The Logic of Existence and the Objective-Subjective Distinction in Metaethics


Contemporary metaethics is a very technical zoo of categories and terminology that is used inconsistently from author to author. Here I'll digress on some aspects of the use of the interrelated terms 'existence', 'reality' and 'objectivity' for some posterior discussions I intend to make.

Nihilism and Existence

'Nihilism' names a family of loosely-related theses from XIX century european moral philosophy. Still, as it is commonly used in contemporary anglophone philosophy, the term 'nihilism' carries much less conceptual baggage. I shall address this "thicker" sense of 'nihilism' in the future but here I'll be solely preoccupied with the "thinner" sense.

Nihilism simpliciter is an ontological stance forming a schema that demands a class of variables out of a given domain of discourse. It is the denial of the objective existence of a certain class of entities from a certain domain of discourse. A nihilist on x is someone that stands by the claim that x does not objectively exist.

For instance, in analytic metaphysics, a mereological nihilist is someone that contends that there are no aggregates of proper parts in a particular sense - only proper parts have objective existence.

A causation nihilist would be someone that claims that causes and effects lack objective grounding. We can imagine in political philosophy a defender of individual nihilism, one that claims that objectively-existing individual agents have no place in political theory and that we presumably may only populate our political ontology with groups or classes of political agents.

In this very philosophical tradition, a rough rule of thumb would be that outside of axiological fields, 'nihilism' is a descriptor term can be used interchangeably with 'eliminativism' and 'anti-realism'. But definitely not so in metaethics; as I'll claim, contemporary metaethical discussion is committed to not just the existence of two kinds of things but to two kinds of existents, two ways under which universals and particulars can be real. Confusingly enough, a moral nihilist is not necessarily a moral anti-realist - hopefully I'll be able to eradicate this terminological confusion.

Existence and the Objective-Subjective Distinction

The previous use of 'objectivity' here demands extensive clarification. This term comprises a mess of cluster concepts that conflate epistemological and ontological claims but I'll accept the burden of presenting an informative exposition while at the same time attempting being charitable to this complicated field.

Let's talk a bit about existence itself, what may strike us as the most fundamental notion in metaphysics. What seems to be the default thesis in Western philosophy concerning the formal nature of existence is that existence is of a different logical type than a property (and presumably, this is also reflected ontologically). This was famously championed, for instance, by Immanuel Kant in his critique of the ontological arguments for the existence of God. Standing by of our contemporary conceptual apparatuses, we could say that our sense of 'existence' in natural language is exhaustively picked up by the concept of existential quantification in mathematical logic. I.e., it would be a mistake to represent existence by a predicate.

If we are to say that an aurochs exist, this is formally captured by the sentence:

\exists x, Ax

I'll stand by something bold; I think current metaethical discussion is implicitly committed to the alternative, more controversial view of existence as a property. I am very sympathetic towards this viewpoint of existence but I'll not utter my reasons for that here.

Metaethics constantly divides reality in two different kinds of stuff; there is an objective and a subjective realm. It is my impression that the in this field, the most natural way to understand the nihilist schema I've exposed is considering 'objectivity' to be a certain higher-order property of an entity.

If an aurochs exists, an aurochs instantiates the property 'existence', as in the sentence:

\exists x, Ex \& Ax

Formally, 'existence' itself is represented as a predicate that ranges over a given variable and 'objectivity' and 'subjectivity' are higher-order predicates that range over the predicate 'existence'.

In this view, there are two different modes under which something that is real may be realized. For the sake of clarity in this already complicated discussion, let us use 'reality' or 'realness' to name this property and use 'existence' in a more abstract sense that is supposed to be captured by the use of existential quantification in predicate logic.

Objective reality (or existence, if you will) is a type of reality that is contrasted with subjective reality. To put it simply, it is the thesis that are two distinct ways in which some thing can be real, either objectively or subjectively.

'Objectivity' and 'subjectivity' are n-order predicates for the (n-1)-order predicate 'reality', that I am representing by the predicate 'E'.

It looks like this; take 'objectivity' to be a property represented by the 2nd-order predicate '\mathcal{O}'. To say that aurochs are an objective item of reality in second order logic is to write:

\exists \mathcal{O}[\exists x, \mathcal{O}Ex \& Ax]

In a Fregean view of existence, for instance, that would make 'objectivity' and 'subjectivity' third-order predicates - more than enough to certainly make many logicians twist their stomachs, I'm sure. An for good reason; the implicit higher-order model theory to deal with the higher-order structures of higher-order logic can be theoretically are very tricky.

Entities that have objective reality are often assumed to have a more special ontological status in comparison to that which only exists subjectively. Something that is subjectively real is often assumed to do a poor job at existing, as a second-class metaphysical citizen.

A common claim that we see reiterated in various ways is that it is indispensable in ethics for at least certain forms of normativity to have objective grounding. Normative force that does not have objective standing is either not good enough (it is suboptimal) or not good at all (it adds nothing).

The crown of objective reality is endorsed as an ideal and if it is the case that our most cherished values are plebeians incapable of being crowned, there is a line of thought that argues that this would be the worst kind of tragedy, to the point of despair. This is a theme present in both modern and contemporary continental european and contemporary anglophone philosophy which will be the subject of another entry that is still work in progress.

Moral Nihilism, Moral Subjectivism and Moral Anti-Realism

It's time to make things transparently clear for the uses of 'nihilism', 'subjectivism' and 'anti-realism' in moral philosophy and why it is wrong to conflate them.

Let us expand a bit the definition for moral nihilism; a moral nihilist is someone that holds that there are no objectively real moral posits. No objective moral properties such as 'cruelty', no objective moral particulars such as The Form of the Good. According to a traditional framework, if there are no objectively moral properties to be exemplified, there are no objective moral facts and no objective moral truths either.

Take x to be the relevant posit or posits of the domain of discourse in question. 'Anti-realism' is the stance with the greatest scope. It claims that it is not the case that x have any kind of reality whatsoever.

'Subjectivism' on x is therefore inconsistent with 'anti-realism' on x for subjectivists on x hold that x are subjectively real. When the late moral nihilist J.L. Mackie [1] writes: doubt if moral values are not objective they are in some very broad sense subjective...

...he is endorsing the subjective reality of moral values.

Philosopher Jesse Prinz [2] has the same position; he denies objectivity to moral values without being a moral anti-realist.

Inconclusive Thoughts And Some Personal Remarks

I have said very little about the alleged metaphysical difference between that which is objectively real from that which is subjectively real. That is an extensive topic that will be the subject of my next entry.

I must add that I am extremely unsatisfied with this traditional framework, which reeks of bad neo-scholasticism. And the centerpiece is the perennial distinction between subject and object itself. I believe that not only this distinction is deeply misleading and unnecessarily ensnarls important philosophical problems but that it is incompatible with a scientifically responsible view of the world. I have no fully-fledged alternative framework to replace it but I believe many hints on how it could be done have been advanced by contemporary researchers.

A framework with some of the viewpoints expressed here is found for instance in the third version of the Real Pattern Theory of Ontology [3]. There, we have no second-class (or third-class, etc) metaphysical citizens. There are no degrees of reality; either something exists or it doesn't. Finer distinctions relating the 'ontological dependence' of certain Real Patterns towards certain intentional systems are always local in character, relating to etiology, history or pragmatical considerations. A band of ruminating aurochs in the cold plains of The North are just as real as the market value of Valyrian Steel in Westerosi society.

The objective-subjective distinction is not going away in philosophy anytime soon. But I long for a future in an academic setting were the distinction and all the misleading baggage it carries will be seen, as Bertrand Russell once put it, as a 'relic of a bygone age'.

Personal Acknowledgement

I am grateful for my friend and brilliant logician Dante Cardoso Pinto de Almeida for personal discussions I've had in the process of writing this entry.


[1] J. L. Mackie, Ethics: inventing right and wrong, Penguin, 1977.
abstract = {John Mackie's stimulating book is a complete and clear treatise on moral theory. His writings on normative ethics-the moral principles he recommends-offer a fresh approach on a much neglected subject, and the work as a whole is undoubtedly a major contribution to modern {philosophy.The} author deals first with the status of ethics, arguing that there are not objective values, that morality cannot be discovered but must be made. He examines next the content of ethics, seeing morality as a functional device, basically the same at all times but changing significantly in response to changes in the human condition. He sketches a practical moral system, criticizing but also borrowing from both utilitarian and absolutist views. Thirdly, the frontiers of ethics, areas of contact with psychology, metaphysics, theology, law and politcs, are {explored.Throughout}, his aim is to discuss a wide range of questions that are both philosophical and practical, working within a distinctive version of subjectivism-an "error" theory of the apparent objectivity of values. John Mackie has drawn on the contributions of such classic thinkers as Plato, Aristotle, Hobbes, Hume, Kant and Sidgwick, and on more recent discussions, to produce a thought-provoking account that will inspire both the general reader and the student of philosophy.},
author = {Mackie, J. L.},
citeulike-article-id = {13591438},
number = {1},
pages = {134--137},
posted-at = {2015-04-24 19:10:16},
priority = {2},
publisher = {Penguin},
title = {Ethics: Inventing Right and Wrong},
year = {1977}
[2] J. J. Prinz, The emotional construction of morals, Oxford University Press, 2007.
abstract = {Jesse Prinz argues that recent work in philosophy, neuroscience, and anthropology supports two radical hypotheses about the nature of morality: moral values are based on emotional responses, and these emotional responses are inculcated by culture, not hard-wired through natural selection. In the first half of the book, Jesse Prinz defends the hypothesis that morality has an emotional foundation. Evidence from brain imaging, social psychology, and psychopathology suggest that, when we judge something to be right or wrong, we are merely expressing our emotions. Prinz argues that these emotions do not track objective features of reality; rather, the rightness and wrongness of an act consists in the fact that people are disposed to have certain emotions towards it. In the second half of the book, he turns to a defense of moral relativism. Moral facts depend on emotional responses, and emotional responses vary from culture to culture. Prinz surveys the anthropological record to establish moral variation, and he draws on cultural history to show how attitudes toward practices such as cannibalism and marriage change over time. He also criticizes evidence from animal behavior and child development that has been taken to support the claim that moral attitudes are hard-wired by natural selection. Prinz concludes that there is no single true morality, but he also argues that some moral values are better than others; moral progress is possible. Throughout the book, Prinz relates his views to contemporary and historical work in philosophical ethics. His views echo themes in the writings of David Hume and Friedrich Nietzsche, but Prinz supports, extends, and revises these classic theories using the resources of cutting-edge cognitive science. The Emotional Construction of Morals will stimulate and challenge anyone who is curious about the nature and origin of moral values},
author = {Prinz, Jesse J.},
citeulike-article-id = {13591439},
posted-at = {2015-04-24 19:10:16},
priority = {2},
publisher = {Oxford University Press},
title = {The Emotional Construction of Morals},
year = {2007}
[3] J. Ladyman and D. Ross, Every thing must go: metaphysics naturalized, Oxford University Press, 2007.
author = {Ladyman, James and Ross, Don},
citeulike-article-id = {12534918},
posted-at = {2013-07-30 07:13:13},
priority = {2},
publisher = {Oxford University Press},
title = {Every Thing Must Go: Metaphysics Naturalized},
year = {2007}

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.


[1] N. Goodman, Fact, fiction, and forecast, Harvard University Press, 1955.
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.
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.
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.
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}