Showing posts with label inconsistency. Show all posts
Showing posts with label inconsistency. Show all posts

12 Sept 2018

Dupréel (1.7) La consistance et la probabilité constructive, sect 1.7, ‘Hiérarchie des notions’, summary

 

by Corry Shores

 

[Search Blog Here. Index tabs are found at the bottom of the left column.]

 

[Central Entry Directory]

[Eugène Dupréel, entry directory]

[Dupréel, La consistance et la probabilité constructive, entry directory]

 

[The following is summary and not translation. Bracketed commentary is my own, as is any boldface. Proofreading is incomplete, so typos are present, including in the quotations. Please consult the original text to be sure about the contents. Also, I welcome corrections to my interpretations, because I am not especially good with French.]

 

 

 

Summary of

 

Eugène Dupréel

 

La consistance et la probabilité constructive

 

Part 1

“La consistance”

 

1.7

Hiérarchie des notions

 

 

 

Brief summary:

(1.7.1) We turn now to an examination of degrees of consistency in the second class of beings, namely, notions, which we divide into two categories: {1} sensible ideas, which are based more or less directly on perceptions, and {2} intelligible or rational ideas, which are applied to knowledge and conduct and which include fundamental notions of right, morality, economic relations, aesthetics, philosophy, and science in general. (1.7.2) Perceptual notions are grounded in sensory experience. They are assigned names, and given that we have and use our perceptual faculties in common, we can trust that when we refer to perceptual notions that they will be correctly understood by others. (1.7.3) Sensible notions can always be refined and divided when broadening applications lead one to distinguish species among a genus. (1.7.4) Intelligible or rational ideas are formulated (élaborées) notions, but in fact they have less consistency than perceptual notions; for, they undergo variations of their meanings depending on the context and circumstances under which they are formulated, and thus they can be considered confused ideas. (1.7.5) These intelligible notions, although being confused ideas, still make-up the fabric of human society; for, they include such notions as justice, right, morality, and so forth. Given their important role in keeping society together, we feel the need for our actions to accord with these mutually agreed upon notions. However, whenever we wish to act in a way that does not accord with the conventional meaning of the notion, we will insist on changing its meaning to suit our desired actions. So it is because each individual will insist on a different meaning for a commonly held notion that these notions will inevitably lack consistency. (1.7.6) These social-fabric forming but sense-varying notions can be fixed when particular groups settle upon just one definition for the notion. But that does not assure the continued fixity of that definition, because by the same process other definitions can be assigned instead.

 

 

 

 

 

 

 

 

Contents

 

1.7.1

[The Two Types of Notions: Sensible and Intelligible/Rational Ideas]

 

1.7.2

[Perceptual Notions]

 

1.7.3

[Refinements of Sensible Notions]

 

1.7.4

[Intelligible Ideas as Having Less Consistency, Given Their Contextual Variances, and as Thus Being Confused Ideas]

 

1.7.5

[Intelligible Notions as Keeping the Social Fabric but Varying Inconsistently on Account of Individual Needs]

 

1.7.6

[Arbitrary and Unstable Definitional Fixations for Intelligible Notions]

 

 

 

 

 

 

 

 

 

Summary

 

 

1.7.1

[The Two Types of Notions: Sensible and Intelligible/Rational Ideas]

 

(p.14: “Sommairement, en vue seulement de ce que nous avons ...”)

 

[We turn now to an examination of degrees of consistency in the second class of beings, namely, notions, which we divide into two categories: {1} sensible ideas, which are based more or less directly on perceptions, and {2} intelligible or rational ideas, which are applied to knowledge and conduct and which include fundamental notions of right, morality, economic relations, aesthetics, philosophy, and science in general.]

 

[First recall from section 1.2.2 that the consistency of a being is its capacity to endure throughout a series of its vicissitudes. In section 1.5.1 we saw that a thing can only influence and be influenced by things of the same sort. So sensible, material things can only touch and be touched by other spatial objects. The same goes for abstract entities. Numbers can only interrelate with other numbers, pure ideas with other pure ideas, propositions with other propositions, and judgments with other judgments. And, as we saw in section 1.5.2, there are three main types of beings: {1} sensible or perceptible beings (which are also spatial and material), {2} notions, which are those things that depend on a subject to know or express them, like sensations, feelings, thoughts, reveries, and so on, and {3} values, which are dynamic beings, because they lead one to commit deliberative actions. Our concern at the moment is examining the “hierarchy” of beings in each category, meaning that we want to see how within each type of being, they can be scaled according to their levels of consistency. In the previous section 1.6, we examined spatio-temporal beings. The lowest sort (the ones with the least consistency) are “inconsistent” things, which are physical bodies that have properties that depend strongly on the consistencies of external objects. For example, the shape of a liquid or gaseous body depends on the shape of the more solid container enveloping it (see section 1.6.2.) At the middle stage are solids, which are things that are directly perceivable and that are capable of enduring for some time all while undergoing slow degradations, for example: stones, tools, jewels, and even whole planets (see section 1.6.1). And the highest sort of spatio-temporal beings are those that not only can resist and endure detrimental external influences but as well are able to repair themselves after undergoing such alterations, with the outcome of that self-repair often increasing their consistency to a higher degree than before the attack. Examples of the highest kind of spatio-temporal beings (those with the greatest consistency) are living beings, with thinking beings as the highest among them (see section 1.6.3). We now turn to the second class of beings, namely, notions. For the sake of examining their degrees of consistency, we divide notions into two categories: {1} sensible ideas, which are based more or less directly on perceptions, and {2} intelligible or rational ideas, which are applied to knowledge and conduct and which include fundamental notions of right, morality, economic relations, aesthetics, philosophy, and science in general.]

Sommairement, en vue seulement de ce que nous avons à en dire quant au degré de consistance, nous répartissons les notions en ces deux catégories : 1° les idées dites sensibles, fondées plus ou moins directement sur les perceptions, 2° les idées dites intelligibles ou rationnelles élaborées par le raisonnement en vue de leur application au savoir et à la conduite, telles sont les notions fondamentales du droit, de la morale, des relations économiques, de l’esthétique, de la philosophie et de la science en général (1).

(14)

(1) Les idées relevant des mathématiques et de la logique pure, trop incompétent pour aborder ici ce qu’elles peuvent avoir de particulier, je ne puis que les intégrer dans la seconde des deux catégories, au titre de notions élaborées en vue de l’expression de l’état de nos connaissances. A ce titre, et quelle que soit leur clarté immédiate ou leur simplicité apparente, ces idées ne peuvent que se régler quant à la signification qu’il importe de leur conserver, sur le progrès de la connaissance dont elles sont le moyen d’expression. Point donc ni d’idée à priori parfaitement immuable quant à la somme de ses propriétés, ni de système d’axiomes unique, péremptoire, imposant définitivement ses affirmations aux développements ultérieurs des connaissances. Une théorie de la consistance relative est donc du côté des partisans d’une « philosophie ouverte », telle, par exemple, que la représentent M. Gonseth et Dialectica.

(14)

[contents]

 

 

 

 

 

 

1.7.2

[Perceptual Notions]

 

(p.14-15: “Les notions à base de perception et leurs propriétés ”)

 

[Perceptual notions are grounded in sensory experience. They are assigned names, and given that we have and use our perceptual faculties in common, we can trust that when we refer to perceptual notions that they will be correctly understood by others.]

 

[Dupréel turns first to perceptual notions. I do not follow all this very well, so please see the quotation below. I will be guessing for now that the ideas are the following. My first guess is that Dupréel is saying that there are various different perceptual notions, and they are distinguished by a certain consistency that would group them altogether, with the consistency of that grouping being seen in how the word assigned to the grouping consistently refers to the same grouping regardless of the context of the word usage. As far as I can tell, this seems like something Hume would say about sensory impressions and how they are grouped by similarity and assigned by convention and habit a certain word. While I would have thought an example might be an impression of a color along with its word, like “red,” Dupréel gives the example of a thousand horse-power of a motor. No one will mistake this sensible notion, because it has a strong consistency, and that can be seen in how well the notion refers straightforwardly to the perceptions from which they originated and in how little variation there is in that reference to originating perceptions despite differences in the contexts of usage. I am not sure what those perceptions might be however for this horse-power example. Perhaps it is observing the motor operate all while a gauge displays its house-power. I am not sure, sorry. Next Dupréel seems to appeal to a notion of common sense faculties of all humans, because he says that we all have the same means of perception and that we are obliged to use them in a common way. On this basis we can be assured of the certainty of perceptual notions.]

Les notions à base de perception et leurs propriétés apparentes ou immédiatement déduites se distinguent par une consistance bien marquée. L’accord sur la signification du mot ou de la propo- | sition qui les exprime est assez facile et durable pour n’entraver qu’exceptionnellement la combinaison des besoins individuels et les relations entre associés. Autrement dit leur expression garde assez exactement la même signification quel que soit le discours dans lequel on les rencontre. Les autres mots de la phrase n’exercent sur cette signification aucune pression déformante. Ou si cela arrive le changement de sens qu’ils imposent est assez clair pour que l’on sache que c’est en réalité d’une autre notion qu’il est question dans ce cas. Personne ne se trompe sur la nature des mille chevaux d’un moteur. La raison de cette constance dont profitent les notions sensibles c’est que l’accord sur leur signification est facile à obtenir et à maintenir : il suffit de s’en référer aux perceptions qui sont à leur origine. Comme tous les sujets percevants ont les mêmes moyens de perception, on tombe d’accord en les exerçant en commun. La perception renouvelée, recours à l’expérience commune, maintient au profit de la notion et de son sens une sorte d’évidence assurée.

(14-15)

[contents]

 

 

 

 

 

 

1.7.3

[Refinements of Sensible Notions]

 

(p.15: “Si l’usage conduit à étendre la portée d’une expression ...”)

 

[Sensible notions can always be refined and divided when broadening applications lead one to distinguish species among a genus.]

 

[I will probably missummarize the next idea, so please see the quotation below. I am guessing for now the idea is the following. Often times we have a name for some sort of thing. For example, we see a wolf, and we call it such. But then we also see dogs, which seem at first to be wolfy enough to also call wolves, because in fact they are something like domesticated wolves. And we also see coyotes, and given how wolfy they are too, we call them wolves. But eventually as we find more wolfy things, like  jackals and whatever, we realize that our original term is being applied too generally, and it is missing important diversity. We certainly will want to distinguish a dog from a wolf in many cases, even though they are also similar enough to take a general name encompassing both. So we call any such wolfy thing a canis, being the genus, of which we have various species, like dogs, wolves, coyotes, etc. I do not follow Dupréel’s main point here, which he states at the end, but maybe he is saying the following, if I may guess wildly here. While sensible notions may lose consistency as they become over-applied, by making genus-species distinctions we see that they all along had consistency, only they were misnamed. Insofar as the notion was referring to the broader group, it gets the genus name and is understood to be a notion for that genus, and insofar as it was referring to the narrower group, it gets the species name and is understood as being a notion for that species alone. Please see the following to be sure of the idea here.]

Si l’usage conduit à étendre la portée d’une expression à un nombre de plus en plus grand d’objets, de plus en plus divers, l’accord sur une définition pourra rétablir la consistance menacée en écartant certains sens adventices ; lesquels auront à être pourvus d’une appellation particulière. Lorsqu’une espèce animale ou végétale plus complètement explorée pose aux naturalistes la question de savoir si la rubrique consacrée convient encore pour désigner indistinctement tous les individus observés, ils se décident à passer de la considération d’une espèce unique à celle d’un genre comportant plusieurs espèces distinguées chacune par quelque différence. La consistance propre aux notions sensibles assure donc à celles-ci l’avantage de ne pas varier de sens à travers la diversité des occasions d’en insérer l’expression dans un discours ou un raisonnement.

(15)

[contents]

 

 

 

 

 

 

1.7.4

[Intelligible Ideas as Having Less Consistency, Given Their Contextual Variances, and as Thus Being Confused Ideas]

 

(p.15-16: “2° En dépit de leur importance et de leur prestige, ...”)

 

[Intelligible or rational ideas are formulated (élaborées) notions, but in fact they have less consistency than perceptual notions; for, they undergo variations of their meanings depending on the context and circumstances under which they are formulated, and thus they can be considered confused ideas.]

 

[We turn next to intelligible or rational ideas. We normally give them greater importance and prestige than sensible ideas, because we call intelligible ideas “formulated” (élaborées) notions. This might make us think, then, that they have greater consistency than sensible ideas. However, normally the opposite is the case. Unlike sensible notions, which as we saw in section 1.7.2, maintain a high degree of consistency despite various contextualizations on account of our commonly held perceptual faculties, intelligible notions often undergo variances to their meaning, making them relatively inconsistent. We thus may say that the formulated notions of this second category are confused ideas in that their meaning is subject to variation according to the circumstances under which they are formulated.]

2° En dépit de leur importance et de leur prestige, les notions dites intelligibles ou rationnelles que nous opposons, quant à nous, aux idées sensibles en les appelant élaborées (1), loin d’être caractérisées par une consistance qui serait supérieure à celle des notions sensibles, sont au contraire affligées d’une propension à varier quant à leur sens, qui leur vaut une inconsistance relative | très caractérisée. Nous pourrons dire que les notions élaborées de notre deuxième catégorie sont en fait des idées confuses en ce que leur signification est sujette à varier selon les circonstances où elles sont formulées.

(15-16)

(1) En fait toutes les notions, même sensibles, sont plus ou moins élaborées. La distinction que nous faisons ici est donc pratique l’t provisoire.

(15)

[contents]

 

 

 

 

 

 

1.7.5

[Intelligible Notions as Keeping the Social Fabric but Varying Inconsistently on Account of Individual Needs]

 

(p.16: “Il ne s’ensuit nullement un manque de valeur ...”)

 

[These intelligible notions, although being confused ideas, still make-up the fabric of human society; for, they include such notions as justice, right, morality, and so forth. Given their important role in keeping society together, we feel the need for our actions to accord with these mutually agreed upon notions. However, whenever we wish to act in a way that does not accord with the conventional meaning of the notion, we will insist on changing its meaning to suit our desired actions. So it is because each individual will insist on a different meaning for a commonly held notion that these notions will inevitably lack consistency.]

 

[The variance of intelligible notions (also called confused ideas) that we saw above in section 1.7.4 does not mean that they are entirely devoid of any value. For, all social order and all individual conduct rest on a relative agreement on the meaning of such notions as right or law, morality, economic agreement, and philosophical and religious thought. The common sense (of a society) is formed entirely from these agreements, and the concern for promoting and preserving these mutual understandings is the source of social order and peace. So, for the sake of the social order, it is important that our actions accord with these socially agreed upon notions (like what is right, moral, wise, practical, etc.) But then, when we find that the actions we are inclined to make do not accord with the conventional understanding of the notions, then we often struggle to redefine those notions to conform with the actions we wish to take, as a sort of way to socially sanction and legitimize those actions. Thus we might want to insist on an understanding of justice that suits our own convenience, even if others insist on a meaning that inconveniences us. For this reason, despite the importance of such notions that form our social fabric, they will always be inconsistent on account of each individual’s insistence on a variation of their meaning that suits their own interests.]

Il ne s’ensuit nullement un manque de valeur qui serait totale ; tout l’ordre social et toutes les conduites individuelles reposent sur un accord relatif quant à la signification des notions du droit, de la morale, des ententes économiques, de la pensée philosophique et religieuse ; le sens commun est tout formé de ces accords et le souci de favoriser l’entente ou de la conserver est à la source de l’ordre social et de la paix. Mais c’est justement du fait qu’il y a urgence d’établir que nos agissements sont conformes aux accords fondés sur ces notions qu’il s’ensuit que chacun de nous est porté à les interpréter conformément à ses convenances personnelles : « Je n’appelle pas justice ce que mon adversaire prétend qu’elle est, la vraie justice, au contraire c’est etc . . . ». Ce n’est pas seulement la chicane sans probité qui ébranle de la sorte le sens vacillant des notions confuses, même les meilleures intentions incitent à proposer d’une même notion une interprétation particulière : la noblesse même de la cause qu’on défend incite à déduire l’interprétation qu’on préfère, et à repousser un sens qui la contredirait.

(16)

[contents]

 

 

 

 

 

 

1.7.6

[Arbitrary and Unstable Definitional Fixations for Intelligible Notions]

 

(p.16-17: “Ainsi, plus une notion est haute et prestigieuse, ...”)

 

[These social-fabric forming but sense-varying notions can be fixed when particular groups settle upon just one definition for the notion. But that does not assure the continued fixity of that definition, because by the same process other definitions can be assigned instead.]

 

[In section 1.7.2 we saw that sensible notions lend themselves to high degrees of consistency, because on account of the common sense faculties of all people, they will refer to the same sorts of perceptual experiences and thereby maintain their meaning across various contexts of application. More abstract notions, as we saw above in sections 1.7.4 and 1.7.5, are less grounded in such fixed referents, and on account of differing individual needs, they will take on various meanings for different people. Thus the more a notion is detached from the brute reality of fact and for that reason be considered to be of a higher worth, the more its meaning will diverge into opposite directions. (The next ideas I might get wrong, so see the quotation below.) However, a group may collectively decide upon a definition for an intelligible notion and exclude the other variations on it. But nonetheless, such a procedure for fixing a definition is an arbitrary one that leaves the notion open to other re-definitions.]

Ainsi, plus une notion est haute et prestigieuse, éloignée qu’elle est de l’expérience brute des faits, construite au contraire à partir d’autres idées déjà sujettes à interprétation, plus elle sera exposée à voir sa signification diverger dans des directions opposées. Mais cette analyse ne doit pas conduire à un pessimisme trop marqué : la vie sociale, qui souffre de l’imprécision de ses notions les plus élevées, réagit opportunément par des conventions renouvelées. Un sens moins équivoque sera reeconnu à telle notion importante par l’accord sur une définition expresse, faite à dessein d’exclure les sens multiples qui ont proliféré, au profit exclusif du sens retenu. Ce recours à des définitions renouvelées réussit dans certaines limites, fortifiant à tout le moins l’accord des membres d’un groupe. Mais les définitions des notions élaborées sont toujours un cas particulier du même système d’élaboration, elles emploient à leur tour des notions confuses sur lesquelles la discussion pourrait se prendre. Les définitions convenues, multiples et opposables, laissent chimérique la prétention de saisir de la | notion discutée un sens précis, unique et cohérent, définitivement exclusif de tout autre.

(16-17)

[contents]

 

 

 

 

 

Dupréel, Eugène. (1961). La consistance et la probabilité constructive. (Classe des lettres et des sciences morales et politiques 55, no.2). Brussels: Académie Royale de Belgique.

PDF at:

http://www.academieroyale.be/fr/les-publications-memoires-detail/oeuvres-2/la-consistance-et-la-probabilite-constructive/.\

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Dupréel (1.6) La consistance et la probabilité constructive, sect 1.6, ‘Hiérarchie des êtres spatio-temporels’, summary

 

by Corry Shores

 

[Search Blog Here. Index tabs are found at the bottom of the left column.]

 

[Central Entry Directory]

[Eugène Dupréel, entry directory]

[Dupréel, La consistance et la probabilité constructive, entry directory]

 

[The following is summary and not translation. Bracketed commentary is my own, as is any boldface. Proofreading is incomplete, so typos are present, including in the quotations. Please consult the original text to be sure about the contents. Also, I welcome corrections to my interpretations, because I am not especially good with French.]

 

 

 

Summary of

 

Eugène Dupréel

 

La consistance et la probabilité constructive

 

Part 1

“La consistance”

 

1.6

Hiérarchie des êtres spatio-temporels

 

 

 

Brief summary:

(1.6.1) At the middle stage of consistency of spatio-temporal objects is the solid stage. Solids are things that are directly perceivable and that are capable of enduring for some time all while undergoing slow degradations, for example: stones, tools, jewels, and even whole planets. (1.6.2) At the lower stage of consistency of spatio-temporal beings are inconsistent objects. They are inconsistent in that they lack consistency in Dupréel’s sense of being self-holding and independent (and not in the sense of having contradictory properties). Inconsistent objects have properties that vary in relation to the consistencies of other objects they relate to physically. For example, the shape that liquids and gasses take on is determined by the shapes of the more solid objects that contain them. (1.6.3) The highest beings are those that not only can resist and endure detrimental external influences but as well are able to repair themselves after undergoing such alterations, with the outcome of that self-repair often increasing their consistency to a higher degree than before the attack. Examples of the highest kind of beings (those with the greatest consistency) are living beings, with thinking beings as the highest among them. (1.6.4) While this consistency-building repair process may happen for simple solids, it would not be something we could easily observe; however, it is very easy for us to see it in humans and non-human animals. (1.6.5) When we examine and discuss the degrees of consistency of beings, we must give special attention to collective beings in general, which include assemblages of differents and also mixtures of similars and differents. Too often such collective beings or groups – especially with regard to how they can be distinguished from the mere sums of their parts – are ignored and neglected.

 

 

 

 

 

 

 

 

Contents

 

1.6.1

[Solids]

 

1.6.2

[Inconsistent (Not Very Self-Holding) Spatio-Temporal Beings]

 

1.6.3

[Living Beings at the Highest Level of Consistency]

 

1.6.4

[Humans and Non-Human Animals as Obvious Cases for Consistency-Building Self-Repair]

 

1.6.5

[The Importance of Consistent,  Heterogeneous Groupings]

 

 

 

 

 

 

 

 

 

Summary

 

 

1.6.1

[Solids]

 

(p.13: “Sujet immense qui demanderait la compétence du savant ...”)

 

[At the middle stage of consistency of spatio-temporal objects is the solid stage. Solids are things that are directly perceivable and that are capable of enduring for some time all while undergoing slow degradations, for example: stones, tools, jewels, and even whole planets.]

 

[Recall from section 1.2.2 that the consistency of a being is its capacity to endure throughout a series of its vicissitudes. In section 1.3, we saw that sets of things often undergo a filtering process on the basis of shared powers of affection. We had for example the set of things first found together: sand, gravel, and large stones. They were all placed under the influence of wind. Each of these three things shares powers of affectivity, so the stones were largely unmoved and stayed in place, the gravel was pushed off a little bit away from the stones, and the sand was blown far away but deposited in the same depression in the ground some ways off. In section 1.4, we saw how such filtered groupings, under continued shared influences and vicissitudes, came to become more and more accommodated to one another. This causes the whole grouping they form to gain consistency all while its parts gain consistency too. However, there comes a point where there are two possible ways this group consistency-building can go. One way is toward solidification. Here the parts start to lose individuality and thus consistency as they fuse and homogenize all while the whole they form continues to gain consistency on account of that solidification of its parts. The other direction is toward increased consistency of both the parts and the whole. We see this in life-forms, for example, where the parts continue to diversify and maintain heterogeneity and relative individual independence  all while the whole living being they form also gains consistency on account of its internal heterogeneity that enables it to survive more vicissitudes and variational affections. In our current section, we will now discuss spatio-temporal beings, evaluated on a scale of more or less consistency. As we saw in section 1.4.2, many of the spatio-temporal beings around us tend toward the solidification process. There are three stages here, the middle one being that of the solid, where things are compact and inert. Examples of spatio-temporal things at this stage are stones, tools, jewels, and even a whole planet. They are any thing which is directly perceptible and capable of enduring for some time while also undergoing slow degradation.]

Sujet immense qui demanderait la compétence du savant jointe à l’expérience de l’homme d’action. Pour en marquer seulement la mise en place nous y relèverons trois étages. L’étage du milieu est celui du solide, compact et inerte ; tels sont une pierre, un outil, un bijou, même une planète!, toutes choses directement perceptibles, capables d’une longue durée tout en subissant une lente dégradation.

(13)

[contents]

 

 

 

 

 

 

1.6.2

[Inconsistent (Not Very Self-Holding) Spatio-Temporal Beings]

 

(p.13: “Au dessous de cet étage moyen on rangera tous les êtres ...”)

 

[At the lower stage of consistency of spatio-temporal beings are inconsistent objects. They are inconsistent in that they lack consistency in Dupréel’s sense of being self-holding and independent (and not in the sense of having contradictory properties). Inconsistent objects have properties that vary in relation to the consistencies of other objects they relate to physically. For example, the shape that liquids and gasses take on is determined by the shapes of the more solid objects that contain them.]

 

[Below this middle stage of solids are all the beings that we might call inconsistent beings. But here we should be careful it seems. We do not seem to mean inconsistent as lending to contradictions or heterogeneities. It seems rather to mean not consistent in Dupréel’s sense of “consistency”. So such inconsistent beings are ones that lack their own consistency, meaning that they do not hold well together on their own. Rather, they depend on beings at a higher level of consistency. I do not quite grasp the next point, but I will guess until we get to an example, which is much clearer. So such bodies with a low degree of self-consistency (meaning that they vary in accordance to variations with respect to the higher being they depend upon) will have certain qualities or properties that will undergo those variations, even though the whole body itself will maintain. Fox example, a liquid or a gas has among its properties its physical form in the sense of the shape it finds itself having at some moment. That shape will often depend on the shape of the container that is holding it. So its consistency is not null, because it remains as the liquid or gas that it happens to be, but its consistency is subject to the consistency of an external consistency of another object with its own greater consistency.]

Au dessous de cet étage moyen on rangera tous les êtres que l’on peut appeler les inconsistants en voulant marquer par là leur dépendance de quelque être du niveau supérieur, ainsi les qualités ou attributs des solides, comme la couleur ou une partie d’un corps, varieront comme variera le corps dont elles sont un complément ; un liquide, un gaz, incapables de se soutenir sont soumis au récipient qui les porte ou les retient et dont ils partageront plus ou moins la plupart des variations. Leur consistance n’est jamais nulle, mais toujours soumise à une consistance étrangère.

(13)

[contents]

 

 

 

 

 

 

1.6.3

[Living Beings at the Highest Level of Consistency]

 

(p.13-14: “Les Êtres supérieurs. – Il y a enfin au dessus ...”)

 

[The highest beings are those that not only can resist and endure detrimental external influences but as well are able to repair themselves after undergoing such alterations, with the outcome of that self-repair often increasing their consistency to a higher degree than before the attack. Examples of the highest kind of beings (those with the greatest consistency) are living beings, with thinking beings as the highest among them.]

 

[Beings at the highest level of consistency obtain their consistency on the basis of their own means of action. Such beings cannot only avoid or endure detrimental external influences that cause alterations to them, they can also repair themselves after having been detrimentally altered, sometimes even being stronger than before. (Perhaps we might here think about building immunities to pathogens or repairing damaged muscle material, which builds those muscles stronger.) Beings of this highest level of consistency are living beings, and highest among them are thinking beings. (I am guessing the next point is: So as we can see, we can order beings on the basis of consistency in this way where the higher ones are those that are most resistant to external attacks and that even increase in consistency as a result of them.)]

Les Êtres supérieurs. – Il y a enfin au dessus des solides et des inconsistants les êtres dont la consistance particulière repose sur des moyens d’action desquels ils sont intérieurement pourvus. Ceux-là ne sont pas seulement capables d’atténuer les altérations subies, ou d’éviter certains d’entre elles, mais il leur arrive même de restaurer les dégradations subies par le fait de l’extérieur, au point de se retrouver dans le même état qu’avant le détriment, voire dans un état plus avantageux. Ce troisième étage est celui des êtres vivants ; à leur sommet sont les êtres pensants. Notre analyse de la consistance en général nous permet d’y joindre les | êtres collectifs en voie de progression et qui doivent à la similitude de leurs éléments de riposter aux attaques du dehors par un progrès relatif de leur consistance.

(13-14)

[contents]

 

 

 

 

 

 

1.6.4

[Humans and Non-Human Animals as Obvious Cases for Consistency-Building Self-Repair]

 

(p.14: “Lorsqu’il s’agit de collections de solides simples, ...”)

 

[While this consistency-building repair process may happen for simple solids, it would not be something we could easily observe; however, it is very easy for us to see it in humans and non-human animals.]

 

[(I do not grasp the next idea. I am for now guessing it is the following. In section 1.6.3 above we saw that beings of the highest level of consistency can self-repair after detrimental external influences and even thereby attain yet a greater consistency as a result (perhaps like muscle-building or immunity-building). Maybe now Dupréel is saying that such processes could be found among simple solids, only these processes are too hard to detect by means of normal human observation; however, this process we very easily can observe among non-human animals and humans. See the quotation below.)]

Lorsqu’il s’agit de collections de solides simples, ce processus est toujours trop rare, ou plutôt trop peu accusé, trop partiel, interrompu ou trop lent pour tomber directement sous notre observation, mais il se confirme entièrement quand la collection est celle d’éléments déjà pourvus du plus haut degré de consistance, tels que les animaux et les hommes.

[contents]

 

 

 

 

 

 

1.6.5

[The Importance of Consistent,  Heterogeneous Groupings]

 

(p.14: “Dans l’enquête sur le degré de consistance des êtres ...”)

 

[When we examine and discuss the degrees of consistency of beings, we must give special attention to collective beings in general, which include assemblages of differents and also mixtures of similars and differents. Too often such collective beings or groups – especially with regard to how they can be distinguished from the mere sums of their parts – are ignored and neglected.]

 

[(ditto)]

Dans l’enquête sur le degré de consistance des êtres une place importante est à réserver aux êtres collectifs en général (y compris les rassemblements de différents, et les mélanges de semblables et de différents). L’importance des être collectifs, des groupes en tant que tels, à distinguer de la simple somme de leurs éléments, a toujours été méconnue et négligée.

[contents]

 

 

 

 

 

 

 

 

Dupréel, Eugène. (1961). La consistance et la probabilité constructive. (Classe des lettres et des sciences morales et politiques 55, no.2). Brussels: Académie Royale de Belgique.

PDF at:

http://www.academieroyale.be/fr/les-publications-memoires-detail/oeuvres-2/la-consistance-et-la-probabilite-constructive/.\

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6 Apr 2016

Agler (3.4) Symbolic Logic: Syntax, Semantics, and Proof, "Truth Tables Analysis of Sets of Propositions", summary

 

by Corry Shores
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[The following is summary. Boldface (except for metavariables) and bracketed commentary are my own. I highly recommend Agler’s excellent book. It is one of the best introductions to logic I have come across.]

 

 

 

Summary of

 

David W. Agler

 

Symbolic Logic: Syntax, Semantics, and Proof

 

Ch.3: Truth Tables


3.4 Truth Tables Analysis of Sets of Propositions

 

 

 

Brief Summary:
We can use decision procedures with truth tables to determine whether or not a set of propositions are equivalent or consistent. If the truth table for a set of propositions shows them each to have identical truth values for any truth assignments, then they are logically equivalent. And they are not equivalent otherwise. Another way to conduct this test is to combine the propositions into one larger proposition using the biconditional operator. If the new proposition is a tautology, then the original two propositions are logically equivalent. A set of propositions are consistent if there is at least one value assignment that makes them all true. So on the truth table, we look for at least one line where all the propositions in question have the value true, and that tells us they are consistent. The propositions are inconsistent if no truth value assignment makes all the propositions jointly true. This can also be tested by combining a pair of propositions with a conjunction. If the new proposition is a contradiction, then the original propositions are inconsistent.

 

 

Summary

 

3.4 Truth Tables Analysis of Sets of Propositions

 

Previously we used truth tables to analyze singular propositions [to see if they were tautologies, contradictions, or contingencies]. Now we will use truth tables to evaluate sets of propositions to test them for logical equivalence and consistency (81).

 

 

3.4.1 Equivalence

 

Consider the following two sentences:

John is a married man.
John is not an unmarried man.
(81)

No matter what truth assignments we make, these two sentences will always have the same truth value, and thus they are logically equivalent.

Equivalence: A pair of propositions ‘P’ and‘Q’ is logically equivalent if and only if ‘P’ and ‘Q’ have identical truth values under every valuation. In a truth table for an equivalence, there is no row on the truth table where one of the pair ‘P’ has a different truth value than the other ‘Q.’
(81)

 

So first consider a truth table that evaluates both propositions:

P→Q
Q∨¬P

Agler 3.4.1 equivalence a

 

We see that under the same truth assignments, they have the same evaluations, and thus they are logically equivalent:

The truth table above shows that ‘P→Q’ is logically equivalent to ‘Q∨¬P’ because whenever v(P→Q) = T, then v(Q∨¬P) = T, and whenever v(P→Q) = F, then v(Q∨¬P) = F.
(Agler 81)

 

[So this methodology involves us using our eyes and comparing two columns. The next method will involve an extra step, but it will display one column of values which will make the equivalence obvious.] Another way to determine whether or not a pair of propositions is logically equivalent is by joining the two with the biconditional and then seeing if that biconditional relation produces all true values, that is, seeing if it is a tautology. [Recall from section 3.3 our decision procedures for singular propositions. A proposition is a tautology when all the truth values are true, regardless of the truth assignments. Here was one example for P→(Q→P).

Agler.3.3.tautology-c_thumb1

This biconditional technique involves taking the two different propositions and making them one larger proposition and then applying the decision procedure for singular propositions to see if it is tautological.] The the biconditional is true whenever both sides have the same truth value, and false otherwise. Thus a biconditional is a tautology if both sides have the same truth value, regardless of the truth assignments. So let us take our two propositions from before:

P→Q
Q∨¬P

And we will make it into a singular biconditional:

(P→Q) ↔ (Q∨¬P)

Now when we make the truth table for it, we see that the biconditional is true for all assignments, thus the biconditional proposition is a tautology; and hence furthermore, both of the original propositions are logically equivalent.

Agler 3.4.1 equivalence c

And of course, if the biconditional relation between the two original propositions is not a tautology, then they are not logically equivalent (82).

 

 

3.4.2 Consistency

 

Consider the following three propositions.

John is a bachelor.
Frank is a bachelor.
Vic is a bachelor.
(83a)

It is possible for them all to be, that is to say, there are value assignments where all three are jointly true, and thus these sentences are logically consistent.

Consistency: A set of propositions ‘{P, Q, R, ... , Z}’ is logically consistent if and only if there is at least one valuation where ‘P,’ ‘Q,’ ‘R,’ ... , ‘Z’ are true. A truth table shows that a set of propositions is consistent when there is at least one row in the truth table where ‘P,’ ‘Q,’ ‘R,’ ... ,‘Z’ are all true.
(83)

 

For example, let us consider the following three propositions:

P→Q
Q∨P
P↔Q

And let us make a truth table for them:

Agler 3.4.2 consistency 1

 

As we can see, for line 1, all three main operators have the value true, and thus all three are logically consistent. For, there is at least one value assignment, namely v(P)=T and v(Q) =T, that makes all three propositions true (83).

 

Agler then notes that empirical evidence might say that certain logically consistent propositions are not together true, but that does not make them any less logically consistent. It only makes them factually inconsistent (83). For, “at the level of logical or semantic analysis, they could both be true” (83).

 

Now, whenever a set of propositions cannot all be true together, that is, whenever there is no value assignment that can make them all true, then they are inconsistent.

Inconsistency: A set of propositions ‘{P, Q, R, ... , Z}’ is logically inconsistent if and only if there is no valuation where ‘P,’ ‘Q,’ ‘R,’ ... , ‘Z’ are jointly true. A truth table shows that a set of propositions is inconsistent when there is no row on the truth table where ‘P,’ ‘Q,’ ‘R,’ ... , ‘Z’ are all true.
(84)

 

Agler illustrates by giving the truth table for the following two propositions:

(P∨Q)
¬(Q∨P)

Agler 3.4.2 

inconsistency a

 

As we can see, there is no value assignment where both propositions are jointly true. Thus they are inconsistent.

 

Another way of showing this is by joining the propositions by a conjunction and seeing if they form a contradiction, that is to say, seeing if they are false under all evaluations. As we can see, they are, which indicates that the original two propositions are inconsistent (84).

Agler 3.4.2 

inconsistency b

 

 

 

 

 

Agler, David. Symbolic Logic: Syntax, Semantics, and Proof. New York: Rowman & Littlefield, 2013.

 

 

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