16 Feb 2015

Somers-Hall, (0.4), Deleuze’s Difference and Repetition, ‘0.4 Kierkegaard (5–9/5–10)’, summary


by
Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own.]



Henry Somers-Hall


Deleuze’s Difference and Repetition.
An Edinburgh Philosophical Guide


Part 1
A Guide to the Text

 

 

0 Introduction: Repetition and Difference

0.4 Kierkegaard (5–9/5–10)


Summary



Brief summary:

Kierkegaard presents a notion of repetition in moral life which does not fit the idea of a universal law. Kant says that Abraham should not have assented to God’s request to kill his only son Isaac, since doing so goes against the categorical imperative. Kierkegaard thinks that there is an absolute (God) which is of a higher moral authority than the ethical universal. Repetition in moral life, for Kierkegaard, is not obeying the same law over and over, but rather obeying an absolute whose commands are not homogeneous or self-consistent. What is notable in this conception of repetition is that it is not the reiteration of the same action but rather each time behaving differently in a different situation.

 

 


Summary


“Deleuze claims that there are three thinkers who ‘oppose repetition to all forms of generality’: Kierkegaard, Nietzsche and Peguy (DR 5/6)” (SH 11). SH will treat Nietzsche’s eternal return later and for now focus mainly on “Kierkegaard’s alternative to generality” (11). Deleuze is concerned mostly with Kierkegaard’s Fear and Trembling. Recall that here Kierkegaard tells the story of God testing Abraham’s obedience by commanding him to sacrifice his only son Isaac. Abraham was willing to do so, but God spares Isaac and allows a ram to be sacrificed instead (12). While Kant thinks that Abraham should not have attempted to kill his son, as this goes against the categorical imperative, Kierkegaard thinks that Abraham has a faith so strong that it overrides such ethical laws.

For Kant, the fact that the commandment to commit murder contravenes the categorical imperative means that it could not have been a commandment given by God, and hence Abraham acted immorally in being willing to fulfil it” (12).

[In Kant, the universal is the absolute. But in Kierkegaard, there is an absolute, God, that has a higher authority than the universal.]

The position that Kierkegaard puts forward in Fear and Trembling is rather that the incommensurability of Abraham’s actions with the moral law shows that Abraham’s faith is higher than any ethical considerations [the following sentence quotes Kierkegaard]:

The paradox of faith, then, is this: that the single individual is higher than the universal, that the single individual – to recall a distinction in dogmatics rather rare these days – determines his relation to the universal by his relation to the absolute, not his relation to the absolute by his relation to the universal. (Kierkegaard 1983: 70)

What ultimately justifies Abraham’s actions is a direct relationship with God that is incomprehensible from the point of view of universal law. This is a relationship that necessarily falls outside of the sphere of generality and law.
(12, quoting: Kierkegaard, Søren (1983), Fear and Trembling/Repetition, trans. Howard V. Hong and Edna H. Hong, Princeton: Princeton University Press.)

[I do not find the following point regarding Job to be clear enough for me to summarize. I cannot grasp what about Job’s story is repetition. Is Kierkegaard saying that the reiteration of punishments is repetition, and Bildad argues that by letting them come repeatedly, that they will come to be exhausted? Is the thunderstorm the end of the reiterations, but in Deleuze’s interpretation, somehow a repetition?  I will quote it so you can interpret it properly for yourself.]

Kierkegaard makes clear the relation of this moment of faith to repetition in Repetition, this time with a discussion of Job. Job is also tested by God, who allows him to suffer misfortunes to prove to the devil that Job’s faith is not a consequence of God’s protection of him from misfortune. In this case, Job’s restoration is equated with repetition in a way that mirrors the return of Isaac to Abraham [the following paragraph quotes Kierkegaard]:

So there is a repetition, after all. When does it occur? Well, that is hard to say in any human language. When did it occur for Job? When every thinkable human certainty and probability were impossible. Bit by bit he loses everything, and hope thereby gradually vanishes, inasmuch as actuality, far from being placated, rather lodges stronger and stronger allegations against him. From the point of view of immediacy, everything is lost. His friends, especially Bildad, know but one way out, that by submitting to the punishment he may dare to hope for a repetition to the point of overflowing. Job will not have it. With that the knot and the entanglement are tightened and can be untied only by a thunderstorm. (Kierkegaard 1983: 212–13)

Repetition, therefore, is this moment that falls outside of the categories of reason (the thunderstorm introduced by Kierkegaard). It is not a physi-| cal repetition (the Bible tells us Job gets back twice what he lost, putting the repetition outside of the sphere of quantitative identity). Rather than being based on universality, as it is for Kant, for Kierkegaard (and for Deleuze) it is based on singularity.
(12-13, quoting Kierkegaard, same text)


Deleuze then summarizes the philosophies of Kierkegaard, Nietzsche, and Peguy in terms of repetition, giving “four criteria for a philosophy of repetition” (13).

1. Make repetition something new by connecting it with a test that will affirm one’s freedom even in the face of moral and natural law demanding otherwise.

2. Oppose repetition to the law of nature.

3. Oppose repetition to moral law.

4. Oppose repetition to the generalities of habit and to the particularities of memory (13).

[The criteria seem to continue from the above discussion, except for the memory part. Here perhaps memory ties the present too often to the past, and redundantly so, by means of association.] Deleuze will ultimately reject Kierkegaard’s notion of repetition since it is based on the relationship between a subject and object and for that reason is tied too much to the physical and moral worlds [in where we make these distinctions, but which do not hold when we think more of pure difference itself.] “Nonetheless, Kierkegaard prefigures Deleuze in seeing the need for a radical rethinking of the nature of repetition.” (14).

 



Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.


Or if otherwise noted:

Kierkegaard, Søren (1983), Fear and Trembling/Repetition, trans. Howard V. Hong and Edna H. Hong, Princeton: Princeton University Press.



Somers-Hall, (0.3), Deleuze’s Difference and Repetition, ‘0.3 Kant’s Moral Law (3–5/4–5)’, summary


by
Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own.]



Henry Somers-Hall


Deleuze’s Difference and Repetition.
An Edinburgh Philosophical Guide


Part 1
A Guide to the Text

 

 

0 Introduction: Repetition and Difference

0.3 Kant’s Moral Law (3–5/4–5)



Brief summary:

It might seem that moral laws which tell us to do the same thing in the same situations are instances of real repetition. But they are really just the application of the mechanistic operation of natural laws into our moral life, and thus they are generalities like scientific laws rather than real repetitions.

 

 


Summary


Previously we saw how repetition is not f0und in the laws of nature (found through scientific experimentation). Now we see if it repetition can be found in the moral realm (9). Deleuze works here with Kant, who distinguished natural and rational law (9). Consider if all our actions were mechanically determined. Then we would not be morally responsible for our actions, as we would not have chosen them. In Kant’s ethics, we need instead to be free autonomous beings in order to be moral agents (9). [We might say that there is something irrational about acting mechanistically. There is no deliberate thought involved. In order to conduct moral actions, one needs to be using one’s rational faculties in order to reason about situations and decide on the basis of that reasoning rather than on the basis of mechanical reactions.]

Kant’s essential claim is that if we are to be autonomous, that is, self-legislating, then, given that we are rational creatures, self-legislation must involve giving ourselves rational laws to govern our conduct. Furthermore, in order that these laws be purely rational, they should not contain any empirical content whatsoever. That is, the principles of morals must be purely formal principles. So Kant appears to create a sharp distinction between two realms, and two kinds of laws. On the one hand, empirical laws, which deal with determinate content, and on the other hand, moral laws, which are purely rational and formal.
(9)

We then wonder if in the rational do we find true repetition? (9)


[Any time we contradict ourselves, we are not being rational (you might think). As such, our rational moral behavior would be guided by laws which do not lead to contradictions.]

Kant proposes that if there is to be a formal criterion, it has to be based on the notion of rational consistency. The only way that we can provide a determination as to what we should do in a given circumstance is negatively. If the act can be performed without contradiction, | then it is a moral act. He formulates the key criterion, the categorical imperative, as follows [the following italicized sentence is quotation of Kant]:

Act only in accordance with a maxim through which you can at the same time will that it be a universal law. (Kant 1998: 31)

The central idea behind Kant’s account is therefore that if we can understand an action as hypothetically governed by a maxim that everyone held to without it producing a contradiction, then that action is a moral action.
(9-10, quoting: Kant, Immanuel (1998), Groundwork of the Metaphysics of Morals, trans. Mary Gregor, Cambridge: Cambridge University Press.)

One example is that it would not be moral to promise to repay borrowed money while having the intention of not paying it back. For, if everyone did this, no one would believe such a promise in the first place. [The following is from the Kant text:

2) Another finds himself urged by need to borrow money. He well knows that he will not be able to repay it but sees also that nothing will be lent him unless he promises firmly to repay it within a determinate time. He would like to make such a promise, but he still has enough conscience to ask himself: is it not forbidden and contrary to duty to help oneself out of need in such a way? Supposing that he still decided to do so, his maxim of action would go as follows: when I believe myself to be in need of money I shall borrow money and promise to repay it, even though I know that this will never happen. Now this principle of self-love or personal advantage is perhaps quite consistent with my whole future welfare, but the question now is whether it is right. I therefore turn the demand of self-love into a universal law and put the question as follows: how would it be if my maxim became a universal law? I then see at once that it could never hold as a universal law of nature and be consistent with itself, but must necessarily contradict itself. For, the universality of a law that everyone, when he believes himself to be in need, could promise whatever he pleases with the intention of not keeping it would make the promise and the end one might have in it itself impossible, since no one would believe what was promised him but would laugh at all such expressions as vain pretenses.
(Kant, 32)

]


This seems to be repetition. To universalize the action into a law would appear to mean to suppose it is repeatable.

If an action could become a universal law, that is, if it could be repeated, then it is a moral act. In this sense, repetition is not just something that is present within the moral realm, but is even the test or criterion by which we determine if something belongs to the moral realm.
(SH 10)

We then wonder if Kant provides “an account of repetition as strict universality?” (10).


[Notice a tension here. Natural law is supposedly a generality which applies in all cases. Autonomous rational thinking supposedly is not bound to such mechanistic repetition. However, to be moral for Kant, we need to strip away our autonomy and blindly obey a law of behavior as if we were robotically programmed.]

Deleuze presents the following antinomy in Difference and Repetition [the following quotes DR]:

Conscience, however, suffers from the following ambiguity: it can be conceived only by supposing the moral law to be external, superior and indifferent to the natural law; but the application of the moral law can be conceived only by restoring to conscience itself the image and the model of the law of nature. (DR 4/5)
(SH 10)

Somers-Hall quotes from Deleuze’s Kant’s Critical Philosophy where Deleuze explains that supersensible nature (rational moral law) can only be understood by analogy with sensible nature (natural law). (10-11)


While we may posit the existence of the free moral realm, we lack any way of conceiving of it, since it differs in kind from the world we find around us. Thus, if we are to represent it to ourselves, we have to rely on an analogy with the world we find around us.
(11)

[So we do not find real repetition in moral law, because our understanding of it is contaminated with natural law, which we saw was generality and not repetition.] Deleuze also thinks that Kant’s notion of duty is modeled on habit. [Since habit is also mechanical in the sense of determinism and natural law, then] as such, duty as habit is concerned more with similarities by ignoring the differences between events (equalization). (11)




Citations from:
 

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.


Or otherwise from:

Kant, Immanuel (1998), Groundwork of the Metaphysics of Morals, trans. Mary Gregor, Cambridge: Cambridge University Press.


Somers-Hall, (0.2), Deleuze’s Difference and Repetition, ‘0.2 Science and Repetition (1-3/1-4)’, summary


by
Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own.]



Henry Somers-Hall


Deleuze’s Difference and Repetition.
An Edinburgh Philosophical Guide


Part 1
A Guide to the Text

 

 

0 Introduction: Repetition and Difference

0.2 Science and Repetition (1-3/1-4)


Summary



Brief summary:

Scientific experimentation seem to repeat situations as if all were equivalent. But this is a mistake. They are not equivalent. They seem so, because by artificially selecting certain parameters and excluding others, the real distinguishing differences go unnoticed. Also, all features of the situation, including qualitative ones, are quantified, which equalizes all these differences in kind to the common system of numerical symbolization, which ignores all individuality of the things being quantified. Also, when laws are formulated on the basis of experimentation, it is always just a hypothesized sameness: ‘given the same circumstances …. [expect these same results]’

 

 


Summary


Previously Somers-Hall gave an overview of DR’s Introduction. He noted that repetition is not to understood in terms of generality and law. We do not then encounter repetition in scientific experiment, moral law, and psychological habit, which are matters of generality. Now we address the question, why is there not repetition in science? Bergson notes the idea of reversibility, that physical situations that change can go back to the prior states by moving in reverse (8) [See §10 of Creative Evolution] This is a precondition for the scientific method which recreates situations (8) [I am not sure why the reversibility is needed for replication. Could not a series of non-reversible sequences be reiterated? Or is the assumption that any such reiteration would require that a developed state be returned to a prior one? In other words, is it that we cannot set up an initial state unless we derive it by means of reversal? So might we say for example, if we set up dominoes, they must be down already, and thus have fallen down already?] “It is by recreating the same situation that we are able to develop laws, by showing that bodies always behave the same way, thereby showing that the law is universal” (SH 8). SH then notes the common sense notion of repetition in scientific experiment, which is an idea that Deleuze is trying to over-turn. We might think that for there to be repetition, we somehow need two objects that are identical.

Our common sense conception of repetition (which Deleuze will aim to overturn) seems to require both that we are presented with at least two objects (we need at least a second object to have a repetition of the first), and that they are absolutely identical with one another (otherwise we do not have repetition of an object, but two different objects).
(8)

[I am not entirely clear on the formulation. If the objects were not identical, then the second could not be the first under repetition. However, if it is “absolutely identical” then I would think it is one and the same. So how could it be two objects, as first postulated? The basic insight in Deleuze’s notion of as I had understood it is that you cannot have repetition if each case is identical, because then it is merely the same thing continuing rather than repeating. In other words, if the objects are identical, then you never had a second instance that could have repeated, as you only had one thing to begin with. We might later learn that my interpretation is wrong or maybe that it reflects the non-common-sense view of repetition that SH will later explain.] The reason that scientific experimentation is not true repetition is because scientists artificially recreate situations, arbitrarily including some factors and excluding others. What is also artificial is the idea that there are discrete factors that can be excluded from others. Then, we suppose that these factors are quantitative. [If we say we have two of something, that numeralization ignores all differences between them so that they can be understood as two of the same things. See this sort of thinking about quantity in § 395 of Hegel’s Science of Logic.]

in order to conduct an experiment, we presuppose that the pertinent features of a system can be understood in numerical terms. Once this has been done, ‘phenomena necessarily appear as equal to a certain quantitative relation between chosen factors’ (DR 3/3). Deleuze therefore argues that physics comes to natural phenomena with a mathematical understanding of them, which opens the possibility of different situations being equal.
(8)

Even properties are understood as quantifiable. [We have different orders of generality, perhaps for example, the order of qualities (color as frequency, warmth as vibrational energy, sound as wave frequencies) and the order of transfers (exchange of motional energy, heat, etc), and other such orders, all reduced and inter-relatable by means of quantification.] “We can say, therefore, that science presupposes a principle of repetition that allows it to relate different orders of generality to one another, but it doesn’t explain this principle.” (8)


Also, repetition in scientific experiment is hypothetical. “The experiment generates a law of the form, ‘given the same circumstances’, i.e. a hypothetical law.” (8) [The next point seems to be that even if the scientist equates one situation with the next, that does not mean they cannot be different in kind. I am not sure how to exemplify this. Perhaps we might draw from the idea Bergsonist/Deleuzean idea that the entirety of the world changes each moment, so even though in controlled circumstances an experiment shows the same quantitative functional relations, we are forgetting that it is a small part of larger and larger systems, the largest of which having changed in kind, thus the smallest of which doing the same as well, even though we blind ourselves to it by artificially sectioning off systems and imposing on them parameters we bring from prior experiments.]

In this case, repetition is given as an extrapolation from experiments which provide at best similar circumstances. As Deleuze writes, ‘repetition can always be “represented” as extreme resemblance or perfect equivalence, but the fact that one can pass by degrees from one thing to another does not prevent their being different in kind’ (DR 2/2).
(9)

 

 

 


 

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.


10 Feb 2015

Somers-Hall, (0.1), Deleuze’s Difference and Repetition, ‘Introduction [to DR’s Introduction]’, summary


by
Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own.]



Henry Somers-Hall


Deleuze’s Difference and Repetition.
An Edinburgh Philosophical Guide


Part 1
A Guide to the Text

 

 

0 Introduction: Repetition and Difference

0.1 Introduction


Summary



Brief summary:

In the Introduction to Deleuze’s Difference and Repetition, he argues repetition is commonly understood in terms of generality and law, when in fact it is not related to these concepts. We are mistaken when we think we encounter repetition in scientific experiment, moral law, and psychological habit. These are generalities and not repetitions.

 

 


Summary


The Introduction of Difference and Repetition is mostly about how repetition is not generality. One dimension of this has to do with law. Laws normally apply generally to many similar particular situations. For example, “the laws of gravitation apply to particular bodies in so far as they have mass” (7). When laws are applied generally, it would appear that we are dealing with repetitions of the same particulars.

Scientific laws are formulated by repeated experimentation, and Kant’s moral law appears, in the form of the categorical imperative, to provide a test of what actions can be repeated.
(7)

Deleuze then discusses three ways that we might relate to the world and think we are encountering repetition: scientific experiment, moral law, and the psychology of habit (7). Somers-Hall then explains Deleuze’s basic strategy in this section:

[a] show what is wrong with the notion of law in scientific experiment is that we never encounter real repetition,

[b] argue that cases of moral law and psychological habit are based on this scientific model and thus do not go beyond its limitations. (7)

 


Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.


Somers-Hall, (Intro.4), Deleuze’s Difference and Repetition, ‘How to Use this Guide’, summary


by
Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own.]



Henry Somers-Hall


Deleuze’s Difference and Repetition.
An Edinburgh Philosophical Guide


Introduction

 

Intro sect. 4
How to Use this Guide'



Brief summary:

Somers-Hall’s guide is best read alongside Deleuze’s Difference and Repetition, however it could also be read alone. Somers-Hall also provides many helpful supplements in the book as well.

 

 


Summary


Although this guide can be read alone, it would be most productive to read it alongside Difference and Repetition.


In cases where there are multiple English editions, Somers-Hall will cite both, and this includes Difference and Repetition. He also will translate to English when the original text is lacking an English translation. At the end of the book, there are “aids” for studying Deleuze, a further reading section, a glossary, and a section that offers advice for writing about Deleuze. (6)


Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.


8 Feb 2015

Priest, (8) ‘Dialectic and Dialetheic’, section 8, “Identity in Difference”, summary

 

by Corry Shores
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[The following is summary. All boldface, underlying and bracketed commentary are my own, unless otherwise indicated.]




Graham Priest


“Dialectic and Dialetheic”


8 Identity in Difference



Brief Summary:

Hegel’s dialectic takes the form of identity in difference, formulable as (a=b)&(a≠b). This is a variation on the dialetheic formulation A&~A.




Summary 


At the end of section 4, Priest noted that although dialetheic logic says that there are true cases of A&~A, this formulation might not apply to Hegel’s dialectics, which calls for a more unified, intimate, internal, intensional relation/contradiction between the terms. He returns now to this issue so to better describe “the exact nature of dialectical contradictions” (410). [First recall what Priest says regarding the dialetheias of nature and spirit in Hegel:

For spirit, s, is | then both spirit and not spirit. In the notation of section 3: (s=s)&(s≠s). Alternatively, nature, n, which is not spirit, is spirit: (n≠s)&(n=s). The existence (truth) of this contradiction allows spirit to think (understand) what it is: spirit and nature, spirit and not spirit; and thus to achieve its telos, in which form it is the Absolute.
(401-402)

] We previously have encountered many contradictions taking the form (a=b)&(a≠b), “something’s being identical with, and different from something (else?)” (410). This is Hegel’s notion of identity in difference. Priest “will now argue that this is the form of a dialectical contradiction, to which all others reduce” (410).


We have also encountered contradictions of the form: (a=a)&(a≠a). “They are obviously of this form” (411) [(a=b)&(a≠b), the form of ‘identity in difference’.] We also encountered the contradiction of something

being identical with its opposite: ^A=^~A. Thus for example, that something, a is free (Fa) is identical to its being bound (not free): ^Fa=^~Fa. This, too is a special form of identity in difference. For, as we noted in section 3, it is always true that ^A≠^~A. Thus, identity of opposites is just the identity in difference (^A=^~A)&(^A≠^~A).
(411)

[Perhaps Priest understands “identity in difference” to mean that both something equals its negation and it does not equal its negation.]


[In this next paragraph, Priest refers to the Tarski T-scheme. Recall that Tarski uses quotations around a sentence to mean the name for that sentence. For example:

“snow is white” is true if and only if snow is white.

In our article here, (see sect.3) Priest is doing something similar with the ^ symbol, meaning we would put ‘that’ in front of the sentence. The basic operations Priest seems he is doing is that if we have a sentence, let us say: snow is white; we can then make it: that snow is white is true iff snow is white. Since snow is white, then we can just say: that snow is white is true. However, we can substitute the  ‘quoted’ or ‘that-ed’ term with its negation, since we equated the two. Thus this means that the negation is true as well.]

In fact, the identity of opposites ^A=^~A is doubly contradictory, since it also gives rise to the contradiction A&~A. For either A or ~A; without loss of generality, suppose the former. Then ^A is true, by the T-scheme (^A is true iff A). But if ^A=^~A, ^A is true implies ^~A is true  (by the substitutivity of identicals). Hence ^~A is true too. It follows that ~A, again by the T-scheme. Thus, both A and ~A.
(411)


[In the above, we began by assuming either only A or not-A. No matter which we assume, the other holds by consequence (when one is also equated to the other). We did not assume a third possibility. It is not completely clear to me how this factors in. It might have something to do with truth gaps, in which a proposition is neither true nor false, and so if A were valueless, we would not say A or not-A. For, it need not be that one is true, since A is valueless. See discussion of valueless statements, and Priest’s defense of the law of excluded middle in these situations, in section 1.3 and section 4.7 of In Contradiction.] One objection to the above reasoning is that it uses the law of excluded middle, but Hegel spoke against it. Priest replies that it is still valid given our semantics (outlined in section 3 of this article), and also that Hegel’s objection to the law is not that it is untrue but rather that it is trivial; “it may be false (as well)!” (411).


Priest will now address two particular cases of identity in difference. The first is “something’s being identical with itself is its being different from itself. This is just the identity of opposites (^a=a)=(^a≠a)” (411). The second is the dialectics of motion that he discussed in section 4. This as well can be understood as the identity of opposites. [[The reasoning here seems to be as follows. Consider an instantaneous state of contradiction. For an object to be in one position is for it to be in another. If it were only in the same position, it would not be in motion. Thus we can equate its being in a position with its not being in that position. Because this affirms both terms, we can conjoin them even though one can be seen as the negation of the other. Priest furthermore says that any such equation of a term with its negation can be seen as one term ‘changing’ into its opposite, perhaps because the equation brings one term upon the other. This is important, because it could explain the collapsing of one term upon the other. In logic this seems to be a mode of substitution. ~A passes into A in the sense that it supplants A, or overlays it. It is also important to note that Priest here distinguishes the equality of opposites with the conjunction. The conjunction does not imply the passing of one into the other, even though the passing of one into the other implies the conjunction of the terms.]]

we may take the instantaneous contradiction produced in a state of motion to be that the body’s being in a certain place is its not being in that place, ^A=^~A. This will imply that it both is and is not in that place, A&~A, as I have just observed. Moreover, because this type of contradiction is identified as a state of change, it is natural to describe any state of the form ^A=^~A as a state where ^A is changing into its opposite ^~A, or vice versa. Thus, the identity of opposites is frequently described in this way, as, for example, the opposites going over into each other.
(411)


So recall again the objection that A&~A does not do justice to the intimacy of the terms in dialectical contradiction. Priest shows how dialectical contradictions take the form (a=b)&(a≠b) [which is a variation on A&~A]. The intimacy here is that the terms are identical.

We have now seen that all the dialectical contradictions we have met are instances of identity in difference: (a=b)&(a≠b). We may therefore take this to be the general form of a dialectical contradiction. This is an excellent way of doing justice to the point we noted in section 4, that the poles of a dialectical contradiction must have a tighter relation than mere extensional conjunction. For the poles of the identity in difference (a=b)&(a≠b), a and b, are actually identical with (though different from) each other; (dialectical) identity is therefore the relationship between the poles of a dialectical contradiction.
(412)



Citations from:

Priest, Graham. ‘Dialectic and Dialetheiç’. Science & Society, 1989/1990, 53 (4) 388–415.


 



 

 

 

 

 

 

Priest, (6) ‘Dialectic and Dialetheic’, section 6, “Contradiction in Hegel’s Dialectic”, summary

 

by Corry Shores
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[The following is summary. All boldface, underlying and bracketed commentary are my own, unless otherwise indicated.]




Graham Priest


“Dialectic and Dialetheic”


6 Contradiction in Hegel’s Dialectic



Brief Summary:

In Hegel’s dialectical movement, contradictory categories result from one another and are conjoined. It is in this ways that Hegel is a dialetheist [someone who thinks that there exist true contradictions].




Summary 


Previously Priest established, on the basis of his influences, that Hegel is a dialetheist [he believes that true contradictions exist]. Now Priest will examine the role of dialetheias in Hegel’s dialectics. Priest begins by distinguishing three aspects of Hegel’s dialectic.

(1) “the fundamental movement of Geist,” which Priest will call “the global dialectic”,

(2) the local developments by which the fundamental movement of Geist is achieved. Among these local developments is the development of the categories. Priest will call these developments “the logical developments”. And,

(3) the development of people and societies, which Priest will call “the historical dialectics”.
(401)


We begin then with the global dialectic, which Priest says is Hegel’s version of Fichte. (401) [Recall what Priest wrote about Fichte and the ego in the prior section:

there is nothing to think about except itself; and it is impossible to think something unless there is something else to contrast it with. (So at least thought Fichte.) Hence, the self had to create something different, the non-self, against which it could conceive itself. (This is precisely Reason leading a life of its own.) It therefore produces contradiction. Specifically, the non-self must also be self, since nothing else exists. […] as Fichte puts it […]: self = not-self and not-self = self.
(400)

]

The transcendental ego, or spirit (Geist) as it has become, has as its essence, or telos, to think. Since it is all there is, it must think about itself. And since it cannot do this without a contrast, it must create its opposite, nature.
(Priest, citing Taylor, 1975)


[With Fichte, we noted, this dialectic generates a self contradiction: self = not-self.] Just like with Fichte, this situation in Hegel creates a contradictory situation.

For spirit, s, is | then both spirit and not spirit. In the notation of section 3: (s=s)&(s≠s). Alternatively, nature, n, which is not spirit, is spirit: (n≠s)&(n=s). The existence (truth) of this contradiction allows spirit to think (understand) what it is: spirit and nature, spirit and not spirit; and thus to achieve its telos, in which form it is the Absolute.
(401-402)

Priest then notes that nature and spirit do not annihilate one another, but somehow there is resolution [it seems in the sense of solving a puzzle, where the puzzle remains even though it has been solved].

It should be noted that the Absolute is still a contradictory state. Nature and spirit do not annihilate each other; each still exists, requiring the other. In the final state of the dialectic, the contradiction is said to be resolved; or aufgehoben; but as Hegel is often at pains to point out, the state which is aufgehoben continues to exist. Resolution, in this context, is more like the resolution of a puzzle: we know the answer. The puzzle does not cease to be a puzzle; it just ceases to puzzle us. (A riddle is still a riddle even if we all know the answer.)
(402)

[[Note, in another context, regarding “the positive” and “the negative”, Hegel says that their contradiction created by their unity destroys both sides, creating “the Null”. I am not sure at all how this relates to Nature and Spirit, but I think it would be important for the terms to subsist rather than annul one another, for otherwise the conjunction of incompatible terms will not hold.

Thomas Bole, discussing this in his “Contradiction in Hegel's Science of Logic,” writes of the positive and the negative that:

Each pole of contradiction annuls itself and posits its contrary. Both poles are destroyed (WL II, 51:33-35 [SL 433]). Indeed, this mutual self-annihilation by its poles is the “formal determination” (WL II, 51:37 [SL 433]) of contradiction. Thus, “the initial unity which results from contradiction is the Null” (WL II, 51:12-13 [SL 433]); in whatever respect anything can be said to be self-contradictory, it is indeterminate.
(Bole, 525)

In the Giovanni translation, the quoted sentence reads:

In the self-excluding reflection we have just considered, the positive and the negative, each in its self-subsistence, sublates itself; each is simply the passing over, or rather the self-translating of itself into its opposite. This internal ceaseless vanishing of the opposites is the first unity that arises by virtue of contradiction; it is the null.
(Hegel, 376)

In the German:

In der sich selbst ausschließenden Reflexion, die betrachtet wurde, hebt das Positive und das Negative jedes in seiner Selbständigkeit sich selbst auf; jedes ist schlechthin das Ubergehen oder vielmehr das sich Ubersetzen seiner in sein Gegenteil. Dies rastlose Verschwinden der Entgegengesetzten in ihnen selbst ist die nächste Einheit, welche durch den Widerspruch zustande kommt; sie ist die Null.
(67)

]]

There is a long process which leads to the Absolute where thought thinks itself.

The achievement of the Absolute in the global dialectic is not, however, arrived at in a trice. Rather, the production of a category that allows spirit to think itself is achieved only after a period of conceptual evolution, the logical dialectic. The most primitive category, being, produces a contradiction. This contradiction produces a novel category, which is itself contradictory. This, in turn, produces a novel category. And so it goes, until we arrive at the Absolute Idea (Taylor, 1975, 339) – a category which applies to the biggest contradiction of them all, the Absolute. This allows thought to think itself.
(Priest 402)


For Hegel, all categories are contradictory (402).


Priest will take the example of being and becoming to illustrate. [[Priest here seems to be saying this. If something has no properties, it does not have being. Pure indeterminate being has no properties, thus it both has being as being and it does not have being as something without properties. This also means that one of being’s properties is its non-being, and thus the being of being is its non-being. Now we think of a being with no properties. The same would follow that its being is its non-being. I still cannot figure out what things in motion have to do with being propertiless. But let us consider striking a match and wood turning to fire. Insofar as it is wood, it has being, and insofar as it is not-wood, it does not have being. One of its properties is changing from one to the other. So its being is its being both itself and not itself. I am not entirely sure, but it seems he is referring to the opening paragraphs of The Science of Logic. Here I understand Hegel making a slightly different point. We begin with pure being, which has no determination (it is indeterminate). But since it has nothing to determine it, to distinguish it from anything else, it is (conceptually) empty. “There is nothing to be intuited in it”. Thus “Being, the indeterminate immediate is in fact nothing, and neither more nor less than nothing”. So out of the category of pure being arises the category of pure nothingness. It as well is indeterminate. But this means there is nothing to distinguish it from being. We can intuit nothing as being different from being, but we cannot distinguish them in our intuitions. This means “Pure being and pure nothing are therefore the same”. We saw how the category of being “passes over” to nothing, which then “passes over” to being. They are indistinguishable yet not the same, and “each immediately vanishes in its opposite”. This movement of vanishing into its opposite then is what characterizes both of them. And since movement into something’s opposite is its becoming something else, the two categories together give rise to the category of becoming. I will quote from the first three paragraphs of Hegel’s Science of Logic.

Chapter 1
Being
A. Being
Being, pure being – without further determination. In its indeterminate immediacy it is equal only to itself and also not unequal with respect to another; it has no difference within it, nor any outwardly. If any determination or content were posited in it as distinct, or if it were posited by this determination or content as distinct from an other, it would thereby fail to hold fast to its purity. It is pure indeterminateness and emptiness. – There is nothing to be intuited in it, if one can speak here of intuiting; or, it is only this pure empty intuiting itself. Just as little is anything to be thought in it, or, it is equally only this empty thinking. Being, the indeterminate immediate is in fact nothing, and neither more nor less than nothing.

B. Nothing
Nothing, pure nothingness; it is simple equality with itself, complete emptiness, complete absence of determination and content; lack of all distinction within. – In so far as mention can be made here of intuiting and thinking, it makes a difference whether something or nothing is being intuited or thought. To intuit or to think nothing has therefore a meaning; the two are distinguished and so nothing is (concretely exists) in our intuiting or thinking; or rather it is the empty intuiting and thinking itself, like pure being. – Nothing is therefore the same determination or rather absence of determination, and thus altogether the same as what pure being is.

C. Becoming
1. Unity of being and nothing
Pure being and pure nothing are therefore the same. The truth is neither being nor nothing, but rather that being has passed over into nothing and | nothing into being – “has passed over,” not passes over. But the truth is just as much that they are not without distinction; it is rather that they are not the same, that they are absolutely distinct yet equally unseparated and inseparable, and that each immediately vanishes in its opposite. Their truth is therefore this movement of the immediate vanishing of the one into the other: becoming, a movement in which the two are distinguished, but by a distinction which has just as immediately dissolved itself.
(Hegel, 59-60)

]]

it may help to illustrate the process with one example, that of being and becoming (Hegel, 1969, Vol. I, book 1, section 1, ch. 1). Consider being. If something, a, were merely to be, that is, to have no | properties other than being, then there would be nothing to distinguish it from an object that has no properties at all, i.e. , that is not. It would therefore both be and not be, Ba&~Ba (where B is the one place predicate of being). Thus, we are led to a category of things, a, whose being is their non-being ^Ba=^~Ba. These are the things that are coming into being or out of it. (Recall the discussion of change in section 4.) This is therefore the category of becoming.
(Priest, 402-403)


The logical dialectic [by which the categories generate one another dialectically] is not a process in time. But spirit is embodied in nature, and the dialectic unfolds through history. These parts in time are involved in a series of destructions, even though the whole stands. [Here Priest cites Charles Taylor’s book on Hegel. Let me quote some of it first:

Hegel thinks of contradiction as the source of movement because whatever is in contradiction must pass over into something else, be this passage the ontological one between levels of being which go on existing coevally, or the historical one between different stages of human civilization. But it would seem impossible to have it both ways. If contradiction is the source of passage from one level to another, it is because it is fatal to continued existence, or so one would think from the commonsense principle that nothing contradictory can exist. Hegel seems to be using this commonsense principle when he explains dialectical passages in this way. And yet on the other hand things do go on existing (in the chain of being, if not in history) even after being convicted of contradiction, and indeed contradiction is said to be everywhere. How can we reconcile these affirmations?

The answer is that contradiction, as Hegel uses the term, is not wholly incompatible with existence, and as such perhaps does not really deserve the name. When we say that the whole is in contradiction, we mean that it unites identity and opposition, that it is opposed to itself. Perhaps one might want to amend this way of putting it to get over the apparent paradox. We might want to say, for instance, that ‘identity’ and ‘opposition’ are not to be considered incompatible. But to put it this way would miss part of the point, for in a way, | Hegel wants to retain some of the force of the clash between ‘identity’ and ‘opposition’. For Geist is in struggle with himself, with his necessary embodiment, and only comes to realization out of this struggle. So that we would have to say that ‘opposition’ is both compatible and incompatible with ‘identity’.
(Taylor, 105-106)

We can now see more clearly the underlying principle of those ascending dialectics in which Hegel will show that finite things cannot exist on their own, but only as part of a larger whole. The motor of these dialectics is contradiction; and the contradiction consists in this, that finite beings just in virtue of existing externally in space and time make a claim to independence, while the very basis of their existence is that they express a spirit which cannot brook this independence. The ascending dialectic reveals the contradiction in things and shows from the nature of the contradiction how it can only be understood and reconciled if things are seen as part of the self-movement of the Absolute. Thus contradiction, in the strong sense which involves combining ontological conflict with its denial, is mortal. But since this ‘denial’ is not just an intellectual error by us who observe, but is essential to the whole which is in ontological conflict itself, we can see that contradiction in the strong sense is what makes things move and change. It is their inherent changeability (Veränderlichkeit); while contradiction in the sense of ontological conflict is the source of this changeability.

Contradiction is thus fatal to partial realities, but not to the whole. But this is not because the whole escapes contradiction. Rather the whole as Hegel understands it lives on contradiction. It is really because it incorporates it, and reconciles it with identity that it survives. This the partial reality –material object or finite spirit – cannot encompass. It is stuck with its own independent existence, and since this independence clashes with the basis of its existence, it is caught in contradiction and must die. It must die because it is identified with only one term, the affirmation, and cannot encompass the denial.

Not so the whole. The absolute goes on living through both the affirmation and the denial of finite things. It lives by this process of affirmation and denial; it lives via the contradiction in finite things. Thus the absolute is essentially life and movement and change. But at the same time, it remains itself, the same subject, the same essential thought being expressed, throughout this movement. It reconciles identity and contradiction by maintaining itself in a life process which is fed on ontological conflict. This combination of incessant change and immobility is described by Hegel in a striking image from the preface of PhG: ‘The true is thus the bacchanalian whirl in which no | member is not drunken; and because each, as soon as it detaches itself, dissolves immediately - the whirl is just as much transparent and simple repose’ (PhG 39).
(Taylor, 107-108)

]]


The logical dialectic, though a development, is not a process in time. It is, however, connected with one that is. For spirit is embodied in nature, and, particularly, humankind and its social institutions; and these change in the historical dialectic. Each social institution, being a fragment of Geist, reflects its properties to a certain extent. (Rather as the whole of an image is visible in any fragment of a hologram.) In particular, it is contradictory. Thus, it also has its own telos which it must try to achieve by producing a contradictory state. However, unlike the similar maneuver with the whole, this maneuver results in the destruction and replacement of the situation. Contradictions are therefore fatal to parts of the whole (finite beings); not so the whole itself (Taylor, 1975, 105ff). It follows that the state which succeeds the old does not transcend (aufhebt) it in quite the same way that the Absolute transcends the spirit/nature contradiction. In particular, the old contradiction is no longer true (though new ones will be).
(Priest 403)


Hegel has the famous example for this, the master-slave relationship. People need recognition from others in order to develop themselves. At first they obtain it by force and enslave the other to obtain their recognition. But since this dehumanizes the other, the master cannot be recognized by someone who really matters to him. The slave, meanwhile, labors and [somehow] gains control of the world, granting him/her freedom. Also, the slave knows they can be killed any moment, granting them greater self-awareness, also allowing them to become aware of their freedom. By those means, the slave is on the road to overthrowing the master. (403)


As we can see, the slave in the enslaved situation is in a contradictory state, as “he is both free and bound (not free)” (404). Priest further illustrates with a passage by Sartre where he explains that the Nazi oppression only heightened their awareness of the freedom they should and really deep down do have. (404)

There is an objection that these dialectical sorts of contradiction are not really contradictory, since it is free in one sense and bound in another. Priest admits that some contradictions that dialetheists cite are merely apparent contradictions and are “dispelled once the respects in which the contradictory predicates apply are spelled out” (404).


Priest also replies that it is not always so clear that two senses of the same term are meant.

The quotation from Sartre illustrates this. What are the senses in which the occupied, people were free and not? They were not free in that they could not, because of the occupation, do exactly as they chose. But, as Sartre stressed, this made them realize that they could do exactly as they chose. But this is no consistent disambiguation: it is just as contradictory.
(404)

The trouble here is that the notion of having a choice does not have the crystal precision of, e.g., mathematical predicates.
(405)



Citations from:

Priest, Graham. ‘Dialectic and Dialetheiç’. Science & Society, 1989/1990, 53 (4) 388–415.


Or if otherwise noted:

Bole, Thomas J. “Contradiction in Hegel's Science of Logic.” The Review of metaphysics 40, no. 3 (1987): 515-534


Hegel, Georg Wilhelm Friedrich. The Science of Logic, edited and translated by George di Giovanni. Cambridge: Cambridge University, 2010.


Hegel, Georg Wilhelm Friedrich. Wissenschaft der Logik II. Frankfurt: Suhrkamp, 1969.
 

Taylor, Charles. Hegel. Cambridge: Cambridge University, 1975.

 

 

 

 

 

Priest, (5) ‘Dialectic and Dialetheic’, section 5, “The History of Hegel’s Dialectic”, summary

 

by Corry Shores
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[The following is summary. All boldface, underlying and bracketed commentary are my own, unless otherwise indicated.]




Graham Priest


“Dialectic and Dialetheic”


5 The History of Hegel’s Dialectic



Brief Summary:

If we look at three of Hegel’s influences – Neo-Platonists, Kant, and Fichte – we see that Hegel borrowed self-contradictory ideas from each of them. Thus Hegel is a dialetheist, that is, he believes that true contradictions exist.




Summary 


Priest will now offer a dialetheic interpretation of Hegel and Marx’s ideas on dialectic.

I will argue historically: given the philosophical influences acting on Hegel and Marx, and what Hegel, in particular, says about them, there is no other very sensible interpretation.
(398)


One of Hegel’s major influences were “medieval (and especially Christian) Neo-Platonists and their Renaissance successors” (398). The Neo-Platonists held contradictory true things about the One, for example, that it is everything and nothing, everywhere and nowhere. Hegel’s concept of the absolute was influenced by this Neo-Platonic concept of the One.


Another of Hegel’s influences is Kant. In his Critique of Pure Reason, Kant has a section called the ‘Antinomy of Pure Reason’. Here there are four pair of arguments, each one contrary to its partner, but neither of each pair is fallacious on its own. (399) But Kant is not using dialectical logic, because he diagnoses a flaw in the antinomies. The flaw is that they apply a category outside its legitimate bounds. Priest takes as an example, “everything has a cause”. [Priest seems to be saying here that Kant’s reasoning is that “everything has a cause” belongs to objects of intuition, but “the World” is only apprehended by reason. Therefore, we cannot apply “everything has a cause” to “the World.”] (399)


Kant uses the antinomies to show that reason and its categories depend on experience to provide it content (399). Priest says “It is difficult to find direct arguments for this assumption, other than some very strong form of positivism (such as Hume’s)” (399). [I am not sure what Priest means here, perhaps that the best argument Kant has, or that we can provide him, is that in all cases we seem always to get our conceptual content from experience.] But if we reject this hypothesis, then reason, in its independence from experience, generates contradictions. This is the route that Kant’s successors took. [I am not sure if Priest here is referring to German Idealists or perhaps some other group like neo-Kantians]. Priest then provides a long quote by Hegel where he makes this point. [I will just place a couple sentences in the following.]

The blemish of contradiction, it seems, could not be allowed to mar the essence of the world; but there could be no objection to attaching it to the thinking Reason, to the essence of mind. [...] It is no escape to turn round and explain that Reason falls into contradictions only by applying the categories. For this application of the categories is maintained to be necessary . . . . (Hegel, Lesser Logic, section 48, 76–77, qtd in Priest 400)


Priest lastly considers Fichte’s influence on Hegel. Fichte criticized Kant’s thing-in-itself and instead was concerned with the ego, whose nature is to think. Yet,

there is nothing to think about except itself; and it is impossible to think something unless there is something else to contrast it with. (So at least thought Fichte.) Hence, the self had to create something different, the non-self, against which it could conceive itself. (This is precisely Reason leading a life of its own.) It therefore produces contradiction. Specifically, the non-self must also be self, since nothing else exists. […] as Fichte puts it […]: self = not-self and not-self = self.
(400)


In Fichte’s account, by the self (thesis) conceiving the not-self (antithesis), they coexist happily and give birth to a new antithesis (synthesis). (400)


Hegel had a two-fold criticism of Fichte:

first, that Fichte had not elevated the transcendental ego into something grander, Geist; and second, that he had misunderstood the nature and significance of the final synthesis (1895, 499).
(401, citing Hegel, Lectures on the History of Philosophy, Vol. III)


Nonetheless, Hegel takes up this dialectic of the self, including “the contradictory nature of the alienated state of the self” (401). Priest concludes: “Hegel’s dialetheism is therefore established” (401).


 

 

 



Citations from:

Priest, Graham. ‘Dialectic and Dialetheiç’. Science & Society, 1989/1990, 53 (4) 388–415.


 



 

 

 

 

 

 

Priest, (4) ‘Dialectic and Dialetheic’, section 4, “Motion: An Illustration”, summary

 

by Corry Shores
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[The following is summary. All boldface, underlying and bracketed commentary are my own, unless otherwise indicated.]




Graham Priest


“Dialectic and Dialetheic”


4 Motion: An Illustration



Brief Summary:

One way we can illustrate how dialetheic logic can apply to dialectics is by accounting for motion in a Hegelian way. An object in motion is at a certain point at a certain instant, but since it is in motion, in that instant it is already leaving that point. Thus it is both true and false that the object is at that point in that instant.




Summary 


Priest has been discussing the dialetheism of Hegel’s and Marx’s dialectics. He will now illustrate with the example of motion. If we think of an object in motion as both being in its spot and already leaving it, then the statement that it is in that spot is both true and false.

 

Suppose a body, b, occupies a certain spot, s, at a certain time. What is the instantaneous difference between its being in motion and its being at rest? A Russell would say “none”: being in motion is not an intrinsic, but a relational state. Hegel would say “consistency.” Let A be the sentence “b is at spot s.” Then if b is at rest, A is true, and true only (T). If b is in motion, then A is true, since b does indeed occupy the spot s; but, equally, since it is in motion, it has already started to leave that spot; hence b is not still there: ~A is true. Thus A is both true and false (T and F).
(396)

But there is a problem with this formulation. [I am not exactly sure of the situation Priest describes in the following. It seems that because we have A and ~A separated by conjunction, we are misrepresenting the fact that the opposing terms in dialectics are somehow more intimately related. This has something to do with extension and intensional contradictions. I am not sure what these are. A classical example in intensional logic is ‘the son of Jocasta is the husband of Jocasta’. The extensional meaning is the set too which the terms refer, in this case, they both refer to a set with one member, Oedipus. For the motion example to be an extension rather than an intensional contradiction, perhaps the matter is that we are speaking of two spots, the object being in those two spots, which taken apart from one another is not a contradiction but together they are. But for some reason, dialecticians would say that there is instead internal intensional contradiction. I am not sure how, but perhaps they are saying that somehow ‘the object is at point b’ is in itself already self-contradictory. Priest replies to this objection first here it seems by saying that this is such a conjunction where both parts of the conjunct need to be together for correct information to be conveyed. So in that way they already exhibit an intimate link. However, since dialecticians do not think that the conjunction can be accidental but rather somehow depend on each other, and in that way are very intimately linked, we will need to have more than just an extensional (external) conjunction. Priest will return to this in section 8, so I will quote it for now.]

Some dialecticians would argue that Hegelian contradictions cannot be of the kind illustrated here. For this contradiction is a merely extensional contradiction: a logical contradiction of the form A&~A, where there is no essential connection between the conjuncts. One can, for example, infer each of A and ~A from this contradiction and assert each independently. By contrast; dialectical contradictions are intensional. There is an internal relation between the conjuncts which is not captured by a mere extensional conjunction. Thus, dialectics | [the following is block quotation]

lays stress on the fact that this two-fold interrelation of opposites is to be conceived, not "eclectically," as ·mere. conjunction or succession, but dialectically, in· the sense that these opposites are so far intertwined that the one cannot exist without the othr. Not only do they not exclude each other, they presuppose and reciprocally condition each other. (Wetter, 1958, 340.) [from bibliography: Wetter, G. A. 1958. Dialectical Materialism. London: Routledge and Kegan Paul.]

In particular, it is not permissible to detach either conjunct from the other and assert it, without falsifying the description. (This criticism is made in Havas, 1981.) To a certain extent this objection is simply answered. Less than the whole (relevant) truth can itself be quite misleading and give a false picture of the situation. Thus, suppose your car runs out of petrol and you ask me where the nearest garage is. If I detach and assert only the first conjunct of “There is a garage around the corner but it is closed” my answer will be highly misleading. There is a conversational implicature, to use the notion of Grice (1975), that relevant information has not been omitted. But in dialectical contexts, the distinction between something’s being true (only) and its being true and false is quite crucial. Thus to assert only A when A&~A is true is equally misleading. As Hegel himself puts it (1969, Vol. I, book 1, section 1, ch. 10, 91) [from bibliography: Hegel, G. W. F. 1969 (1812). The Science of Logic. London: Allen and Unwin.]: [the following is block quoted]

The commonest injustice done to a speculative [i.e., dialectical] content is to make it one-sided, that is, to give prominence only to one of the propositions into which it can be resolved. It cannot then be denied that this proposition is asserted; but the statement is just as false as it is true, for once one of the propositions is taken out of the speculative content, the other must be equally considered and stated.

Nonetheless, as Hegel and most other dialecticians have stressed, dialectical contradictions are no mere “accidental” conjunctions. In some sense the contradictory conjuncts depend on each other, so that the one could not exist without the other. Thus, there should indeed be a more intimate relation between dialectical contradictories than mere extensional (external) conjunction. What this is, we will be in a position to see by section 8.
(396-397)

 

 

 

 



Citations from:

Priest, Graham. ‘Dialectic and Dialetheiç’. Science & Society, 1989/1990, 53 (4) 388–415.


 



 

 

 

 

 

 

7 Feb 2015

Priest, (3) ‘Dialectic and Dialetheic’, section 3, “Dialetheic Logic”, summary

 

by Corry Shores
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[The following is summary. All boldface, underlying and bracketed commentary are my own, unless otherwise indicated.]




Graham Priest


“Dialectic and Dialetheic”


3 Dialetheic Logic



Brief Summary:

Dialetheic logic is just like orthodox logic except that it allows for true contradictions, and when there are true contradictions, we cannot infer from them any other proposition we want.




Summary 


Previously Priest explained that those who argue Hegel’s and Marx’s dialectics do not involve self-contradiction (or that they do and for this reason are flawed) are adhering to the modern Frege/Russell logic, which forbids contradiction. However, this is merely an assumption made in this kind of logic, and other assumptions have been called into question. Now Priest will give an informal overview of what dialetheic logic is. In Frege/Russell logic, a sentence can be assigned only one of two truth values, T (true) and F (false). However, in dialetheic logic, a sentence can also take both values. “(Thus, technically, semantic values are non-empty subsets of {T,F}.)” (393). So if a sentence is true, that does not rule out that it is also false, and vice versa. Priest then explains the “truth table” conditions for computing truth values of more complex sentences. The conditions for negation, conjunction, and disjunction are all orthodox. So ~A is true iff A is false, and ~A is false iff A is true. Everything is as you know it for conjunction (true only if both conjuncts are true), and disjunction. [In the next part, Priest seems to be explaining why when something is both true and false, the conjunction of it with its negation is also true and false, and thus at least true.] “Notice that if A is true and false, so is ~A; and so, moreover, is A&~A. In particular, it is true, as dialetheists claim” (393). [The next definitions seem to establish validity and implication:]

 

Logical truth and logical consequence are also defined in the orthodox fashion:

A is a logical truth just if A is (at least) true under all assignments of values

A is a logical consequence of B just if every assignment of values that makes B (at least) true makes A (at least) true
(393-394)

[Priest’s next point seems to be that dialetheic logic and classical logic give the same set of logical truths. I am not exactly sure how this is so. I can understand that all logical truths in classical logic are also true in dialetheic logic. But there are true formulations, like A&~A which are true in dialetheic and not true in classical. So you will have to read the following to interpret it for yourself.]

It may be interesting to note that A is a logical truth if A is a two-valued tautology. Thus, these semantics give the same set of logical truths as does orthodox logic. Thus, both Av~A and ~(A&~A) are logical truths. The second of these may seem surprising initially. But if a certain contradiction, A&~A, may be true, there is no reason why the “secondary contradiction” (A&~A)&~(A&~A) should not also be true.
(394)

[Priest’s next point seems to be that the principle of explosion does not apply in dialetheic logic. So an inference is valid if there is no situation where all the premisses are true and the conclusion false. If we have A&~A, in classical logic we can derive B, because there is no way to make the premise true. But since it can be true in dialetheic logic, we can say A&~A is true and B is false, and thus we cannot validly infer B from the conjunction. Let me quote from Priest’s Logic: A Short Introduction.

an inference is valid provided that there is no situation which makes all the premisses true, and the conclusion untrue (false). That is, it is valid if there is no way of assigning Ts and Fs to the relevant sentences, which results in all the premisses having the value T and the conclusion having the value F.
(Priest, Logic: A Short Introduction, p.13)

 

image

It certainly doesn't seem valid. The wealth of the Queen – great or not – would seem to have no bearing on the aviatory abilities of pigs.
(Priest, Logic: A Short Introduction, p.8)

What about the inference with which we started: q, ¬q/p? Proceeding as before, we get:

image

Again, the inference is valid; and now we see why. There is no row in which both of the premisses are true and the conclusion is false. Indeed , there is no row in which both of the premisses are true. The conclusion doesn’t really matter at all! Sometimes, logicians describe this situation by saying that the inference is vacuously valid, just because the premisses could never be true together.
(Priest, Logic: A Short Introduction, p.14)

{Later, Priest discusses the ‘new assumptions’ that a formulation can be both true and false.}


it is worth returning to the inference with which we started in Chapter 2: q, ¬q/p. As we saw in that chapter, given the assumptions made there, this inference is valid. But given the new assumptions, things are different. To see why, just take a situation where q has the values T and F, but p has just the value F. Since q is both T and F, ¬q is also both | T and F. Hence, both premisses are T (and F as well, but that is not relevant), and the conclusion, p, is not T. This gives us another diagnosis of why we find the inference intuitively invalid. It is invalid.
(Priest, Logic: A Short Introduction, p.35)

I continue by quoting from the Dialectic paper. The ‘as might be expected’ in the following perhaps refers to our intuition that any sentence whatsoever does not validly result from a contradiction.]

The semantics do, however, give a notion of logical consequence different from the orthodox one. In particular, and as might be expected, B is not a consequence of A&~A, as may be seen by simply assigning B the value F, while assigning A both T and F.
(394)


Priest shows how we can “extend these propositional semantics to a semantics for full first-order logic” in another text [Chapter 5 of In Contradiction]. Priest also says that we can say that identity statements taking the form a = b can be both true and false, if enough care is taken “concerning how, exactly, truth values are assigned” [he does not go into those details here] (394). However, if that care is taken, then “all the principles of identity, such as the law of identity (a = a) and the substitutivity of identicals, are assured. As usual, I will write a ≠ b for ~a = b.” (394)


Priest will need another operator which will turn sentences into objects. In English we can use ‘that’ to turn ‘John is happy’ into ‘That John is happy…’ or we can use a gerund, ‘John’s being happy.’ Priest will use the ^ symbol to mean “that”, such that

if A is any sentence, ^A is a noun phrase, and therefore denotes an object. […] it is fairly clear that in some sense ^A and ^~A are opposites. (Think of John’s being happy and his not being happy […].) Since an object is not the same as its opposite, it is natural to require that ^A ≠ ^~A.
(395)


As we can see, all this is orthodox logic, except for the condition that some formulations can be assigned both T and F. Hence “orthodox logic is just a special case of these semantics which ignores a dialectically important case” and “Thus we may stretch Hegel's claim a little as follows:(Frege/Russell) formal logic is perfectly valid in its domain, but dialectical (dialetheic) logic is more general” (395).


Classical logic’s domain is ‘the consistent’, which is what? “dialecticians have had a standard line here: the static is consistent; only when change enters the picture do contradictions arise” (395). Thus we can argue if want that dialects is based on dialetheism. (395)


But “Dialetheic logic is certainly not dialectics”, yet we can at least say that dialetheic logic is a rigorous non-trivial formal logic, and dialectics is compatible with it. [Priest writes: “Dialetheic logic is certainly not dialectics; but it is quite sufficient to show that dialetheism is compatible with the rigor of a non-trivial formal logic” (396).] Priest will move onto dialectics, now that we have established that it can be logically valid to have contradictions in one’s systems.

 

 

 



Citations from:

Priest, Graham. ‘Dialectic and Dialetheiç’. Science & Society, 1989/1990, 53 (4) 388–415.

Or if otherwise noted, from:

Priest, Graham. Logic: A Very Short Introduction. Oxford / New York: Oxford, 2000.