On how events can have meaning, 2

That events can have symbolic meanings can be shown from paradigm cases (note: this is how induction was generally understood to work prior to some changes in the concept in the late medieval period) : the 9/11 attacks on the Pentagon and the World Trade Center, for instance, and the attempted attack on the White House on the same day, were rightly interpreted as respectively targeting American imperialism in war, finance capitalism in economics, and representative democracy in political economy. Understanding these three as pillars of contemporary western civilization, the attack was viewed as an attack on western civilization itself. The date of the attack, on the anniversary of two critical defensive victories for western Christian armies over Muslim advancements (the end of the Great Siege of Malta in 1565, and especially the beginning of the Battle of Vienna in 1683), suggested a renewed struggle between Western, specifically Christian, and Islamic civilizations.

In the above instances, the meaning of the event is taken from the meaning its parts: the attack on the World Trade Center was an attack on finance capitalism because the World Trade Center was already an established symbol of the latter. The case is similar with the attack on the pentagon and the planned attack on the White House. The meaning of the event in each case is expressed by substituting some symbolized being for what symbolizes it in a sentence straightforwardly describing the original event.

Going further, the World Trade Center was able to be a symbol of finance capitalism because the buildings themselves were places dedicated to its practice. The Pentagon was seen as a symbol of American imperialism because it was a sight for the planning of military strategy and operations, and imperialism is necessarily a way of failing, by way of excess, to carry out the essential task of a military. The White House serves as a symbol for democratic governance because it is likewise dedicated to that end. In short, the first and third substitutions are each of a being with its end, while the second is of a being with a way of falling away from its prescribed end.

A glimpse of early Hebrew metaphysics in the book of Genesis

At Genesis 29:16-17, we find the following description of Laban’s daughters, both of whom the patriarch Jacob would wed.

‘Now Laban had two daughters; the name of the older was Leah, and the name of the younger was Rachel. Leah had weak eyes, but Rachel had a lovely figure and was beautiful. (NIV)’

The translation in other versions is similar. The King James Version, for instance, has ‘Leah was tender eyed; but Rachel was beautiful and well favoured’. The Hebrew text calls Leah rak`ayin, which is fairly well-represented by the KJV text above. The Latin Vulgate has ‘Sed Lia lippis erat oculis: Rachel decora facie, et venusto aspectu. – ‘But Leah was with watery/inflamed eyes; Rachel, [with] stately face and beautiful appearance.’ The Greek Septuagint (which predates the earliest extant Hebrew text) states that Leah’s eyes were ασθενεις – literally, ‘lacking in strength’ (οι δε οφθαλμοι λειας ασθενεις ραχηλ δε καλη τω ειδει και ωραια τη οψει)

That the original meaning of the text is not conveyed by any of the above is clear from its context: the current text has Leah’s weak eyes contrast with Rachel’s beautiful appearance. But the state of Leah’s eyes is not the right type of thing to contrast with Rachel’s beauty.

There is, however, something in the vicinity that does belong to an appropriate contrast class: Leah’s sight – not, that is, her capacity to see, but rather the sight of her, how she appears to others.

The original sense of the text would be that Leah was a weak sight – or, if Saint Jerome was cribbing from a Greek variant, a fat sight (lippus is cognate with the Greek λίπος, ‘fat’) – while Rachel was beautiful. We’ll assume the first.

It’s unlikely that a text that unambiguously referred to Leah’s appearance would have been corrupted to the point of referring instead to her eyes. What’s more likely is that an ambiguity in the original meaning was lost.

Today, sight is regarded as a power present in an organ, namely the eye. The appearances of things external to the eye is itself consequent on this power to see. In more extreme forms of this view, qualities like color and brightness do not exist in the thing, but in the mind: beauty is, as they say, in the eye of the beholder. In this construal, the being of a certain class of beings (the look of things) is reduced to that of a power (sight), which is in turn reduced back to the being of a part (the eye), which is itself grounded in the being of a subclass of objects (sighted animals).

But this isn’t the only way to view the matter. Alternatively, one can begin with the being of the sight itself taken as a whole, within which the seer, the seen, the showing of the seen as its manifestation to a seer, etc., all play various roles. The term used to refer to the whole can then be transferred by synecdoche to its various parts, with different specified interpretations appropriate to different uses. Words like ‘look’ and ‘sight’ still have this ambiguity in English today. Over time, words sometimes ossify to refer to a part where they once referred to a whole. Hence, the English ‘deer’ is cognate with the German Tier, ‘animal’, while ‘jealous’ and ‘zealous’ partition positive and neutral-charged versions of a phenomenon described by the same Greek root.

But in the biblical case, the direction of the reduction is important. In the thinking of the passage we’ve charted out, one finds a weakness in the sight of Leah, and a sight of beauty with Rachel. In the reductive reading, it is not merely that the sight of Leah’s is reduced to the wrong object – her eyes, rather than her appearance – the same reduction is present ‘correctly’ with Rachel’s beauty: it is no longer what is present with her in the event of her presence before Jacob; instead, it is a property of her appearance which stands opposite the eye of Jacob. In the second case, then, the reduction of the whole to a relation of properties to objects brings with it a duplication of correlated properties, e.g. the gaze of Jacob and others, and the task of explaining their correlation.

From this arise the two characteristic tasks of later western metaphysics everywhere we find it: the explanation of the unity of being by reduction of some beings to others as real, and by the correspondence of beings which belong together as truth.

The political philosophy of distributism: a very short introduction

What is distributism?

Distributism is a political ideal according to which property ownership should be as widely distributed as feasible.

How does distributism differ from capitalism?

Taken broadly, ‘capitalism’ refers to an economic system wherein property ownership is private. Its opposite is socialism, a system in which private ownership does not exist. In this sense, distributism is a political ideal that may be achieved within a capitalist system.

In practice, the term ‘capitalism’ often has a more specific meaning than that above, referring to a
system wherein property is concentrated in the hands of a few, and markets purportedly operate with little or no government interference. In this more restricted sense, distributism differs from capitalism, in that its policies aim at the establishment of property in more hands.

Notwithstanding political mythology to the contrary, capitalism and distributism don’t differ with respect to quantity of government interference: they differ with respect to its aims.

In capitalism, government intervention often occurs in order to enforce the rights of the few over the many (e.g. property and patent laws), to coerce the many to work for the few (e.g. laws connecting welfare to seeking employment), and to set up the few as the caretakers of the many (e.g. laws exempting workers from liability, and requiring liability of employers). That is, capitalist use of government intervention tends towards the establishment of what Hilaire Belloc called the Servile State – an arrangement of society according to which the masses are granted a minimal level of security and care, but lack substantial wealth or political capital, and are under the mercy of those few rich persons granted legal responsibility over them in various ways.

How does distributism differ from socialism?

Though the term has come to have a broad range in popular discourse, ‘socialism’ strictly refers to a system in which the right to private property is abolished. Distributism is one wherein it is affirmed. The difference is that the one affirms, the other denies, a right to private property.

In practice, socialist policies tend towards the establishment not of social ownership, but – like
capitalism – of the Servile State. That is, they tend towards the establishment of control of property in the hands of a few, who are granted the responsibility to care for the masses at the behest of the state. So distributism differs practically from socialism in exactly the way that it differs from capitalism, because these latter tend in practice to the same thing.

Is distributism a hybrid of left and right thought on economics?

No. It is better to regard the left and the right as closer to each other than usually suggested.
Government interference on both the left and the right tends toward the establishment of the Servile State. Distributist economic interventions aim at its abolition.

One important way socialist and distributist economic regulations often differ is in that the former tend to be ‘positive’ interventions, while the latter are more often ‘negative’ interventions.

Positive interventions include things like the establishment of bureaucracies to handle economic
necessities for the poor, health care, college costs etc. When these exist in a mixed capitalist-socialist economy, big businesses often leverage market forces to effectively turn these subsidies into a new ‘floor’ relative to product demand, and product costs go up. In this way, positive interventions both create large managerial bureaucracies and often translate in practice into indirect subsidization of large corporations. In the absence of corresponding negative interventions, they also tend toward the ballooning of government debt.

Negative interventions advocated by distributists include things like differential taxation relative to the number of stores owned or number of areas in which a ‘big-box’ company trades, the enforcement of anti-trust legislation, the taxation of ‘externalities’ like highways and pollution, and generally, various uses of taxation to directly prevent companies from serving too many sectors or too much of one sector. To the degree that negative interventions tend to involve less bureaucracy than positive interventions where the transfer of wealth must be directly managed, distributist interventions tend to be fewer, less invasive, and more efficient. Their difficulty is a purely political one: it is politically easier to advocate for subsidies than penalties, even when penalties would be of greater benefit to the class targeted for benefit than direct subsidization.

How does distributism handle the distribution of goods?

It doesn’t. That’s the beauty of it. In an economy where wealth is well-distributed, and the laws tend to prevent its concentration, this is accomplished by what Smith called ‘the invisible hand of the market’.

In this connection, it is important to see just how often this myth of the invisible hand fails to apply in typical capitalist economies. In practice, capitalism doesn’t use markets to manage everything: prices are often set in various ways by large monopolies, in a way not substantially different than in a socialist planned economy. For instance, a large supermarket chain that owns the store fronts, the factories that make the bread sold in the stores, the trucks used to transport the product, etc. does not determine the prices of its internal transactions by the market. Likewise, fisheries dependent on having their products sold by large chains aren’t in a position to sell their goods at a better price to different stores: the price for their labor are effectively dictated to them by those who control the means of distribution. Hence, product cost in archetypical capitalist economies is often determined much more bureaucratically than capitalist rhetoric would suggest.

By advocating policies that weaken and sometimes directly break up these large conglomerates,
distributists allow the costs of goods to more accurately reflect their true market price, and hence to achieve the equality requisite for a genuinely free and competitive market.

Previously published at https://www.imagodeipolitics.org/2017/08/16/the-political-philosophy-of-distributism-a-very-short-introduction/

On how events have meaning, 1

notre-dame-cathedral-stained-glass-window-rose-religion-e93c67-1024.jpgAs I began writing this, Notre Dame Cathedral was burning. I visited and attended mass at the cathedral just this past June, while on a trip to France to do manuscript research in Paris and present at a logic conference in Vichy. I broke down in tears upon coming home as I tried to tell my wife what had happened.

Inevitably, one comes to question the meaning of all of this. This, in turn, prompts the question of whether the question ‘what is the meaning of all this’, referring to this or any event, is even a sensible one. As many would have it, asking for the meaning of an event is a senseless question, like asking for the weight of pi.

To think through this question requires one to begin by taking the data given in these sorts of common phrases seriously. This is not to say that every question is ultimately a meaningful one. But it is to say that advancement on any given issue, even to the conclusion that the issue at hand is meaningless, is only made by following a path of inquiry. This, in turn, requires a kind of fidelity to the matter that presents itself which is incompatible with naysaying. Blessed is he who sits not in the seat of the scoffers.

Changes to site: a forthcoming experiment


Since starting this site, the blog portion of the website has been based on a very specific concept of what a philosophy blog can do better than other forms of philosophy literature: provide high-quality self-contained, short-form work on a topic that is disentangled from the academic literature and jargon associated with it, especially on ‘big-picture’ questions in metaphysics. For some of the better examples of this, I refer you to the highlighted posts page, especially the pieces listed under section 2.1, ‘What is philosophy?’.

Few philosophy blogs I am aware of actually attempt to do this. Among the better ones, one mostly finds tentative, informal approaches to topics the author hashes out better elsewhere, commentary on current events in politics and in the philosophy profession, and drafts of work that will ultimately find their way into academic publications.

Given the incentives associated with both philosophy writing and blogging generally, this is understandable. On the philosophy side, current incentives encourage writers to publish research that engages with the work of their peers, who in turn judge that work’s merits. An unfortunate side-effect of this is that professional philosophy writing tends toward insularity, and much philosophy blog writing merely becomes pre-professional writing. Philosophy work explicitly intended for a popular audience, e.g. many good pieces written in Aeon, tends to either distill academic work for a popular audience or focus heavily on trendy topics and current events. On the blogging side, algorithms that determine which pieces are recommended to others in aggregate blog sites like WordPress or Medium.com are biased towards a high quantitative output – even when, as is the case with the latter, there is an explicit attempt to do otherwise.

Nothing is wrong with this per se. But there is room for another, different sort of philosophy work than that dominant at present (either on this blog or elsewhere), and the need to strategically address the challenges post by search engine and blogging platform algorithms can’t be ignored. While I’m happy with most of the work I’ve published here to present, it hasn’t reached the limits of the first, and hasn’t even attempted to address the second problem.

That being said, there are several changes I’m making to the site:

The first set of changes affects the kind of content to be found here. I’ll begin posting on a wider variety of topics, including ethics, politics, religion, philosophy of technology, and economics. To now, I’ve avoided discussions of many of these issues on two assumptions: first, that most disagreements in these areas are consequent upon deeper metaphysical disagreements – ethical tips of metaphysical icebergs, so to speak. Second, that many topics in these areas are controversial, and my arguments on any of them would likely alienate some readers. Thought I still think these things are true, it now seems to me that the costs of engagement may not be as steep as I originally envisioned, (and that in the interests of truth I can only care so much if they are), and that there are likely benefits I had hitherto ignored to be had in engaging such topics – both in engaging other potential readers and in giving examples of greater disciplinary integration to a world where the sciences remain badly fractured. The one caveat is that I will continue to avoid writing material connected to news cycles, which inevitably comes to look badly dated after a short time. Even when engaging in topics of increased public interest, the directive of philosophy remains what it has been since Plato: to find what what is stable and lasting behind the changing and ephemeral.

Next come qualitative changes, of which there are three:

First, I’ll begin posting shorter blog posts close to daily. Since it would be foolish to pretend that the depth of analysis will remain the same after this change as when posts appeared less periodically, this leads to the next two changes.

The second change is the inclusion of best-of posts on weekly, monthly, quarterly, and annual bases, which will gather a subset of the best posts at the end of each of the aforementioned periods.

The third change is the launch of my medium.com author page (where all my posts can be found), and a medium.com publication, Philosophy Outside the Text, devoted to precisely the sort of work this blog was originally intended for: expositions that cut out obligatory academic references and jargon with no corresponding sacrifice of philosophical depth. The site will incorporate both new material and some of the better legacy posts from this site. It will also include posts behind medium’s premium paywall structure. If you have a medium.com account, you can ‘clap’ for these posts, which medium calls ‘stories’ – Medium’s clap is similar to Facebook’s like button, but allows the user to clap multiple times, which is intended as a way for readers to rate pieces according to quality. If you appreciate my writing, clap for me. At the end of each month, I’ll receive a payment based on the number of claps my stories receive. Lastly, I am considering adding other authors to Philosophy Outside the Text in the medium- to long-term. So if you or someone you know is interested and capable of doing the kind of work for which the site is intended, send me an email with a sample post at [myFirstNameMyLastName][theAtSign]gmail.com.

New edited volume: Consequences in medieval logic. Vivarium 56:3-4

For those that may have missed this when it came out in late October: I recently guest-edited a volume of Vivarium on medieval theories of consequence. The volume covers major figures from Boethius to Marsilius of Inghen, and includes contributions on a wide variety of topics from Chris Martin, Joke Spruyt, Milo Crimi, Graziana Ciola, Bianca Bosman, and myself. The volume may be found here.

Here is an excerpt, from the introduction:

2 Medieval and modern definitions of consequence

In common English, ‘consequence’ usually refers to the result or outcome of an action, ‘inference’, to a subject’s act of asserting or coming to believe something on the basis of something else, and ‘implication’, to a suggestion communicated in a veiled manner through something else stated explicitly. In logicians’ English, these terms are naturally used interchangeably to refer to none of these things. In logic today, ‘consequence’ ‘inference’ and ‘implication’ refer to an ordered pair whose first element, called the antecedent, is usually a set (or multiset, or list)[1] of sentences, propositions, or even arguments,[2] and whose second element, called the consequent, is a single object of the same type. A consequent is said to follow from its antecedent, and an antecedent is said to entail its consequent.[3]

In medieval logic, ‘consequence’ (consequentia) usually refers to a relation between an antecedent and a consequent, variously described as a habit (habitudo), inference (illatio), or a following (sequela).[4] Some medieval logicians define a consequence according to its part of speech,[5] others in terms of its function,[6] and still others, seemingly throwing up their hands, regard it as a clustering of its various parts.[7] Others pass over the definition of consequence altogether and begin by listing good consequences or divisions of consequences.[8]

Modern logicians make a strong distinction between consequences and conditionals: a conditional is a connective appearing in formulae within a regimented language, called the object language, employed in a proof system. Consequence is a relation of following asserted to hold between [schemata for] formulae in the object language, and whose written expression does not appear in the object language but in a second, more expressive language called the meta-language (usually a natural language augmented with various mathematical symbols) which is used to evaluate the expressions of the object language.

Medieval logicians do not strongly distinguish consequences from conditionals, and certainly do not do so in the above way. Humanist scruples aside, medieval logicians worked within natural language. In accord with the range of source material from which it arises, the medieval concept of consequence comes to include conditional statements, categorical and hypothetical syllogisms, conversions, enthymemes, and other argument forms.[9]

None of this yet tells us what counts as a good consequence, either for medieval logicians or their modern counterparts. Today, the two most common ways of providing criteria for determining when a consequence exists are one, relying on the techniques of proof theory and called proof-theoretic, and the other relying on model theory, called model-theoretic or semantic.[10]

In the semantic approach to consequence, a consequence from a premise set  to a conclusion  – written  – is valid if and only if every model of  is, at the same time, a model of . In early model theory, e.g. that of Tarski, a model  of a sentence  [set of sentences ] in a recursively-defined language  presupposes a division of the basic elements of  into logical and non-logical kinds, and is a sequence of objects satisfying (roughly, making true) each sentential function obtained by uniformly replacing each non-logical element in the sentence  [set of sentences ] with a variable – like variables replacing like constants, unlike replacing unlike. In classical model theory today, a model  is a pair  consisting of a (possibly infinite, possibly empty) set of objects , called the domain, and an interpretation  that assigns non-logical constants in  to elements in , and thereby provides the basis for recursively determining the truth value on  of each sentence  in . Modal, non-classical, and other model theoretic approaches to consequence generally arise by expanding the number or adjusting the interpretation of the logical constants of a language, and/or by modifying the notion of a model in interesting ways e.g. by the addition of Kripke frames in modal logic, or of further truth values in many-valued logics.

In modern proof-theoretic approaches to consequence, a consequence  occurs from premises  to conclusion  in a proof system  if and only if there exists a derivation of  in  from (open) assumptions .[11] Here, a proof system consists of a set of rules (and possibly, axioms) for obtaining certain formulae of a language  from others,[12] and commonly consists of rules for introducing and eliminating logical connectives, along with structural rules governing matters like the introduction of assumptions and repetition of formulae. The definition of an open or closed assumption, and the corresponding notion of an open or closed argument, are given in a manner parallel to the treatment variables and formulae in syntax: just as a variable  [formula of a language ] is said to be bound [closed] just if it occurs within the scope of a quantifier  [all of its variables are bound], and free/unbound [open] otherwise, an assumption [argument] is said to be bound – that is, discharged – just if it occurs within the ‘scope’ of an inference [all of its assumptions are bound].[13] Consequently, the basic idea behind modern proof-theoretic approaches to consequence is that a consequence exists when, given a certain set of premises as inputs, there is a precise, rule-governed procedure for obtaining the consequent as output. The proof-theoretic approach to consequence traces its origins back to David Hilbert’s work on mathematical proof and Gerhard Gentzen’s on natural deduction, and has since been heavily influenced by the contributions of Dag Prawitz, Michael Dummett, and others.[14]

Medieval ways of explicating consequence have parallels to both of these approaches. Instead of models, some medieval accounts of consequence rely on a notion of causes of truth, which shares similarities with the modern notion of a truthmaker.[15] And instead of rule-governed proof systems, several medieval logicians appeal to inference-licensing rules called maximal propositions which arise out of discussions of topical argument.[16]

But what likely strikes the non-logician about these accounts is their abstraction from the actual content of an inference.[17] Since Tarski’s advances in model theory, for instance, classical models for standard formal representations of ‘Socrates runs’ have also served to model ‘Plato jumps’.[18] And since Hilbert’s advances in geometry, proof systems have been constructed with the intent of making the interpretation of the symbols occurring in them a matter of indifference. In accord with this characteristic, modern theories of consequence tend to focus almost entirely on formally valid inference.

Medieval approaches to consequence generally lack this feature. Rather, the earliest medieval criteria for consequence state that a consequence is good, true, valid, or holds when it is impossibile for the antecedent to be true and the consequent false, and later criteria for consequence generally consist of more sophisticated variations on this same theme – to avoid problems with self-falsifying propositions, for instance, several authors state a version on which a consequence is good when things cannot be as the antecedent signifies without being as the consequent signifies.[19] Another popular criterion, now called the ‘containment criterion’ and later used in characterizations of formal consequence, holds that a consequence is good when [the understanding of] the consequent is ‘contained’ in [the understanding of] the antecedent.[20] Some authors appeal to versions of both criteria, while others use one to the exclusion of the other. Both continue to be regarded as basic, intuitive criteria for consequence and to serve as the basis for its modern formalizations.[21]

4 Introduction to the articles

The articles collected in this issue survey a wide array of topics in the theory of consequence, beginning with the contributions of Boethius (which properly antedate the theory but are central to its later development) and following with discussions of subjects from the mid-twelfth through the later fourteenth century. Following the scholastic commitment to the question of the right order of reading,[1] the articles in this collection are ordered to facilitate reading from beginning to end, moving from material likely to be more basic for the understanding of other authors, more widely discussed in secondary literature, and more accessible from the standpoint of modern logic, to less familiar figures and broader thematic discussions.

Much of the basic material out of which the doctrine of consequence arose comes from Boethius. In ‘The Roots of the Notion of Containment in Theories of Consequence: Boethius on Topics, Containment, and Consequences’, Bianca Bosman addresses the question of whether and to what extent the containment criterion for consequence, common in both earlier discussions of natural consequence and later British discussions of formal consequence, is anticipated in the logical works of Boethius. Bosman argues that, while the containment criterion does draw on Boethian source texts, those sources are different from those standardly assumed. Bosman shows that the later criterion draws much from texts not devoted to conditionals, including Boethius’ discussions of per se predication in his treatment of the Porphyrian predicables, and of the locus from a genus in his commentary on Cicero’s Topics.

The best-known medieval accounts of consequences are those of William of Ockham and John Buridan. But the relation between these accounts remains obscure. In particular, Ockham classifies certain consequences as formal which Buridan admits only as material, and the exact reason for these differences has not been sufficiently explored. In ‘The Distinction between Formal and Material Consequences in Ockham and Buridan’, Milo Crimi provides a classification of consequences both figures treat as formal, those both treat as material, and those which Ockham calls formal and Buridan calls material. Crimi then shows that the taxonomical discrepancy between Ockham and Buridan’s accounts is not due to differences in their propositional hylomorphism, but to Ockham’s endorsement of relational characterizations of formal consequences.

One of the more outstanding continental authors writing on consequences after Buridan is Marsilius of Inghen, later founder and rector of the University of Heidelberg. Marsilius calls Buridan ‘my teacher’[2] and with Albert of Saxony Marsilius is traditionally regarded as a prominent member of a Buridanian school of logic. Though neither Marsilius nor Albert held such a relation to Buridan in any institutional sense,[3] their approach to consequences share some broad similarities when compared to that of later British writers, particularly in their use of a substitutional criterion for formal consequence. In ‘Marsilius of Inghen on the Definition of consequentia’, Graziana Ciola compares Marsilius’ account of consequences with those of Buridan and Albert, and finds that Marsilius diverges from Buridan and Albert in several important respects. Specifically, Buridan and Albert affirm, while Marsilius denies, that a consequence is a propositio hypothetica. Instead, Marsilius characterizes a consequence as an oratio, further distancing the theory of consequences from that of the conditional and more clearly establishing it as an entailment relation. In addition, Marsilius rejects, where Buridan and Albert accept, ut nunc, or as-of-now consequence. This rejection is found with some frequency among British and Italian logicians,[4] and the adoption of the position in Marsilius suggests the interaction between British and continental traditions may be more complex than currently recognized.[5]

With Ockham and Buridan, Walter Burley is often regarded as one of the most influential logicians of the later middle ages. One of the earliest extant consequentiae treatises, and the earliest with a known author, belongs to Burley. In addition, Burley is one of the few early authors to discuss both the natural/accidental division and formal/material division of consequences at some length. In ‘Consequence and Formality in the Logic of Walter Burley’, Jacob Archambault provides a comprehensive overview of Walter Burley’s account of consequences. After reviewing Burley’s division and enumeration of consequences, Archambault shows how Burley relates his own theory of natural and accidental consequence to the division into formal and material consequence found in Ockham. The article then compares Burley’s work to the earliest anonymous treatises on consequences and to Ockham and Buridan’s treatises on the subject. Archambault highlights Burley’s advances over the former treatises’ treatment of existential import in consequences, his disagreements with Ockham and Buridan on rules governing consequences, and his influence on the broader place of the study of consequences in logic.

Next, Joke Spruyt provides an overview of consequences in the thirteenth century. Successively examining thirteenth-century discussions of syllogisms, syncategoremata, and sophismata, Spruyt shows that across these genres, thirteenth-century work on consequences often assimilated the relation of a consequent to its antecedent(s) to that of an effect to its cause(s). Though thirteenth-century logicians typically regarded premises as causes not of being, but of following, the assimilation played an important role in thirteenth-century treatments of inferences from impossible antecedents or to necessary consequents. Many thirteenth-century logicians rejected the validity of these inferences, and those who admitted them to be valid in some respect did not regard them as unqualifiedly so.

This issue closes with Christopher Martin’s analysis of the development of the theory of natural consequence from Peter Abaelard to the turn of the fourteenth century. Martin argues that the early theory of natural consequence provides a medieval theory of relevant consequence, specifically one conforming to principles which today characterize connexive logic, and he shows the crucial role played by changes in the account of disjunction in the shift away from this relevantistic account of consequence. According to Martin, Abaelard distinguishes between extensionally-defined predicate disjunction for categorical propositions, on the one hand, and propositional disjunction, on the other, and employs an intensional account of propositional disjunction on which this kind of disjunction is equivalent to a conditional with the negation of the first disjunct as antecedent and the second disjunct as consequent. Like his account of the conditional, Abaelard’s account of propositional disjunction thus also conforms to connexive principles. As logic texts shifts from twelfth century manifestos for the doctrines of rival schools to more irenic thirteenth century textbooks, Abaelard’s distinction is lost, and largely replaced by an extensional account of propositional disjunction. But the need for a stronger form of consequence than that holding merely in virtue of a standard semantic requirement – namely, the impossibility of the antecedent holding with the consequent not holding – is found in authors through the thirteenth and into the fourteenth century, and was especially acute in a species of disputational exercises, or obligation, involving the positing of an impossible proposition, called positio impossibilis. It is in this disputational context, and specifically in the different treatments of impossible positio in Scotus and Ockham, that the seeds of Ockham’s alternative analysis of consequence, and the replacement of the earlier one, would be sown.

[1] A set is a grouping of elements without respect to their order or repetition. {A, B} and {B, A} and {A, A, B} all name the same set. A list respects both the order of elements and the number of times an element occurs. Hence,  and  are all different lists. Multisets are like sets but respect the number of times a given element occurs. Hence, though [A, B], and [B, A], and [A, A, B] all name the same set, only the first two refer to the same multiset. See David Ripley, ‘Comparing Substructural Theories of Truth’, Ergo 2 (2015), 300.

[2] James W. Garson, What Logics Mean (Cambridge, 2013).

[3] Both consequence and inference have been suggested as appropriate translations for the Latin consequentia. For discussion, see Peter King, ‘Consequence as Inference: Mediaeval Proof Theory 1300-1350’, in Medieval Formal Logic: Obligations, Insolubles and Consequences, ed. Mikko Yrjönsuuri (Dordrecht, 2001), 117–45; also Catarina Dutilh Novaes, ‘Buridan’s Consequentia: Consequence and Inference Within a Token-Based Semantics’, History and Philosophy of Logic 26 (2005), 277–97.

[4] Niels Jørgen Green-Pedersen, ‘Two Early Anonymous Tracts on Consequences’, Cahiers de L’Institut Du Moyen-Âge Grec et Latin 35 (1980), 1–28, 4: ‘Consequentia est habitudo inter antecedens et consequens. Antecedens est illud ad quod sequitur aliud. Consequens est illud quod sequitur ex alio’. W. K. Seaton, ‘An Edition and Translation of the Tractatus de Consequentiis of Ralph Strode’ (University of California at Berkeley, PhD Thesis, 1973), 1: ‘Consequentia dicitur illatio consequentis ex antecedente’. Rodolphus Anglicus: ‘Consequentia est quaedam habitudo vel sequela in qua consequens se habet ad antecedens’, in Niels Jørgen Green-Pedersen, ‘Early British Treatises on Consequences’, in The Rise of British Logic: Acts of the Sixth European Symposium on Medieval Logic and Semantics, Balliol College, Oxford, 19-24 June 1983, ed. P. Osmund Lewry (Toronto, 1985), 306.

[5] John Buridan, Tractatus de Consequentiis, ed. Hubert Hubien (Louvain, 1976) I, c. 3, 22.60-62: ‘Consequentia est propositio hypothetica ex antecedente et consequente composita, designans antecedens esse antecedens et consequens esse consequens’. Pseudo-Scotus, Quaestiones Super Libros II Priorum Analyticorum, Joannis Duns Scoti Doctoris Subtilis Ordinis Minorum Opera Omnia, vol. 2 (Paris, 1891) I. q. 10, 104-105: ‘Consequentia est propositio hypothetica, composita ex antecedente, et consequente, mediante conjunctione conditionali, vel rationali, quae denotat, quod impossibile est ipsis, scilicet antecedente, et consequente simul formatis, quod antecedens sit verum, et consequens falsum’.

[6] Niels Jørgen Green-Pedersen, ‘Bradwardine(?) On Ockham’s Doctrine of Consequences: An Edition’, Cahiers de L’Institut Du Moyen-Âge Grec et Latin (1982), 85–150, 92: ‘Circa definitionem nota quod consequentia est argumentatio composita ex antedente et consequente. ‘Argumentatio’ ponitur in definitione consequentiae, quia omnis consequentia sumitur ad aliquod argumentum producendum. ‘Composita’ dicitur, quia nullum incomplexum est consequentia. ‘Ex antecedente et consequente’ additur, quia in omni consequentia adminus requiruntur duae propositiones categoricae’.

[7] See no. 6 in Green-Pedersen, ‘Early British Treatises on Consequences’, 300: ‘Consequentia est quoddam aggregatum ex antecedente et consequente ad idem consequens cum nota consequentiae. Et sunt notae consequentiae ‘ergo’, ‘ideo’, ‘quia’, ‘igitur’, ‘idcirco’’. Also nos. 7, 9, and 15, ibid., 300–306.

[8] Green-Pedersen, ‘Two Early Anonymous Tracts on Consequences’ 11: ‘In omni consequentia bona quicquid sequitur ad consequens sequitur ad antecedens; ut sequitur ‘Socrates currit, ergo animal currit’ et sequitur ‘animal currit, ergo substantia currit’; ergo a primo ad ultimum sequitur ‘Socrates currit, ergo substantia currit’. William of Ockham, Summa Logicae, in Opera Philosophica, ed. Philotheus Boehner, Gedeon Gàl, and Stephen Brown, vol. 1 (St. Bonaventure, NY, 1974) III-3, c. 1, 587.4-9: ‘Habito de syllogismo in communi et de syllogismo demonstrativo, agendum est de argumentis et consequentiis quae non servant formam syllogisticam. Et primo ponam aliquas distinctiones quae sunt communes aliis consequentiis multis, quamvis non sint enthymemata, ex quibus omnibus faciliter patere poterit studioso quid de omnibus syllogismis non demonstrativis est tenendum’. Cf. Lorenzo Pozzi, Le ’Consequentiae’ Nella Logica Medievale (Padova, 1978), 262.

[9] Green-Pedersen, ‘Bradwardine(?) On Ockham’s Doctrine of Consequences’ 92: ‘Etiam ex ista definitione sequitur quod omnis argumentatio generaliter potest vocari consequentia, sive sit syllogistica sive inductiva sive exemplaris sive enthymematica’. William of Ockham, Tractatus Minor Logicae, in Opera Philosophica: Opera Dubia et Spuria, ed. Eligius M. Buytaert, Gedeon Gàl, and Joachim Giermek, vol. 7 (St. Bonaventure, NY, 1988), 1–57 V. c. 1, 31.4-5: ‘Sic syllogismus et inductio, conversio et multi alii modi considerandi sunt consequentiae formales’. Pseudo-Scotus, Quaestiones Super Libros II Priorum Analyticorum I. q. 20, 130: ‘Notandum est, quod quaedam est consequentia enthymematica, et quaedam syllogistica’.

[10] Cf. Alfred Tarski, ‘On the Concept of Following Logically’, trans. Magda Stroińska and David Hitchcock, History and Philosophy of Logic 23 (2002), 155–96; Dag Prawitz, ‘On the Idea of a General Proof Theory’, Synthese 27 (1974), 63–77.

[11] The definition is taken from Nissim Francez, ‘On Distinguishing Proof-Theoretic Consequence from Derivability’, Logique et Analyse 238 (2017), 152.

[12] Or, in the case of sequent calculi, arguments from arguments. The array of proof systems in logic today is vast, and the above description only captures a fraction of them.

[13] The definition given here is a simplification which leaves aside problems pertaining to the normal form of inferences. For fuller discussion, see Dag Prawitz, ‘Remarks on Some Approaches to the Concept of Logical Consequence’, Synthese 62 (1985), 153–71.

[14] Gerhard Gentzen, ‘Untersuchungen über Das Logische Schliessen’ Mathematische Zeitschrift 39 (1935), 176-210; Prawitz, ‘On the Idea of a General Proof Theory’; Michael Dummett, The Logical Basis of Metaphysics (Cambridge, MA, 1991); Peter Schroeder-Heister, ‘Validity Concepts in Proof-Theoretic Semantics’, Synthese 148 (2006), 525–71; Curtis Franks, ‘Cut as Consequence’, History and Philosophy of Logic 31 (2010), 349–79.

[15] John Buridan, Tractatus de Consequentiis I. c. 2, 19-20. An early application of model-theoretic consequence has recently been traced to the 12th century Arabic logician Abū al-Barakāt. See Wilfrid Hodges, ‘Two Early Arabic Applications of Model-Theoretic Consequence’, Logica Universalis 12 (2018), 37–54.

[16] Walter Burleigh, De Puritate Artis Logicae, ed. Philotheus Boehner (St Bonaventure, NY, 1955), 76.5–7.

[17] Catarina Dutilh Novaes, ‘The Different Ways in Which Logic Is (Said to Be) Formal’, History and Philosophy of Logic 32 (2011), 303–32.

[18] Should this entail that ‘Plato jumps’ follows from ‘Socrates runs’? No: though every model of the former is a model of the latter, it is not so ‘at the same time’, and hence fails the semantic criterion for following.

[19] John Buridan, Tractatus de Consequentiis I, c. 3, 20-22, Pseudo-Scotus, Quaestiones Super Libros II Priorum Analyticorum I, q. 10, 103-105.

[20] Petrus Abaelardus, Dialectica, ed. Lambertus M. de Rijk (Assen, 1966), 283–84.

[21] José M. Sagüillo, ‘Logical Consequence Revisited’, Bulletin of Symbolic Logic 3 (1997), 216–41, 218-219; Kit Fine, ‘A Theory of Truthmaker Content I: Conjunction, Disjunction and Negation’, Journal of Philosophical Logic 46 (2017), 625–74; Volker Halbach, ‘The Substitutional Analysis of Logical Consequence’, Noûs, Forthcoming; Dag Prawitz, ‘The Fundamental Problem of General Proof Theory’, Studia Logica, forthcoming.

[1] Sten Ebbesen, ‘Ancient Scholastic Logic as the Source of Medieval Scholastic Logic’, in The Cambridge History of Later Medieval Philosophy, ed. Norman Kretzmann, Anthony Kenny, and Jan Pinborg (Cambridge, 1982), 104.

[2] Marsilius of Inghen, Quaestiones Super Libros de Generatione et Corruptione (Venice, 1501), fol. 106va.

[3] William J. Courtenay, ‘The University of Paris at the Time of Jean Buridan and Nicole Oresme’, Vivarium 42 (2004), 1–17; J. M. M. H. Thijssen, ‘The Buridan School Reassessed: John Buridan and Albert of Saxony’, Vivarium 42 (2004), 18–42.

[4] Green-Pedersen, ‘Bradwardine(?) On Ockham’s Doctrine of Consequences’ 92-93.

[5] Cf. Niels Jørgen Green-Pedersen, ‘Nicholas Drukken de Dacia’s Commentary on the Prior Analytics–with Special Regard to the Theory of Consequences’, Cahiers de L’Institut Du Moyen-Âge Grec et Latin 37 (1981), 46.

The problem of evil does not exist


The existence of evil does not constitute evidence against the existence of God. On the contrary, it constitutes a condition without which God could not be God, and hence could not exist.


The conditions necessary for the possibility of an object existing do not contradict those necessary for the possibility of understanding the concept of that object:

Therefore, the conditions necessary for the possibility of a god existing do not contradict those necessary for the possibility of understanding the concept ‘God’.

But a standard condition assumed necessary for the possibility of god’s existence, namely, a world in which there neither was nor can be any evil, is one in which it is impossible to grasp the concept ‘god’.

Therefore, a world in which there neither was nor can be evil is not a condition necessary for the possibility of god’s existence.


The condition of a world in which in which there neither was nor can be any evil is one in which it is impossible to grasp the concept ‘God’. That is, a world in which it is possible to grasp the concept ‘god’ is one in which there was or can be evil.

Proof: I am not concerned here with more philosophical definitions of God, but with a simple one present in every popular theistic religion: by a god, I mean a being to which one should pray. The two chief forms of prayer are petition and gratitude. Petition presupposes the possibility of deprivation. Gratitude presupposes the avoidance of possible deprivation. Deprivation is evil. Without evil, there is thus no concept of prayer; without prayer, no concept of God. Thus, the existence of evil cannot constitute evidence against the existence of God, as a matter of principle.


Eternity is not, strictly speaking, a world distinct from this. If the saints give thanks, it is because they have known evil. If they petition, it is because evil is possible.

The formulation of problem of evil requires some distance from evil itself. This is empirically confirmed by the growth of atheism in proportion with material comfort, i.e. the existence of atheism as essentially a bourgeois phenomenon.

God is called a father, as one who supports and protects; one in heaven, for the altogether simple reason that that is whence the sun and rain come, without which there is no life.

What makes medieval philosophy medieval?

We begin with some standard answers to the question “What is Medieval Philosophy?”

Taking philosophy as primary, ‘Medieval philosophy’ is a name for philosophy as it was done in that period following late antiquity and stretching until the dawn of the modern period.

Taking Medieval as primary, ‘Medieval philosophy’ names an aspect of Medieval civilization, and less generally, a component medieval intellectual life. In this case, philosophy is taken to be the highest knowledge the mind is capable of attaining apart from the grace of revelation.

The oddity of putting these two terms together should strike us more strangely than it does. ‘Philosophy’ is, presumably, a name for an intellectual discipline; ‘Medieval’, an adjective specifying a time period. The matchup between the subject of predication and what is predicated of it should come across as a category mistake. It sounds strange, for instance, to describe Thomas Aquinas or William of Ockham as ‘doing’ Medieval philosophy. Philosophy isn’t the kind of thing that can be Medieval.

As an intellectual discipline, as a discipline preoccupied with getting ‘the right answers’ to the questions it poses – answers to questions supposed to be perennial – philosophy aims to have nothing to do with time. Even if philosophy is in fact always done from a given temporal standpoint, ideally, insofar as it aims to be a scientia, it would prefer that this weren’t the case. This helps to explain the neglect of the history of philosophy by a great many mainstream philosophers. To study philosophy qua medieval is not to study philosophy at all, but rather, the history of philosophy, now construed as something distinct from philosophy itself. Philosophy, it is said, thinks about and attempts to answer philosophical questions; but the study of medieval ‘philosophy,’ like any branch of history of philosophy, surreptitiously substitutes the study of thinkers for the study of the questions they are concerned with.

Medieval philosophy, then, can also be taken to be a subdiscipline of the history of philosophy – i.e. that part of philosophy which studies the Medieval Period. Its object of study can be construed as a certain set of thinkers from this time period; or perhaps the content of their thought; or perhaps a common body of doctrines held over that period. Medieval philosophy names a subdiscipline of history, more particularly a subdiscipline of intellectual history.

This definition fails for a reason that attacks the very concept of history as a science. The object of a science must, by virtue of its nature, be present to the mind of one who knows it. While the content of history is ex hypothesi absent, no longer present. If one insists, on the other hand, that it is only the content of the thought of thinkers that is studied, then the grouping of philosophers under the heading ‘medieval’ should seem quite accidental.

From here, I’d like to suggest a concept of Medieval Philosophy that has been little explored, and arises by a peculiar instance of metonymy. If the epithet ‘Medieval’ refers to a time period, what it signifies is something quite different, a distinctive aspect of that time period. On the basis of such – not carvings that we make as part of some ‘conceptual scheme’, but differences that come to the fore in the matter itself – we come to regard, for instance, the distinction between ancient, medieval, and modern philosophy as more natural than that between, say, philosophy before and after the year 923.

One distinctive aspect of medieval Philosophy is its humility. In the Medieval period, philosophy is the ancilla theologiae, and, for the most part, gladly subordinates its aims to those of theology. This same humility shows up in the characteristically Medieval posture towards authority. A philosophical position could scarcely be justified without being attributed to Aristotle, Augustine, Dionysius, or another major figure. Novelty was frowned upon, if only because philosophy itself was animated by the operative presumption that those who came before us knew better than we did.

What is called Medieval philosophy today, a presumed sub-discipline of the history of philosophy, also furnishes us with an interesting sociological phenomenon: Medieval scholarship is often itself characteristically medieval in the above described sense. In a way that isn’t duplicated either in contemporary or other historical areas of philosophy, those who work on certain figures in Medieval philosophy often hold a certain allegiance to those figures.

‘Medieval philosophy’ thus seems to signify a way of doing philosophy, present both in the genre’s primary figures and texts and in much secondary scholarship discussing its sources. It is on account of the presence of this distinctive mode that the name is taken to apply to that historical age which most exemplified this philosophical style; conversely, the waxing and waning of this style provide the period with its relative chronological boundaries. Because the point at which this style ceases to dominate is not exact, neither are the chronological boundaries of the period governed by it. And because the waning of this mode of philosophizing takes place at different times in different places, so, too shall the medieval period be more or less expansive in different locations: medieval philosophy continues to be vibrant, for instance, in Spain and Germany while it’s influence is waning in France and England.

Kierkegaard, on the nature of offense

From Soren Kierkegaard, Philosophical Crumbs (2009), pp. 253-254:

All offense is fundamentally passive. It is here as with that form of unhappy love just mentioned. Even when self-love […] proclaims itself in foolhardy exploits, in astonishing deeds, it is passive, it is injured, and the pain of the injury produces an illusory expression of power which looks active, but can easily disappoint, especially since self-love wants to hide its passivity. Even then, when it tramples upon the object of love, even when it masochistically disciplines itself to a state of hardened indifference and martyrs itself in order to show its indifference, even then when it surrenders itself in triumphant delirium that it succeeded […], even then it is passive.

Thus it is also with offense; it can express itself however it will. Even when it arrogantly celebrates the triumph of spiritlessness, it is suffering independently of whether the offended one sits crushed and stares almost like a beggar at the paradox, paralyzed by his suffering, or whether he arms himself with derision and aims the arrow of wit as if from a distance—he is passive and is not at a distance; even if offense came and took the last crumb of comfort and joy from the offended one or made him strong—offense is still passive, it has wrestled with the stronger and the agility of its apparent strength is, with respect to the body, like that of one whose back is broken, which does indeed give a kind of suppleness.


But precisely because offense is thus passive, the discovery, if one wishes to use such an expression, does not belong to the understanding, but to the paradox, because just as the truth is index sui et falsi, so also is the paradox, and offense does not understand itself, but is understood by the paradox. While offense, however it expresses itself, sounds from somewhere else, yes from the opposite corner, so it is the paradox that echoes in it, and this is an acoustic illusion. But if the paradox is index and judex sui et falsi, offense can be viewed as an indirect test of the correctness of the paradox; because offense is the erroneous calculation, is the consequence of error, which the paradox thrusts away. One who is offended does not speak with his own voice, but with the voice of the paradox, like one who mimics another, who does not produce anything himself, but merely copies another. The more deeply passionate is the expression of offense […], the more it reveals how much it owes to the paradox. Offense is not then an invention of the understanding, far from it. If this were the case, then the understanding would also have to have been able to invent the paradox. No, offence comes to be through the paradox.