to good practice.

    There exists an important dissonance between a practice and the internal and external goods of the practice; and that is the fact that it is possible to acquire the external goods of the practice irrespective of the acquisition of the internal goods of the practice - for instance, by deception, theft and fraud.

    As an example, getting good at powerlifting in an avowed drug-free federation presupposes not using anabolic steroids to aid athletic performance. But powerlifter from a tested federation may nonetheless reach a victory in an official meet and reap the external goods of this practice due to the the leverage received by the use of an illegal substance. In that, he has not acquired the internal goods of the practice, for getting good at powerlifting naturally is distinct from getting good at powerlifting geared, that is, both practices impose different standards of excellence (and that is the point behind the existence of tested and untested powerlifting federations).

    One may object that the geared professional athlete has become skillful at something through diligent training. That is true. In fact, a geared athlete, being able to train on average with higher intensity and frequency due to the anti-inflammatory and injury-recovering properties of some substances, has the opportunity to train more often than a natural athlete. But that is not the point. The point is that getting good at a certain practice, acquiring its internal goods, involves practicing in a certain way, playing by the rules of the practice, diligently following the standards that have been set.

    For many, prohibitions sanctioned by the rules degenerates into simply "not getting caught". Institutions whose organizers consciously deliver external goods - the triad of wealth, power and fame - to practitioners that knowingly do not play by the enforced rules become corrupt. This is rampant in professional sports.

    It should now be clear that in this framework, the link between a practice and its internal goods is ethical. And the traits that enable us to acquire the internal goods of a practice are goods themselves with a very special standing - they are the virtues. Without virtue, a practice may degenerate into a mere means to acquire external goods.

    The Three Cardinal Virtues in MacIntyre's Philosophy

    In After Virtue [5], MacIntyre writes:

    It belongs to the concept of a practice as I have outlined it - and as we are all familiar with it already in our actual lives, whether we are painters or physicists or quarterbacks or indeed just lovers of good painting or first-rate experiments or a well-thrown pass, that its goods can only be achieved by subordinating ourselves within the practice in our relationship to other practitioners. We have to learn to recognize what is due to whom; we have to be prepared to take whatever self-endangering risks are demanded along the way; and we have to listen carefully to what we are told about our own inadequacies and to reply with the same carefulness for the facts. In other words we have to accept as necessary components of any practice with internal goods and standards of excellence the virtues of justice, courage and honesty.

    Under my reading, the case for these three virtues to be preconditions of well-functioning practices seems to be almost analytical.

    Getting good at a practice requires you to be honest concerning the current level of your ability and skill and the level demanded by the entrenched standards of excellence of the practice, i.e., how you may truly reach somewhere closer to "there" coming from "here".

    Justice is important in assessing the different levels of ability of the practitioners according to the standards of the practice and nothing else - other idiosyncratic criteria not contingent to these standards are irrelevante. For instance, while sharing external goods a measure of fairness is explicit, i.e. one must ideally get the wealth, power and fame one truly deserves.

    For MacIntyre, the inherent connection of a practice with courage in the text that follows the above quotation is a bit more abstract; it is related with maintaining the existence of a practice in a given community. For a practice cannot survive without people doing the practice - and doing it the right way. In order to make the practice survive and thrive, one must care about the people doing the activity and the shared goals which are collectively honored. Taking this seriously means that one is expected to risk himself against threats that may appear for the community, both from the inside and the outside. In that, courage also appears to assume compassion and love for the members of a community.

    I see courage as being crucially important in a more directly way; getting good at a practice is inherently risky - it's a continuous exercise in overcoming adversity. Conquering imminent fears of failure and vanquishing probable demotivation require courage.

    When I reflect more deeply more about this, it becomes clear that all these virtues are actually intimately intertwined; for instance, a fair assessment of ability or skill, a prototypical just judgement, requires truthfulness about the information assessed and courage to face truths that can be personally undesirable.

    Examining Moral Carryover

    Given bland virtue causal holism and the MacIntyrean framework I've introduced, what may we tentatively conclude?

    First, if these sketchy considerations are correct, behavior directed to the internal goods of a practice is intrinsically ethical. Second, ethical behavior assumes honesty, courage and justice. Third, these traits subsist in a synergistic relational causal structure.

    How may we connect this to moral character in general? For that, I will have to hastily add additional considerations on what constitutes being a good man under this framework. Being a good man is formally no different than being a good athlete or a good artist for the moral life is itself a practice - albeit the most important of practices. Living well has its own standards of excellence informed according to a tradition. That said, one can only acquire the goods internal to the practice of good life by being honest, courageous and just plus any additional virtues prescribed by a given conception of a good life.

    If this is all there is, then it would appear to be the case that performing any practice yearning for excellence, aiming for its internal goods, would deliver moral carryover to being good.

    Unfortunately, things are not so simple. For instance, one must face the challenges of situationist moral psychology and its skepticism on the existence of robust moral character. For something relevant, a crude version of a thesis originated out of this research program can be described like this; by default, what we call a 'virtue' has an indexical character, is contextually contingent to different practices or domains of social experience and its exercise can go on without much carryover to other practices in other contexts. One can be truthful to his friends at work but a deceiver to his children at home., one can be brave at the gym and a coward at the living room, etc. It is psychologically plausible to have moral excellences which are unequally distributed across the different roles one may have life.

    Triumph_of_Achilles_in_Corfu_Achilleion
    Triumphant Achilles dragging Hector's lifeless body in front of the Gates of Troy, from a panorama by Franz von Matsch.

    The primary answer to this situationist attack on virtue ethics, which acquired quite some steam at the turn of the last century [6], has been anticipated by MacIntyre nearly 35 years ago; these simply are not examples of virtues. To possess a virtue mandates that one exercises it cross-situationally in a robust fashion. MacIntyre writes, with his customary reverence for the Greek Heroic Age, that "Hector exhibited one and the same courage in his parting from Andromache and on the battlefield with Achilles". In my reading, I find that this contention is compelled by a theoretical presupposition of an account of the self and agency where unification, regularity and behavioral homogeneity are normative, but I shall not develop this for now.

    To finish off, again without decisive results, if I had to bet, I'd say there may be something special about the virtue of honesty. Honesty is both a prototypical moral and an epistemic virtue; honesty connects human action with truth and grounds language in reality. It is the ultimate arbiter behind all the tales we willfully tell others - and ourselves.

    Edit: logical mistakes have been corrected by my brilliant friend Dante Cardoso de Almeida.

    [1] R. M. Adams, A theory of virtue: excellence in being for the good, Clarendon Press, 2006.
    [Bibtex]
    @book{Adams2006a,
    author = {Adams, Robert M.},
    citeulike-article-id = {14034276},
    posted-at = {2016-05-13 00:53:24},
    priority = {2},
    publisher = {Clarendon Press},
    title = {A Theory of Virtue: Excellence in Being for the Good},
    year = {2006}
    }
    [2] C. S. Lutz, Tradition in the ethics of alasdair macintyre: relativism, thomism, and philosophy, Lexington Books, 2004.
    [Bibtex]
    @book{Lutz2004a,
    author = {Lutz, Christopher S.},
    citeulike-article-id = {14034275},
    posted-at = {2016-05-13 00:53:24},
    priority = {2},
    publisher = {Lexington Books},
    title = {Tradition in the Ethics of Alasdair Macintyre: Relativism, Thomism, and Philosophy},
    year = {2004}
    }
    [3] K. Knight, "Practices: the aristotelian concept," Analyse & kritik, vol. 30, iss. 2, pp. 317-329, 2008.
    [Bibtex]
    @article{Knight2008a,
    author = {Knight, Kelvin},
    citeulike-article-id = {14034326},
    journal = {Analyse \& Kritik},
    number = {2},
    pages = {317--329},
    posted-at = {2016-05-13 00:58:28},
    priority = {2},
    publisher = {Lucius \& Lucius Verlagsgesellschaft Mbh},
    title = {Practices: The Aristotelian Concept},
    volume = {30},
    year = {2008}
    }
    [4] F. Dretske, Explaining behavior: reasons in a world of causes, The MIT Press, 1988.
    [Bibtex]
    @book{Dretske1988a,
    author = {Dretske, Fred},
    citeulike-article-id = {12534922},
    month = apr,
    posted-at = {2013-07-30 07:13:13},
    priority = {2},
    publisher = {The MIT Press},
    title = {Explaining Behavior: Reasons in a World of Causes},
    year = {1988}
    }
    [5] A. MacIntyre, After virtue: a study in moral theory, Duckworth, 1981.
    [Bibtex]
    @book{MacIntyre1981a,
    author = {MacIntyre, Alasdair},
    citeulike-article-id = {12534836},
    posted-at = {2013-07-30 07:13:11},
    priority = {2},
    publisher = {Duckworth},
    title = {After virtue: a study in moral theory},
    year = {1981}
    }
    [6] N. E. Snow, Virtue as social intelligence: an empirically grounded theory, Routledge, 2010.
    [Bibtex]
    @book{Snow2010a,
    author = {Snow, Nancy E.},
    citeulike-article-id = {14034274},
    posted-at = {2016-05-13 00:53:23},
    priority = {2},
    publisher = {Routledge},
    title = {Virtue as Social Intelligence: An Empirically Grounded Theory},
    year = {2010}
    }

    What is Projectibility?


    Thomas Hill, Emerald Bay, Lake Tahoe (1864)

    The "New Riddle Of Induction" has amassed an enormous literature since the publication of Nelson Goodman's classic essays in the 1940s and 1950s [1]. These works have introduced a very peculiar term to anglo-american philosophy: 'projectibility'.

    An odd word

    Although sharing etymology, this neologism does not have any deep semantic overlap with the set-theoretical term 'projection' employed in many fields of mathematics. It has greater affinity with the looser uses of 'projection' that we may find in science, often interchangeably with (or in the context of) prediction and forecast.

    Dissent starts at the grammatical level. The built-in dictionary called for spellchecking as I write this entry does not recognize 'projectible' and 'projectibility'. Some authors prefer to use what seem to be more natural derivations of the verb 'to project', i.e., 'projectable' and 'projectability'.

    Prima facie, trivia like this may seem unimportant, but I believe that lack of grammatical consensus in philosophical jargon is often symptomatic of weak conceptual standing. It wouldn't be problematic if the concept was deployed consistently and rigorously in the literature, but this is not the case. As a homage to Goodman, the predicate 'projectible' itself does not seem to have been sufficiently well entrenched.

    A place and purpose for projectibility

    What is the role played by the projectibility concept? Why do we need it at all?

    Projectibility is typically deployed in discussions concerning the rationality of inductive inferences and the role of positive empirical confirmation in theoretical predictions.

    Stated informally, the default and most general account is something like this: projectibility is a property of some component (or components) of inductive inferences that is shared by all inductive inferences deemed rationally legitimate. It aims to separate good inductions from bad inductions, if we are to accept the rationality of at least some inductions (I'll leave the topic of which are the bearers of the projectibility property for another entry).

    This picture is probably what Goodman had in mind, according to the exegesis of Remi Israel [2]; projectibility specifies legitimate inductive inferences.

    Nonetheless, this characterization seems to beg the question of projectibility being a non-disjunctive property. Perhaps there are very different ways by which inductive inferences can be rational.

    Samir Okasha [3] states that Goodman’s project was descriptive, that is, it purported to isolate the class of rational inductive inferences, not to justify the practice of inductive inferences - that would be the Old Riddle of Induction. This is reiterated by Peter Turney [4] in the context of the curve-fitting problem in statistics.

    It is not clear if such a through and through separation between description and justification is possible. Grounding the original program of Goodman (and the 'Riddle' it posed) lie certain logical theories of confirmation and epistemological theories of evidential credibility inherited from Jean Nicod and Carl Hempel; what characterizes rational inductive inferences may very well be what justifies their rationality, the constraints themselves being uncontroversially normative epistemically.

    Probing the structure of confirmation

    A deep investigation of Goodman-esque projectibility requires at first a careful delineation of the theory of confirmation that exists in the background - an endeavor that can be very arid. Before considering how empirical evidence may increase or decrease the credibility of a given hypothesis, one must answer if such a relation is held exclusively between linguistic/representational entities or if the empirical world ends up somehow as one of the relata. This is needed to shed light on the bearers of the Goodman property, what kinds of entities are projectible at all.

    References

    [1] N. Goodman, Fact, fiction, and forecast, Harvard University Press, 1955.
    [Bibtex]
    @book{Goodman1955a,
    author = {Goodman, Nelson},
    citeulike-article-id = {12534797},
    posted-at = {2013-07-30 07:13:11},
    priority = {2},
    publisher = {Harvard University Press},
    title = {Fact, Fiction, and Forecast},
    year = {1955}
    }
    [2] R. Israel, "Projectibility and explainability or how to draw a new picture of inductive practices," Journal for general philosophy of science, vol. 37, iss. 2, pp. 269-286, 2006.
    [Bibtex]
    @article{Israel2006a,
    author = {Israel, Rami},
    citeulike-article-id = {12534792},
    journal = {Journal for General Philosophy of Science},
    number = {2},
    pages = {269--286},
    posted-at = {2013-07-30 07:13:10},
    priority = {2},
    title = {Projectibility and Explainability or How to Draw a New Picture of Inductive Practices},
    volume = {37},
    year = {2006}
    }
    [3] S. Okasha, "What does goodman's 'grue' problem really show?," Philosophical papers, vol. 36, iss. 3, pp. 483-502, 2007.
    [Bibtex]
    @article{Okasha2007a,
    abstract = {No abstract},
    author = {Okasha, Samir},
    citeulike-article-id = {13531605},
    journal = {Philosophical Papers},
    number = {3},
    pages = {483--502},
    posted-at = {2015-03-02 22:50:45},
    priority = {2},
    publisher = {Taylor \& Francis},
    title = {What Does Goodman's 'Grue' Problem Really Show?},
    volume = {36},
    year = {2007}
    }
    [4] P. Turney, "The curve fitting problem: a solution," The british society for the philosophy of science, vol. 41, iss. 4, pp. 509-530, 1990.
    [Bibtex]
    @article{Turney1990a,
    author = {Turney, Peter},
    citeulike-article-id = {13112819},
    journal = {The British Society for the Philosophy of Science},
    number = {4},
    pages = {509--530},
    posted-at = {2014-03-21 00:50:00},
    priority = {2},
    title = {The Curve Fitting Problem: A Solution},
    volume = {41},
    year = {1990}
    }

    On the Structure of Pleasure - Representing Quantities

    pythagoras-advocating-vegetarianism

    On the Axiomatic Representational Theory Of Measurement

    The Axiomatic Representational Theory of Measurement ('ARTM') is the default tradition of measurement theory in mathematical psychology. It arguably started in a seminal work by the late philosopher of science and polymath Patrick Suppes and the logician Dana Scott [1].

    It is 'axiomatic' in that it uses rigorous axiomatic-deductive mathematical methods. It is 'representational' by employing set-theoretical structures to represent roughly both the features of the world world and the information expressed by these features [2].

    This kind of theory is contrasted to what is called a classical or realist theory of measurement [3]. Theories of this sort carry the spirit of ancient Greek sage, philosopher and mathematician Pythagoras (depicted in the painting above, proselytizing about the "marvels" of vegetarianism); it is not merely the case that we can use numbers to represent the information about a given measurand - the values of measurands are numbers, and numbers exist right here, in the structure of the world.

    I've mentioned that in the account of Tiresias, pleasure is a ratio-scalable feature of psychological states. What does that mean?

    A bit on the ratio scale-type

    The word 'scale' is ambiguous in contexts of measurement. First, it can mean the choice of what I prefer to call a representation standard of a given measurable feature. Some examples include m, the meter-standard of the feature length [L] and Ω, the Ohm-standard of the feature electric resistance [V][I]^{-1}. But for our purposes, a scale is the kind of mathematical structure under which the numerical values that we assign to a given feature are constrained. Scales in this second meaning come in different types and the modern terminology of scale types (of which we find the ratio scale) was baptized by psychophysicist Stanley Smith Stevens [4, 5].

    Scales in this sense are a kind of mapping, an homomorphism from a structure representing the world to a structure representing the values of features. It's the transformation that allows the relational structure to be preserved, to remain invariant.

    Take for example this excerpt from a book by contemporary moral philosopher Fred Feldman [6], a defender of the thesis that pleasure is a quantitative feature (just like Tiresias):

    We assume that each episode of pleasure contains a certain ‘amount’ of pleasure, and that this amount is in principle subject to measurement. (We need not assume that these amounts can in practice be precisely determined either by introspection or by any existing technology.) The amount of pleasure in an episode depends upon intensity and duration, with longer-lasting and more intense pleasures being said to contain more total pleasure. For purposes of exposition I will imagine that there is a standard unit of measurement for these amounts. I call one unit of pleasure a “hedon”.

    Imagine that Tiresias worked out his own theory of quantitative pleasure and proposed the representation standard eron for pleasure.

    To say that pleasure is ratio-scalable is to say that we can switch from an hedon into an eron by a function of the form y=ax where 'a' is a positive real number. If one eron is 2.38 hedons, we can discover how many erons are in 10 hedons by dividing 10 by 2.38. Simple as that - the proportions are constrained and preserved.

    There is another common type of scale that is intuitively considered to be "quantitative", the interval scale. For the interval scale, the admissable transformation is of the form y=ax+b, again with a' being a positive real number.

    Extensive structures

    Let's go a bit deeper on the proposal of the ARTM. First, we build a set-theoretical structure to represent the province of empirical reality that we're interested - in this case, it is the empirical feature 'pleasure'. Ex hypothesi, let's take Tiresias' word of it; a default contender to represent the quantity pleasure is the triple \langleP,\succeq,\oplus\rangle. I like to call this an example of a material relational structure, but you'll see it with other names throughout the literature - most likely empirical relational structure or system.

    'P' is a nonempty set whose elements are interpreted as pleasure-events or pleasure-states - or 'P-events', for short.

    '\succeq' represents an empirical relation that mimics the abstract binary relation of total order. This roughly means that there is an empirically verifiable procedure to rank two distinct P-events as being either just as pleasurable or one being more pleasurable than the other.

    The last element of our triple, '\oplus', is representing an empirical operation that is traditionally called concatenation. This is also intuitively graspable; it means that there is an empirical procedure that allows us to "stack" or "pile up" our quantities.

    The class of structure with this form most used in science are called continuous extensive structures [7]. They need to satisfy a number of axioms.

    The pioneering analysis and proposal of a set of axioms describing quantities came from Hermann von Helmholtz in 1887 and Otto Hölder in 1901 [8]. Over the 20th and 21st century, the axiomatic system of Hölder was modified by many philosophers of science and measurement theorists. They include Ernest Nagel in 1931 [9], Patrick Suppes in 1951 [10] and Jean-Claude Falmagne in 1975 [11].

    These various adjustments, both minor and major, were motivated by empiricist reasons in an attempt to ground the practice of measurement in a more empirically adequate setting. They involve, for instance, weakening the logical relation of identity '=' into a relation of equivalence and getting rid of background assumptions for non-standard numbers (infinitesimals).

    Speaking of which, now we need some numbers to build our numerical relational structure. This is seemingly more straightforward. For quantities, a common candidate is the triple \langleRe_+,\geq,+\rangle. Here, 'Re_+' is the set of positive reals, '\geq' is the standard relation of total order and '+' is the standard arithmetic operation of addition. A large share of the ARTM is focused on proving theorems concerning homomorphisms from material relational structures to numerical relational structures.

    I hold that there are a series of problems with this particular choice of numerical structure but I'll utter them elsewhere.

    Having set this amount of framework, I still have some things to say about quantities, the qualitative-quantitative distinction and I also have bad news for the defenders of the hypothesis that pleasure is quantitative. It will be discussed in a future entry.

    [1] D. Scott and P. Suppes, "Foundational aspects of theories of measurement," Journal of symbolic logic, vol. 23, iss. 2, pp. 113-128, 1958.
    [Bibtex]
    @article{Suppes1958a,
    author = {Scott, Dana and Suppes, Patrick},
    citeulike-article-id = {13531611},
    journal = {Journal of Symbolic Logic},
    number = {2},
    pages = {113--128},
    posted-at = {2015-03-02 22:50:45},
    priority = {2},
    title = {Foundational Aspects of Theories of Measurement},
    volume = {23},
    year = {1958}
    }
    [2] A. Frigerio, A. Giordani, and L. Mari, "Outline of a general model of measurement," Synthese, vol. 175, pp. 123-149, 2009.
    [Bibtex]
    @article{Mari2009a,
    author = {Frigerio, Aldo and Giordani, Alessandro and Mari, Luca},
    citeulike-article-id = {12534798},
    journal = {Synthese},
    pages = {123--149},
    posted-at = {2013-07-30 07:13:11},
    priority = {2},
    title = {Outline of a general model of measurement},
    volume = {175},
    year = {2009}
    }
    [3] J. Michell, "The logic of measurement: a realist overview," Measurement, vol. 38, pp. 285-294, 2005.
    [Bibtex]
    @article{Michell2005a,
    author = {Michell, Joel},
    citeulike-article-id = {13531643},
    journal = {Measurement},
    pages = {285--294},
    posted-at = {2015-03-02 22:50:46},
    priority = {2},
    title = {The logic of measurement: A realist overview},
    volume = {38},
    year = {2005}
    }
    [4] S. S. Stevens, "On the theory of scales of measurement," Science, vol. 103, iss. 2684, pp. 677-680, 1946.
    [Bibtex]
    @article{Stevens1946a,
    author = {Stevens, S. S.},
    citeulike-article-id = {13112840},
    journal = {Science},
    number = {2684},
    pages = {677--680},
    posted-at = {2014-03-21 00:50:29},
    priority = {2},
    title = {On the Theory of Scales of Measurement},
    volume = {103},
    year = {1946}
    }
    [5] S. S. Stevens, "Mathematics, measurement and psychophysics," in Handbook of experimental psychology, Wiley, 1951, pp. 1-49.
    [Bibtex]
    @incollection{Stevens1951a,
    author = {Stevens, S. S.},
    booktitle = {Handbook of experimental psychology},
    citeulike-article-id = {13112820},
    pages = {1--49},
    posted-at = {2014-03-21 00:50:01},
    priority = {2},
    publisher = {Wiley},
    title = {Mathematics, measurement and psychophysics},
    year = {1951}
    }
    [6] F. Feldman, Pleasure and the good life: concerning the nature, varieties and plausibility of hedonism, Clarendon Press, 2004.
    [Bibtex]
    @book{Feldman2004a,
    abstract = {Fred Feldman's fascinating new book sets out to defend hedonism as a theory about the Good Life. He tries to show that, when carefully and charitably interpreted, certain forms of hedonism yield plausible evaluations of human lives. Feldman begins by explaining the question about the Good Life. As he understands it, the question is not about the morally good life or about the beneficial life. Rather, the question concerns the general features of the life that is good in itself for the one who lives it. Hedonism says (roughly) that the Good Life is the pleasant life. After showing that received formulations of hedonism are often confused or incoherent, Feldman presents a simple, clear, coherent form of sensory hedonism that provides a starting point for discussion. He then presents a catalogue of classic objections to hedonism, coming from sources as diverse as Plato, Aristotle, Brentano, Ross, Moore, Rawls, Kagan, Nozick, Brandt, and others. One of Feldman's central themes is that there is an important distinction between the forms of hedonism that emphasize sensory pleasure and those that emphasize attitudinal pleasure. Feldman formulates several kinds of hedonism based on the idea that attitudinal pleasure is the Good. He claims that attitudinal forms of hedonism - which have often been ignored in the literature -- are worthy of more careful attention. Another main theme of the book is the plasticity of hedonism. Hedonism comes in many forms. Attitudinal hedonism is especially receptive to variations and modifications. Feldman illustrates this plasticity by formulating several variants of attitudinal hedonism and showing how they evade some of the objections. He also shows how it is possible to develop forms of hedonism that are equivalent to the allegedly anti-hedonistic theory of G. E. Moore and the Aristotelian theory according to which the Good Life is the life of virtue, or flourishing. He also formulates hedonisms relevantly like the ones defended by Aristippus and Mill. Feldman argues that a carefully developed form of attitudinal hedonism is not refuted by objections concerning 'the shape of a life'. He also defends the claim that all of the alleged forms of hedonism discussed in the book genuinely deserve to be called 'hedonism'. Finally, after dealing with the last of the objections, he gives a sketch of his hedonistic vision of the Good Life},
    author = {Feldman, Fred},
    citeulike-article-id = {13562104},
    number = {1},
    posted-at = {2015-03-25 19:43:16},
    priority = {2},
    publisher = {Clarendon Press},
    title = {Pleasure and the Good Life: Concerning the Nature, Varieties and Plausibility of Hedonism},
    year = {2004}
    }
    [7] L. Narens, Theories of meaningfulness, Lawrence Erlbaum Associates, 2002.
    [Bibtex]
    @book{Narens2002a,
    author = {Narens, Louis},
    citeulike-article-id = {13531638},
    posted-at = {2015-03-02 22:50:46},
    priority = {2},
    publisher = {Lawrence Erlbaum Associates},
    series = {Scientific Psychology Series},
    title = {Theories of Meaningfulness},
    year = {2002}
    }
    [8] O. Hölder, "Die axiome der quantität und die lehre vom mass," Berichte uber die verhandlungen der koeniglich sachsischen gesellschaft der wissenschaften zu leipzig, mathematisch-physikaliche klasse, vol. 53, pp. 1-46, 1901.
    [Bibtex]
    @article{Holder1901a,
    author = {H\"{o}lder, Otto},
    citeulike-article-id = {13531626},
    journal = {Berichte uber die Verhandlungen der Koeniglich Sachsischen Gesellschaft der Wissenschaften zu Leipzig, Mathematisch-Physikaliche Klasse},
    pages = {1--46},
    posted-at = {2015-03-02 22:50:46},
    priority = {2},
    title = {Die Axiome der Quantit\"{a}t und die Lehre vom Mass},
    volume = {53},
    year = {1901}
    }
    [9] E. Nagel and C. G. Hempel, "Measurement," Erkenntnis, vol. 2, iss. 1, pp. 313-335, 1931.
    [Bibtex]
    @article{Nagel1931a,
    author = {Nagel, Ernest and Hempel, C. G.},
    citeulike-article-id = {13559115},
    journal = {Erkenntnis},
    number = {1},
    pages = {313--335},
    posted-at = {2015-03-23 22:50:07},
    priority = {2},
    publisher = {Springer},
    title = {Measurement},
    volume = {2},
    year = {1931}
    }
    [10] P. Suppes, "A set of independent axioms for extensive quantities," Portugaliae mathematica, vol. 10, iss. 4, pp. 163-172, 1951.
    [Bibtex]
    @article{Suppes1951a,
    author = {Suppes, Patrick},
    citeulike-article-id = {13559116},
    journal = {Portugaliae Mathematica},
    number = {4},
    pages = {163--172},
    posted-at = {2015-03-23 22:50:07},
    priority = {2},
    title = {A Set of Independent Axioms for Extensive Quantities},
    volume = {10},
    year = {1951}
    }
    [11] J. Falmagne, "A set of independent axioms for positive holder systems," Philosophy of science, vol. 42, iss. 2, pp. 137-151, 1975.
    [Bibtex]
    @article{Falmagne1975a,
    abstract = {Current axiomatizations for extensive measurement postulate the existence of infinitely small objects. This assumption is neither necessary nor reasonable. This paper develops this theme and presents a more acceptable axiom system. A representation theorem is stated and proved in detail. This work improves some previous results of the author},
    author = {Falmagne, Jean-Claude},
    citeulike-article-id = {13559114},
    journal = {Philosophy of Science},
    number = {2},
    pages = {137--151},
    posted-at = {2015-03-23 22:50:07},
    priority = {2},
    publisher = {University of Chicago Press},
    title = {A Set of Independent Axioms for Positive Holder Systems},
    volume = {42},
    year = {1975}
    }

    On the Structure of Pleasure - A Tale of Measurement Theory and Classical Mythology

    tiresiaszeushera

    Tiresias, mythical mathematical psychologist

    Tiresias is a legendary blind prophet in Greek myth. His story has many versions. In this tract, I'll draw primarily from the account of ancient mythographer Pseudo-Apollodorus.

    As the narrative goes, while traveling in Mount Cyllene, Tiresias beheld a pair copulating snakes and struck the female with his walking stick. For this display of animal cruelty, he was cursed to live as a woman. With the body and mind of a woman, Tiresias experienced sex; according to versions of the legend, he did so quite intensely, becoming a prostitute of great renown.

    Seven years had passed after this incident and female Tiresias had the opportunity to re-encounter an event similar to the one that caused his transformation. This time, he left the reptiles undisturbed and in that, he was allowed to regain his former manhood.

    Having lived as both a man and a woman, Tiresias was privileged with a unique perspective on the varieties of sexual experience across the sexes. For that, he was consulted by the Olympians themselves. Zeus and Hera willed to settle once and for all the question of who enjoys greater pleasure in carnal love - man or woman. Tiresias provided an outstanding answer for the Gods:

    Of ten parts [of sexual pleasure] a man enjoys one only; but a woman enjoys the full ten parts in her heart.

    This passage is remarkable in theoretical depth. The divine couple requested from the mortal soothsayer an ordinal evaluation and received more than what they had bargained. In his statement, Tiresias is claiming that events of (sexual) pleasure not only can be ranked, but that they have magnitudes whose proportions can be meaningfully compared and expressed.

    In measurement-theoretic terms, this is the claim that pleasure is a ratio-scalable property or attribute. This is what one usually has in mind when someone says that something is 'quantitative'.

    It's a bold ontological claim. The story of Tiresias however is also daring epistemologically; it stipulates that information about the value of the magnitude of pleasure instantiated in a given psychological state is obtainable through introspection with a certain precision. It is also supposedly reliably registrable in long-term memory; the mind is used as a truthful scale of itself.

    From ancient myth to modern science

    It took over two millenia for the ideal of Tiresias to come into fruition. The earliest robust attempts happened in the German tradition of psychophysics, by physicists Gustav Fechner and Hermann von Helmholtz. Somewhat unexpectedly, this tradition arguably culminated with mathematician Otto Hölder [1].

    The quest of psychophysics has been to establish an interface between subjective mind and objective world by uncovering functional relations between 3rd-person fact and 1st-person unknown. For example, the investigation of how psychological brightness co-varies with physical luminance. For these tasks, psychophysicists have developed several methods for subjective magnitude estimation of sensations from given controlled stimuli as input to verbal and motor reports as output.

    Measurement theorist Louis Narens has defended that formally, these forms of measurement can have a foundation as strong as other prototypical practices of experimental science [2].

    A lot of progress has been made on the investigation of the structure of sensations. Affective states such as pleasure and pain, however, still remain very murky.

    Is pleasure quantifiable?

    On closer inspection, Tiresias' proposition that pleasure is quantitative does not seem to be particularly bold after all. It has received widespread uncritical support for quite some time - from the dawn of utilitarianism in modern moral philosophy to the use of visual analog scales for pain assessments in contemporary clinical medicine and cardinal utility in economics. They have become ingrained in our common sense. Queries like "from a scale to 0 to 10, how do you feel?" have become staples of modern managerial society.

    But is it true? Unfortunately for Tiresias, the hypothesis that pleasure and other similar affective states such as pain have a quantitative structure has not been empirically established with satisfaction. Not even the other rather intuitive hypothesis that pleasure and pain have a structure that allows representation as opposite intervals of a same axis.

    To stipulate that a given feature has a quantitative structure is not a matter of pragmatic choice but of experimental fact. This claim has been vigorously defended by measurement theorist Joel Michell [3]. Michell condemns gratuitous cursory admissions that a given psychological feature is quantitative without previous evidential justification. Conceptual residue from operationalist philosophy in experimental psychology is at fault.

    The fact of the matter is that the stakes for an empirical feature to be ratio-scalable are very high. This will be exposed in greater detail in another entry.

    [1] J. Michell and C. Ernst, "The axioms of quantity and the theory of measurement," Journal of mathematical psychology, vol. 41, iss. 4, pp. 345-356, 1997.
    [Bibtex]
    @article{Michell1997c,
    author = {Michell, Joel and Ernst, Catherine},
    citeulike-article-id = {13559112},
    journal = {Journal of mathematical psychology},
    number = {4},
    pages = {345--356},
    posted-at = {2015-03-23 22:50:07},
    priority = {2},
    publisher = {Elsevier},
    title = {The axioms of quantity and the theory of measurement},
    volume = {41},
    year = {1997}
    }
    [2] L. Narens, "The irony of measurement by subjective estimations," Journal of mathematical psychology, vol. 46, iss. 6, pp. 769-788, 2002.
    [Bibtex]
    @article{Narens2002b,
    author = {Narens, Louis},
    citeulike-article-id = {13559113},
    journal = {Journal of Mathematical Psychology},
    number = {6},
    pages = {769--788},
    posted-at = {2015-03-23 22:50:07},
    priority = {2},
    publisher = {Elsevier},
    title = {The irony of measurement by subjective estimations},
    volume = {46},
    year = {2002}
    }
    [3] J. Michell, "Quantitative science and the definition of measurement in psychology," British journal of psychology, vol. 88, pp. 355-383, 1997.
    [Bibtex]
    @article{Michell1997a,
    author = {Michell, Joel},
    citeulike-article-id = {13531650},
    journal = {British Journal of Psychology},
    pages = {355--383},
    posted-at = {2015-03-02 22:50:46},
    priority = {2},
    title = {Quantitative science and the definition of measurement in psychology},
    volume = {88},
    year = {1997}
    }