18 Apr 2018

Priest (1.6) One, “The Aporia”, summary

 

by Corry Shores

 

[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

[Logic and Semantics, entry directory]

[Graham Priest, entry directory]

[Priest, One, entry directory]

 

[The following is summary. You will find typos and other distracting mistakes, because I have not finished proofreading. Bracketed commentary is my own. Please consult the original text, as my summaries could be wrong.]

 

 

 

Summary of

 

Graham Priest

 

One:

Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness

 

Ch.1

Gluons and Their Wicked Ways

 

1.6

The Aporia

 

 

 

Brief summary:

(1.6.1) None of our available options of explaining unity in terms of the factor that binds parts together into the whole (which is called the “gluon”) are viable. (1.6.2) We might say there are no gluons, thereby claiming that there are parts in the world but no wholes. This cannot be so, because in thought there are unified mental entities. (1.6.3) We also cannot argue that there are no gluons on account of the world being one whole without containing any parts. For, even in this case we do in practical life think of wholes with parts, meaning that the mental entities involved in those conceptions are wholes with parts and thus have gluons. (1.6.4) Gluons can be referred to, so we cannot claim they are not objects. (1.6.5) We cannot say that the gluon is an object, because that takes unity for granted rather than explain it. (1.6.6) Our best option for understanding gluons is with the dialetheic claim that they both are and are not objects.

 

 

 

 

 


 

Contents:

 

1.6.1

[The Lack of Available, Viable Options to Explain Gluonic Unification]

 

1.6.2

[The Inadequacy of Rejecting the Existence of Gluons and Positing a Wholeless World]

 

1.6.3

[The Inadequacy of Rejecting the Existence of Gluons and Positing a Partless World]

 

1.6.4

[Gluons as Necessarily Objects on Account of Being Referable]

 

1.6.5

[Gluon as not Being an Object]

 

1.6.6

[Gluons as Dialetheias]

 

Bibliography

 

 

 

 

 

Summary


 

1.6.1

[The Lack of Available, Viable Options to Explain Gluonic Unification]

 

[None of our available options of explaining unity in terms of the factor that binds parts together into the whole (which is called the “gluon”) are viable.]

 

[In section 1.5, we discussed the problem of explaining unity. We noted all of our available options, and we saw how none are satisfactory. The unifying factor we want to give an account of is called the gluon (see section 1.3.4). Priest then notes a point he makes in section 1.3.4 and section 1.3.5, namely, that gluons are contradictory objects, because in order to be what they are, they must both be entities while also not being entities. They are entities in that we are talking about them (and anything you can talk about is an entity, for what else would it be?), and yet they are not entities on account of the Bradly regress (see section 1.4, especially 1.4.2), and so by thinking of a gluon simply as an entity makes it a part of the problem of explaining unity rather than a part of the solution. We are thus at an impasse or aporia. Priest says we have three options:

{1} We can say that there are no gluons.

(I suppose for this option, we are claiming that there is no binding, unifying factor in things. But then we are giving up the question altogether it seems. And that is not what we want, because the question is of great philosophical importance.)

{2} We can reject the claim that a gluon is an object.

(Here we would solve the problem of the Bradley Regress, but then we would seem to be unable to talk about it, which is very unhelpful for trying to account for it.)

{3} We can reject the claim that it is not an object.

(This will allow us to talk about it, but then we encounter the Bradley Regress, which prevents us from accounting for unity or the gluon.) (Note, Priest gives his own reasoning in the following sections.) Given that all these options are highly problematic, we seem not to have any good way to proceed.]

We have, then, an aporia.Whatever it is that constitutes the unity of an entity must itself both be and not be an entity. It is an entity since we are talking about it; it is not an entity since it is then part of the problem of a unity, not its solution. ‘Aporia’ is often glossed as ‘puzzle’ or ‘uncertainly’, but it literally means something like ‘impasse’. An aporia is a source of puzzlement and uncertainty precisely because it seems to leave no way to go forward. In the present case, if we wish to go back, there are only three options:

1. We can say that there are no gluons.

2. We can reject the claim that a gluon is an object.

3. We can reject the claim that it is not an object.

Prospects look bleak.

(14)

[contents]

 

 


 

1.6.2

[The Inadequacy of Rejecting the Existence of Gluons and Positing a Wholeless World]

 

[We might say there are no gluons, thereby claiming that there are parts in the world but no wholes. This cannot be so, because in thought there are unified mental entities.]

 

[Recall the first option from section 1.6.1 above.

{1} We can say that there are no gluons.

Because gluons are the binding factor that unifies parts into wholes, if we deny they exist, we also deny that there can be a difference between a unity that has parts and a simple plurality of those parts. (For, without this factor, there would be nothing to make a plurality of parts unified into a whole, and thus it would be no different from an unified plurality of parts.) One way to work around this could be to say that there are just parts but no wholes, and thus “the world is just a congeries of congeries” (14). But this cannot be so. For, we have unities in thought, which although being mental entities, still qualify as unities and thus their gluonic unification still needs to be accounted for.]

Consider the first case. If there are no gluons, then we are bereft of an explanation as to the difference between a unity with parts and the plurality of the parts, which there certainly is. We could avoid this by supposing that there are no unities: the world is just a congeries of congeries. All parts, no unities. But this does not seem to help either. If there are no unities, there certainly appear to be; that is, there are unities in thought. This means that the mind constitutes unities— as, perhaps, for Kant. But in this case, there are gluons.These are mental entities, but they fall foul of the aporia in the usual way.22

(14)

22. The view that there are no material wholes, only simples, is defended in Unger (1979). There are no tables: only atoms ‘arranged table-wise’ (as van Inwagen puts it (1990), p. 72ff). Sider (1993) points out that this commits the view to the (counterintuitive) necessity of the existence of physical simples (partless wholes). (Gluon theory is not so committed.) And Uzquiano (2004) argues that | attempts to paraphrase away talk of unities in the way suggested is problematic. In any case, the view hardly seems credible for abstract objects. A proposition is a single thing: one can believe it, express it. You can not do this to a plurality of meanings arranged proposition-wise, whatever that might be supposed to mean. (14-15)

[contents]

 

 


 

1.6.3

[The Inadequacy of Rejecting the Existence of Gluons and Positing a Partless World]

 

[We also cannot argue that there are no gluons on account of the world being one whole without containing any parts. For, even in this case we do in practical life think of wholes with parts, meaning that the mental entities involved in those conceptions are wholes with parts and thus have gluons.]

 

[Recall yet again the first option from section 1.6.1 above.

{1} We can say that there are no gluons.

Priest now notes another way this could be so. Suppose the world is one whole unity without any parts. It in this sense would also not have any gluons; for there would be no parts to be bound together into wholes. But this goes against common sense and practical life, where for example our car certainly has parts that would render the car inoperable if they were missing. But someone might say that the car is not really such a unity of parts (I am not sure what else it would be, I suppose we only have the one world, and the car is not some unity within it, but I am not sure), and we only mistakenly think that the car is a whole. But even in that case, we are admitting that we conceive of it as a whole containing parts, which means the mental entity of that conception would still involve gluons.]

At the other extreme, one might suppose that there are unities, but that they have no parts, and hence that there are no gluons. All unities, no parts. A very extreme form of this position is to the effect, not only that there are only unities, but there is only one of them. All else is appearance. The view is to be found in Parmenides and Bradley. Supposing that there are only unities with no parts is a desperate move. It flies in the face of common sense: if someone steals a wheel of my car then it is missing an essential part. And before one says that the car is not really a whole, but we only think of it in that way, recall that this means that there is a unity in intention, and we are back with intentional gluons.

(15)

[contents]

 

 

 


 

1.6.4

[Gluons as Necessarily Objects on Account of Being Referable]

 

[Gluons can be referred to, so we cannot claim they are not objects.]

 

[Now recall the second option from section 1.6.1 above.

{2} We can reject the claim that a gluon is an object.
But “we can refer to it, quantify over it, talk about it.” Priest says that there is little other sense to what would qualify something as being an object.]

In the second case, we must insist that the gluon is simply not an object. But this seems even more desperate: we can refer to it, quantify over it, talk about it. If this does not make something an object, I am at a loss to know what could. Anything we can think about is an object, a unity, a single thing (whether or not it exists). There seems little scope here.

(15)

[contents]

 

 


 

1.6.5

[Gluon as not Being an Object]

 

[We cannot say that the gluon is an object, because that takes unity for granted rather than explain it.]

 

[Now finally recall the third option from section 1.6.1 above.

{3} We can reject the claim that it is not an object.

We have seen from section 1.4 (see especially 1.4.2) that this leads to the Bradley Regress. (But Priest’s point this time seems different. I do not quite grasp it, so consult the quotation below. He seems to be saying the following. Let us suppose the gluon is an object. But what we are trying to explain are unified objects. He next says that the only way an object can constitute the unity of another object is by taking unity for granted. That is the part I do not follow so well. Are we talking about taking the unity of the gluon for granted, so that it does not lead to a regress? Or are we taking the whole thing’s unity for granted? At any rate, this somehow involves simply thinking that the unity of things are obvious or unquestionable. But examples of unities very often involve combinations of parts, and we do not explain their compositional bonding by claiming that gluons are objects ((or by otherwise taking unity for granted)). But I am guessing here.]

Finally, in the third case, we may suppose that the gluon is simply an object. But we have seen that this just leaves us bereft of an explanation of the unity of an entity. How could we even have had the impression that any object could constitute the unity of another bunch of objects? Only because of taking the unity for granted. Thus, we write ‘Socrates is a person’ and the rest is obvious. But putting ‘Socrates’ and ‘is a person’ next to each other does not do the job; it just produces a plurality of two things. When we think of the two as cooperating, the magic has already occurred.

(15)

[contents]

 

 


 

1.6.6

[Gluons as Dialetheias]

 

[Our best option for understanding gluons is with the dialetheic claim that they both are and are not objects.]

 

So we cannot use any of the available options, and we should instead say that gluons both are and are not objects. What prevents us is the Principle of Non-Contradiction. But since it is not a well-founded logical principle and since also it is best not obeyed in all cases, we will take the dialetheic position that Gluons have contradictory properties (again, they both are and are not objects.)

If we cannot go back, then we must go forward. What stands in the way? Evidently, the Principle of Non-Contradiction. If we accept that gluons both are and are not objects, then some contradictions are true. Whilst it must be agreed that horror contradictionis is orthodox in Western philosophy, at least since Aristotle’s canonical –but fundamentally flawed – defence, the friends of consistency have done little as yet to establish that there is anything rational in this.23 So let us go forward. Gluons are dialetheic: they have contradictory properties. Of course, if this were all there were to matters, the situation would not be particularly interesting. Going on means crossing the bridge of inconsistency;24 and what is important is what lies on the other side.

(15)

23. See Priest (2006).

24. Not that there are no other good reasons to do so. See Priest (1987) and (1995a).

[contents]

 

 

 

 

 

 


 

Bibliography:

 

Priest, Graham. 2014. One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University.

 

 

Or if otherwise cited:

 

Priest, G. (1987), In Contradiction, Dordrecht: Martinus Nijhoff; second (extended) edn., Oxford: Oxford University Press, 2006.

 

Priest, G. (1995a), Beyond the Limits of Thought, Cambridge: Cambridge University Press; second (extended) edn., Oxford: Oxford University Press, 2002.

 

Priest, G. (2006), Doubt Truth to be a Liar, Oxford: Oxford University Press.

 

Sider, T. (1993a), ‘Parthood’, Philosophical Review 116: 51–91.

 

Sider, T. (1993b), ‘Van Inwagen and the Possibility of Gunk’, Analysis 53: 285–9.

 

Unger, P. (1979), ‘There are no Ordinary Things’, Synthese 41: 117--54.

 

Uzquiano, G. (2004), ‘Plurals and Simples’, Monist 87: 429–51.

 

 

 

 


.

17 Apr 2018

Priest (1.8) An Introduction to Non-Classical Logic, ‘Subjunctive and Counterfactual Conditionals’, summary

 

by Corry Shores

 

[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

[Logic and Semantics, entry directory]

[Graham Priest, entry directory]

[Priest, Introduction to Non-Classical Logic, entry directory]

 

[The following is summary of Priest’s text, which is already written with maximum efficiency. Bracketed commentary and boldface are my own, unless otherwise noted. I do not have specialized training in this field, so please trust the original text over my summarization. I apologize for my typos and other unfortunate mistakes, because I have not finished proofreading, and I also have not finished learning all the basics of these logics.]

 

 

 

 

Summary of

 

Graham Priest

 

An Introduction to Non-Classical Logic: From If to Is

 

Part I:

Propositional Logic

 

1.

Classical Logic and the Material Conditional

 

1.8

Subjunctive and Counterfactual Conditionals

 

 

 

Brief summary:

(1.8.1) A strong objection to the semantics of the material conditional and its application to natural language conditionals are sentences with similar antecedents and consequents but on account of subtle grammatical differences have opposite truth values. Priest’s examples are: {1} If Oswald didn’t shoot Kennedy someone else did. (which is true), and {2} If Oswald hadn’t shot Kennedy someone else would have. (which is false). (1.8.2) One common way to deal with the apparent inconsistency in the above examples is to distinguish them in terms of grammatical properties and say that one type is not a material conditional. When a conditional sentence is indicative, it could be material, but when it is subjunctive or counterfactual, often using “would,” it is not material. (1.8.3) The English conditional is probably not ambiguous between subjunctive and indicative moods, on account of explicit syntactical differences that maintain a clear distinction. (1.8.4) Conditionals are subjunctive when they articulate a temporal perspective located before the stated event or fact, and they are indicative if they articulate a temporal perspective where that event or fact is established.

 

 

 

 

 

 

Contents

 

1.8.1

[Grammar and the Material Conditional]

 

1.8.2

[Subjunctive or Counter-Factual Sorts of Conditional Formulations]

 

1.8.3

[The English Conditional as Not Ambiguous Between Subjunctive and Indicative Moods]

 

1.8.4

[Temporal Perspective and Conditional Mood]

 

 

 

 

 

Summary

 

1.8.1

[Grammar and the Material Conditional]

 

[A strong objection to the semantics of the material conditional and its application to natural language conditionals are sentences with similar antecedents and consequents but on account of subtle grammatical differences have opposite truth values. Priest’s examples are: {1} If Oswald didn’t shoot Kennedy someone else did. (which is true), and {2} If Oswald hadn’t shot Kennedy someone else would have. (which is false).]

 

[Previously in section 1.7 we examined the material conditional and objections to its semantic evaluation. In section 1.7.1 we noted the paradoxes of material implication, namely, BA B and ¬AA B. And in section 1.7.2 we noted certain English sentences using the conditional that are true according to the semantic evaluation of the material conditional but are intuitively false on account of relevance or breaking the rule of asserting the strongest, as for example, “If New York is in New Zealand then 2 + 2 = 4.” We now will consider two examples with slightly different grammatical sorts of formations which otherwise would seem, formally speaking, to have nearly identical antecedents and consequents.]

A harder objection to the correctness of the material conditional is to the effect that there are pairs of conditionals which appear to have the same antecedent and consequent, but which clearly have different truth values. They cannot both, therefore, be material conditionals. Consider the examples:

(1) If Oswald didn’t shoot Kennedy someone else did. (True)

(2) If Oswald hadn’t shot Kennedy someone else would have. (False)

(13)

[contents]

 

 

 

1.8.2

[Subjunctive or Counter-Factual Sorts of Conditional Formulations]

 

[One common way to deal with the apparent inconsistency in the above examples is to distinguish them in terms of grammatical properties and say that one type is not a material conditional. When a conditional sentence is indicative, it could be material, but when it is subjunctive or counterfactual, often using “would,” it is not material.]

 

[Priest notes a common way to distinguish the two conditionals in section 1.8.1. Ones that are indicative, like:

(1) If Oswald didn’t shoot Kennedy someone else did. (True)

are candidates for the normal semantic evaluation of the material conditional. Ones that are subjunctive or counterfactual, often using the term would, like:

(2) If Oswald hadn’t shot Kennedy someone else would have. (False)

are not instances of the material conditional. Hence, even though its antecedent is false, that does not make the whole conditional true.]

In response to this kind of example, it is not uncommon for philosophers to distinguish between two sorts of conditionals: conditionals in which the consequent is expressed using the word ‘would’ (called ‘subjunctive’ or ‘counterfactual’), and others (called ‘indicative’). Subjunctive conditionals, like (2), cannot be material: after all, (2) is false, though its | antecedent is false (assuming the results of the Warren Commission!). But indicative conditionals may still be material.

(13-14)

[contents]

 

 

 

 

1.8.3

[The English Conditional as Not Ambiguous Between Subjunctive and Indicative Moods]

 

[The English conditional is probably not ambiguous between subjunctive and indicative moods, on account of explicit syntactical differences that maintain a clear distinction.]

 

[I may not follow this next point. He writes, “The claim that the English conditional is ambiguous between subjunctive and indicative is somewhat dubious, though.” I would think that this is not the claim made above. My guess is that there are people who make a different claim, namely, that there is no way in English to clearly determine whether or not a conditional formation is either indicative or subjunctive. I am not sure what the purpose is for that claim, if even that is the claim. At any rate, if I myself think about English, I have trouble making that distinction. “If” formations to me seem like they could all be subjunctive, as if were are saying “were such to happen, then this other thing can be expected.” And then if for example the things were known in fact, then it is like filling out that supposition with actual fact, which would be like affirming the antecedent. So even if we say, “If Oswald shot Kennedy, then ...” then we in that mode of supposition say that something else would have to be so. And then the affirmation of it would not be a conditional, and thus more clearly indicative in English: “Oswald did in fact shoot Kennedy, and so ...”. At any rate, Priest’s point is that we can still distinguish them by means of the tenses or moods of the verbs involved.]

The claim that the English conditional is ambiguous between subjunctive and indicative is somewhat dubious, though. There appears to be no grammatical justification for it, for a start. In (1) and (2) the ‘if’s are grammatically identical; it is the tenses and/or moods of the verbs involved which make the difference.

(14)

[contents]

 

 

 

 

1.8.4

[Temporal Perspective and Conditional Mood]

 

[Conditionals are subjunctive when they articulate a temporal perspective located before the stated event or fact, and they are indicative if they articulate a temporal perspective where that event or fact is established.]

 

[Priest now explains the role of time perspective in evaluating such conditionals. In the first case:

(1) If Oswald didn’t shoot Kennedy someone else did. (True)

we evaluate it from the perspective of the present moment, which happens after the fact. And since, from our temporal perspective after the fact Oswald did in fact shoot Kennedy, we would evaluate it as true. (And for that reason it is indicative. For, from the temporal perspective it involves, it is factual. I think that is what Priest is saying.) But in the second one

(2) If Oswald hadn’t shot Kennedy someone else would have. (False)

we are asked to think of the situation from before the moment when Oswald shot Kennedy was shot. (And for that reason it is subjunctive, because from that temporal perspective, it is hypothetical rather than factual that Oswald kills Kennedy. Again, I am guessing.) Priest then notes that this is the past tense of the conditional. (I guess the idea is that the conditional when referring to a past temporal perspective would be past tense.) Priest lastly explains that were both instances present tense conditional, there would no longer be this important distinction. He gives the example comparison: “‘If I shoot you, you will die’ and ‘If I were to shoot you, you would die’” (13). (I am not certain, but I am guessing the idea is the following. Both sentences hold a present temporal perspective, but the first one takes an indicative mood and the second the subjunctive.

If I shoot you, you will die. (True)

If I were to shoot you, you would die. (True)

But were we to use the past tense of the conditional for the second one, it might not be true. So:

Had I shot you yesterday, you would have died. (Maybe True, Maybe False)

But I do not see how there would be such a difference. Would you not have died then for the same reason that you would die now? As I said above, I have difficulty making this distinction so far. At this moment, I am only able to see every “if” clause as subjunctive, with the distinction being a matter of some having all true components and others not. This is just my naïve and probably mistaken sense for the English language, but I have never, phenomenologically speaking, experienced an “if” clause as having the sense of an indicative mood. Or let me be more precise. The conditional on the whole is always in the indicative mood. It is stating a fact about the conditional relation between the antecedent and the consequent. But the “if” clause for me is always, without any exception I can think of at this moment, in the subjunctive mood. Let me make my distinction more clear.

 

Indicative Conditional with Subjunctive Clause:

If I shoot you, you will die.

 

Indicative Conditional with Another Indicative Conditional Used within a Subjunctive Clause:

Were it the case that ‘if I shoot you, you will die,’ then I would not shoot you.

or

If, ‘if I shoot you, you will die,’ then I would not shoot you.

 

So I guess my sense is rather that the conditional as a whole is always indicative, it being the indication and factual declaration of a conditional relation between two other facts, but within that indicatively mooded compound sentence is a subjunctive clause starting with “if”, meaning something like: suppose it were the case that.... And the fact that it happens to be the case ((either now or at some other time)) would not affect the grammatical mood, which is formed or conceived independently of factual information to confirm or deny it. So I am still working on understanding this. Let me quote:)]

What these differences seem to do is to get us to evaluate the truth values of conditionals from different points in time. Thus, we evaluate (1) as true from the present, where Kennedy has, in fact, been shot. The difference of tense and mood of (2) asks us to evaluate the conditional ‘If Oswald doesn’t shoot Kennedy, someone else will’ from the perspective of a time just before Kennedy was shot. It is, in a certain sense, the past tense of that conditional. Notice that no difference of the kind between (1) and (2) arises in the case of present-tense conditionals. There is no major difference between ‘If I shoot you, you will die’ and ‘If I were to shoot you, you would die.’

(14)

[contents]

 

 

 

 

 

 

 

From:

 

Priest, Graham. 2008 [2001]. An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University.

 

 

 

Priest (1.7) An Introduction to Non-Classical Logic, ‘The Material Conditional’, summary

 

by Corry Shores

 

[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

[Logic and Semantics, entry directory]

[Graham Priest, entry directory]

[Priest, Introduction to Non-Classical Logic, entry directory]

 

[The following is summary of Priest’s text, which is already written with maximum efficiency. Bracketed commentary and boldface are my own, unless otherwise noted. I do not have specialized training in this field, so please trust the original text over my summarization. I apologize for my typos and other unfortunate mistakes, because I have not finished proofreading, and I also have not finished learning all the basics of these logics.]

 

 

 

 

Summary of

 

Graham Priest

 

An Introduction to Non-Classical Logic: From If to Is

 

Part I:

Propositional Logic

 

1.

Classical Logic and the Material Conditional

 

1.7

The Material Conditional

 

 

 

 

Brief summary:

(1.7.1) The material conditional, symbolized as ⊃, is true when the antecedent is false or the consequent is true. It is thus logically equivalent to ¬AB. But also on that account, it generates the “paradoxes of material implication,” namely, BA B and ¬AA B. In other words, suppose we have some given formula that is true. That means we can make it a consequent in a conditional with any arbitrary antecedent. Or suppose we have a  negated formula as true, then we can make the formula’s unnegated form be the antecedent in a conditional with any arbitrary consequent. (1.7.2) The truth conditions for the material conditional allow for technically true but intuitively false sentences that fulfill the conditions for the material conditional but seem false on account of the irrelevance of the antecedent to the consequent, as for example, “If New York is in New Zealand then 2 + 2 = 4.” This seems to contradict the intuitive sense we ascribe to the English conditional, which involves relevance. (1.7.3) The counter-intuitive example conditional sentences are odd because they break certain rules of communication, namely to assert the strongest information.

 

 

 

 

 

 

Contents

 

1.7.1

[The Material Conditional and the Paradoxes of Material Implication]

 

1.7.2

[Irrelevance and the Material Conditional]

 

1.7.3

[Conversational Implicature as an Explanation for the Counter-Intuitive Conditionals]

 

 

 

 

 

Summary

 

1.7.1

[The Material Conditional and the Paradoxes of Material Implication]

 

[The material conditional, symbolized as ⊃, is true when the antecedent is false or the consequent is true. It is thus logically equivalent to ¬AB. But also on that account, it generates the “paradoxes of material implication,” namely, BA B and ¬AA B. In other words, suppose we have some given formula that is true. That means we can make it a consequent in a conditional with any arbitrary antecedent. Or suppose we have a  negated formula as true, then we can make the formula’s unnegated form be the antecedent in a conditional with any arbitrary consequent.]

 

Priest now discusses the material conditional, symbolized as ⊃. [Recall from section 1.3.2 the semantic evaluation for the conditional:

v(A B) = 1 if v(A) = 0 or v(B) = 1, and 0 otherwise.
(p.5, section 1.3.2)

and here are the ones for negation and conjunction:

vA) = 1 if v(A) = 0, and 0 otherwise.
v(AB) = 1 if v(A) = 1 or v(B) = 1, and 0 otherwise.

(p.5, section 1.3.2)

Using the above two conditions, what would be the evaluation for: ¬AB? For the whole disjunction to be true, then either disjunct needs to be true. That means we need either vA) = 1 or v(B) = 1 for the disjunction to be true, otherwise it is false. And for vA) = 1, we need v(A) = 0. Thus we see when we combine the conditions for the disjunction with one negated term, we have the same as for the conditional.

vAB) = 1 if v(A) = 0 or v(B) = 1, and 0 otherwise.

v(A B) = 1 if v(A) = 0 or v(B) = 1, and 0 otherwise.

Priest next shows the paradoxes of material implication, which follow from that equivalence, it seems, but I am not entirely sure I know how it works. For, we start by affirming either the consequent term or the negation of the antecedent term, and we infer the whole conditional from that. One is

BA B

And the other is:

¬AA B

Semantic validity is defined in the following way in section 1.3.3:

Let Σ be any set of formulas (the premises); then A (the conclusion) is a semantic consequence of Σ (Σ ⊨ A) iff there is no interpretation that makes all the members of Σ true and A false, that is, every interpretation that makes all the members of Σ true makes A true. ‘Σ ⊭ A’ means that it is not the case that Σ ⊨ A.

(p.5, section 1.3.3)

So suppose that B is true. That means, were it to happen to be the consequent of any conditional whatsoever, that conditional would have to be true. For, it meets the second condition for the conditional to be true:

v(A B) = 1 if v(A) = 0 or v(B) = 1, and 0 otherwise.

In other words, for any true formula we can derive a conditional with any arbitrary antecedent. I am not sure, but perhaps it results in counter-intuitive derivations, like, on the basis of knowing that water is wet, we can derive, “if the moon is made of green cheese, then water is wet.” I am just guessing, as I am not sure if the problem here is with relevance. The second one would seem to work similarly, that from any true negated formulation we can derive a conditional with its unnegated form as the antecedent and choose any arbitrary consequent. So on the basis of “it is not the case that pigs can fly,” we might derive “if pigs can fly, than the moon is made of green cheese”. Again, I am not sure.]

The connective ⊃ is usually called the material conditional (or material implication). As its truth conditions show, AB is logically equivalent to ¬AB. It is true iff A is false or B is true. Thus, we have:

BA B

¬AA B

These are sometimes called the ‘paradoxes of material implication’.

(12)

[contents]

 

 

 

1.7.2

[Irrelevance and the Material Conditional]

 

[The truth conditions for the material conditional allow for technically true but intuitively false sentences that fulfill the conditions for the material conditional but seem false on account of the irrelevance of the antecedent to the consequent, as for example, “If New York is in New Zealand then 2 + 2 = 4.” This seems to contradict the intuitive sense we ascribe to the English conditional, which involves relevance.]

 

Priest then says that there is reason to think that the conditional in English may not be represented as the material conditional ⊃. He then gives some example sentences to demonstrate this. [I am not sure how the English element factors in here. It seems more to illustrate the paradoxes of material implication. So maybe the objection is to the semantics of material implication, here illustrated in English. Or maybe the idea is that the English conditional form has a certain sense to it that is contradicted by the sorts of counter-intuitive sentences that the material conditional should allow us to make. The first example has an obviously false antecedent and an obviously true consequent, with there being no relation between them. The next one has both an obviously true antecedent and an obviously true consequent, but they again seem unrelated. And the final one has an obviously true antecedent but an obviously false consequent, but again they are unrelated. So the issue seems to be relevance as far as I can tell so far.]

People taking a first course in logic are often told that English conditionals may be represented as ⊃. There is an obvious objection to this claim, though. If it were correct, then the truth conditions of ⊃ would ensure the | truth of the following, which appear to be false:

If New York is in New Zealand then 2 + 2 = 4.

If New York is in the United States then World War II ended in 1945.

If World War II ended in 1941 then gold is an acid.

(12-13)

[contents]

 

 

 

 

1.7.3

[Conversational Implicature as an Explanation for the Counter-Intuitive Conditionals]

 

[The counter-intuitive example conditional sentences are odd because they break certain rules of communication, namely to assert the strongest information.]

 

[Priest next will explain one way to understand why these formulations from 1.7.2 are counter-intuitive even though they are technically true in terms of the semantics of the material condition. I will not summarize this well, so it is best to skip to the quotation below. But let us first look at the ideas here. In actual communication in real situations, we can draw inferences not from the content of what is said but rather from the fact that some particular thing is said. Priest names two such inferences. One is relevance. We suppose that someone asks “How do you use this drill?” That creates a certain context. Then someone says. “There’s a book over there.” We suppose that the person is obeying the rule of conversation that what we say is relevant as a reply. So supposing that “There is a book over there” is relevant to “How do you use this drill?” we can infer that the book is a drill manual of sorts. For otherwise, the reply would be irrelevant. The other rule is “assert the strongest claim you are in a position to make.” This is the important one for the example sentences, but I do not quite get it. What qualifies as the “strongest claim” or “the strongest information”? From the example, my guess is the following. Suppose someone asks, what day is your birthday? and you, knowing the correct answer, say, it is either January 1st or May 2nd. This is true, but maybe the answer is weakened by adding the false alternative. I am wildly guessing. So in Priest’s example, we suppose one person asks, “Who won the 3.30 at Ascot?” then the other person replies, “It was a horse named either Blue Grass or Red Grass,” and from this we can infer that the speaker does not know which. I am guessing that had the person known the correct answer, they would have said which, with that being the “strongest information,” but since both options were given, that means the speaker’s strongest information is not either disjunct, and hence we can infer that they do not know which one is true. Now we need to apply this to the counter-intuitive conditional sentences above. Priest says that they are odd, because the person asserting them is breaking the rule of assert the strongest, on account of them being in a position to assert either the consequent or the negation of the antecedent (or both). So let us look at them, as I am not following so well yet. Suppose someone says:

If New York is in New Zealand then 2 + 2 = 4.

Here the person is in a position to assert the consequent. By also asserting the conditional, they are not asserting the strongest information. Why is that? I am still guessing that by adding the false antecedent, we have “weakened” the statement somehow. But I am not following, because the person is also in a position to assert the negation of the antecedent.

If New York is in the United States then World War II ended in 1945.

Here the person is in a position to assert the consequent.

If World War II ended in 1941 then gold is an acid.

Here the person is in a position to assert the negation of the antecedent or the consequent. I am still missing the point. My best guess at the moment is that on the basis of the rule assert the strongest, when we assert a conditional, it should be that we assert it with the meaning the suggestion that the whole conditional itself is true and not just instead one of the following other options: that in the conditional we asserted only the consequent is true, that only the antecedent is false, or that both. My confusion is still with this example:

If New York is in the United States then World War II ended in 1945.

We supposedly are not objecting on the basis of relevance. But here both the antecedent and consequent are true. So what is the strongest information here? It cannot be the relevance of the antecedent to the consequent. Sorry, let me quote:]

It is possible to reply to this objection as follows. These examples are, indeed, true. They strike us as counterintuitive, though, for the following reason. Communication between people is governed by many pragmatic rules of conversation, for example ‘be relevant’, ‘assert the strongest claim you are in a position to make’. We often use the fact that these rules are in place to draw conclusions. Consider, for example, what you would infer from the following questions and replies: ‘How do you use this drill?’, ‘There’s a book over there.’ (It is a drill manual. Relevance.) ‘Who won the 3.30 at Ascot?’, ‘It was a horse named either Blue Grass or Red Grass.’ (The speaker does not know which. Assert the strongest information.) These inferences are inferences, not from the content of what has been said, but from the fact that it has been said. The process is often dubbed ‘conversational implicature’. Now, the claim goes, the examples of 1.7.2 strike us as odd since anyone who asserted them would be violating the rule assert the strongest, since, in each case, we are in a position to assert either the consequent or the negation of the antecedent (or both).

[contents]

 

 

 

 

 

 

 

 

 

From:

 

Priest, Graham. 2008 [2001]. An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University.

 

 

 

 

 

.

 

Terence Blake. BADIOU’S MATHEMATICAL SEMINARS: a list

 

by Corry Shores

 

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

 

[Central Entry Directory]

[Terence Blake, entry directory]

 

 

 

 

 

Terence Blake

 

BADIOU’S MATHEMATICAL SEMINARS: a list

(published 17-Apr-2018)

 

 

Terence Blake has published a list of Badiou’s seminars on mathematics, with a link to many transcriptions.

 

 

 

 

 

 

Blake, Terence. “BADIOU’S MATHEMATICAL SEMINARS: a list.” Web. Published 17-Apr-2018. Accessed 17-Apr-2018.

https://terenceblake.wordpress.com/2018/04/17/badious-mathematical-seminars-a-list/

 

 

 

 

.

Priest (1.5) One. ‘Explaining Unity,’ summary

 

by Corry Shores

 

[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

[Logic and Semantics, entry directory]

[Graham Priest, entry directory]

[Priest, One, entry directory]

 

[The following is summary. You will find typos and other distracting mistakes, because I have not finished proofreading. Bracketed commentary is my own. Please consult the original text, as my summaries could be wrong.]

 

 

 

Summary of

 

Graham Priest

 

One:

Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness

 

Ch.1

Gluons and Their Wicked Ways

 

1.5

Explaining Unity

 

 

 

Brief summary:

(1.5.1) One possible explanation for what a gluon (the unifying factor in something’s composition)  is, is that it is the binding relationality of the thing’s internal arrangement or structure. (1.5.2) But not all relations are compositional, as for example the relation of child to a mother. (1.5.3) The relational interpretation of the gluon only makes matters worse, because it then presents a difficult metaphysical problem of explaining how something non-physical can bind physical things. (1.5.4) (The relational interpretation of the gluon also fails because the thing’s relationality only presents itself as another entity needing yet another to explain its integration in the whole, and that new binding entity would need yet another, and so on. (1.5.5) Another possible sort of account for unity is ontological dependence. One might claim that whenever the identity of the parts depends on the identity of the whole, that this very dependence itself is what accounts for the thing’s unity. But this fails as an account, because it does not yet explain how the parts cooperate to form a unity. (1.5.6) There are a lack of conventional accounts of unity. Priest will propose a new one, which will involve modifications in our notion of identity. (1.5.7) Accounts of unity that merely describe the causal processes that go into something’s generation or production, like a carpenter’s explanation of how to construct a table, satisfy to some extent the how curiosity we have for an account of unity. But they fall short for a number of reasons. {1} They do not explain the unity brought about but only the processes bringing it about. {2} They lack an explanation for what makes unifying causal processes different from non-unifying ones. And {3} they cannot explain the unity of abstract objects. (1.5.8) Thus, we do not have any easy ways to account for unity.

 

 

 

 

 

Contents:

 

1.5.1

[The Gluon as a Relation That Binds]

 

1.5.2

[Relations as Not Necessarily Compositional]

 

1.5.3

[The Failure of the Relational Interpretation of the Gluon on Account of Metaphysical Incompatibility]

 

1.5.4

[The Failure of the Relational Interpretation of the Gluon on Account of the Bradley Regress]

 

1.5.5

[The Ontological Dependence Account of Unity and Its Failure]

 

1.5.6

[Priest’s Offer]

 

1.5.7

[The Causal Process Account of Unity and Its Failure]

 

1.5.8

[The Lack of Convenient Accounts of Unity]

 

Bibliography

 

 

 

 

Summary

 

1.5.1

[The Gluon as a Relation That Binds]

 

[One possible explanation for what a gluon (the unifying factor in something’s composition)  is, is that it is the binding relationality of the thing’s internal arrangement or structure.]

 

[Previously in section 1.3.4 we discussed the notion of the gluon, which is the unifying factor in the composition of something. Priest now addresses a possible notion of how to explain the gluon. Some might say that what accounts for the unity is the “configuration, arrangement, structure” or the like of the parts. As such, this would be saying that the gluon is a relationship between the parts, and it would cast this relationship as having binding properties.]

A common thought at this point is that what accounts for the unity of the parts of an object, its gluon, is their configuration, arrangement, structure, or some such. Whatever you call it, it is a relationship between the parts, and relationships relate, | by definition. Call relationships objects if you wish; but they are a special kind of object; and they bind together the parts by their very nature.19

(11-12)

19. We are not a million miles away here from Aristotle’s proposed solution to the problem.We will look at the details of his account in Chapter 3.

(12)

[contents]

 

 

 

1.5.2

[Relations as Not Necessarily Compositional]

 

[But not all relations are compositional, as for example the relation of child to a mother.]

 

Priest notes that this conception of the gluon (see section 1.5.1 above) confuses two ideas, namely, between relating and unifying. A relation by its own is not normally something that compositionally unifies what it relates. To illustrate, Priest has us consider for example the relationship of oneself being a child to one’s mother. Here the relationship does not unify the two people. [I would have expected another sort of example, given the biological and psychological bond that such a relation is thought to have. Perhaps the idea is that simply by being a mother’s child is not sufficient a bond to compose a unity of the two into one object. Deleuze when discussing Spinozistic composition gives the example of a married couple composing one composite thing. I would think that a mother-child relation would not be too far off from such a structure, but I am not sure.]

There is already a confusion at the heart of this thought –and not an uncommon one. The confusion is between relating and unifying. Relations do not, in general, unify. I am related to my mother by bearing the relationship of child to her. This may even be an internal relation (whatever, exactly, that means) – at least as far as I am concerned: I could not have been me had I not had that relation. But obviously the relation does not serve to render my mother and myself a unity in the appropriate sense.

(12)

[contents]

 

 

 

1.5.3

[The Failure of the Relational Interpretation of the Gluon on Account of Metaphysical Incompatibility]

 

[The relational interpretation of the gluon only makes matters worse, because it then presents a difficult metaphysical problem of explaining how something non-physical can bind physical things.]

 

[Priest’s next point seems to be the following. The notion of the gluon as a composition-forming relation that we noted above in section 1.5.2 still construes it as an entity. As we noted, it is a different kind of entity than the thing’s parts, namely, it is a relation, and what it relates are “things” more straightforwardly understood. In our example of the house, the bricks are the things, and the gluon under this relational interpretation would be the particular relational organization of the parts on account of which the parts compose a whole house rather than a mere collection of independent bricks. Priest now says that this does not help, and his reasoning seems to be the following. The main problem lies in the fact that not only is a relation a different kind of thing than its parts, it is of such a kind that we now have yet a greater problem of understanding how it can be said to combine with those parts. His raises the mind-body problem, which stems largely from the mind being of such a different kind of thing as the body that it is very difficult to both maintain their conventional distinction while also understanding how they have the intimate relation we think them to have. So suppose we take this relational interpretation of the gluon. We now have the even greater challenge of explaining how a relation, being so very different than a part, especially a physical part, “latches-on” so to speak to the parts and binds them in their physical unity but in a way that is different from the normal physical properties and interactions we assign to the objects. To venture to put it another way, the gluon that organizes the house under this relational interpretation would need to have some sort of “sense” to it, like the houseness or house-form expressed by the bricks in their entire inter-relationality. But this sense cannot be something that is in itself physical. The mortar binding the bricks is physical, but the mortar can bind them haphazardly or under a different sense, like “wall”. The gluon however is not something physical like the mortar is. But as such, how does something not physical bind together physical things? (So as we see, our account of unity must include a notion of a binding factor, hence the gluonics. But that “binding” we seek to explain is not a physical thing but rather a principle to understand how it is that things by being so bound constitute a unity, I think. To venture a rewording, what we seek is a notion of compositional binding that accounts for unity. For, the main aspect of unity to be explained is not the oneness as much as the factor that brings the multiple parts together into a oneness.)]

Even setting aside the confusion, though, the thought still does not work. The fact that a gluon is a different kind of object does not solve the problem of unity. If anything, it simply makes it worse. Thus, what it is that joins the mind and body into a unity is a traditional and vexed problem in dualistic theories of mind. It is the very fact that they are different kinds of thing that seems to make the problem so intractable. In a similar way, suppose that it is the configuration of the bricks that binds them together to form a house. The bricks are physical objects; the configuration is, presumably, an abstract object. (Different sets of bricks can have the same configuration.) Any interaction between the bricks and the configuration would therefore seem just as problematic, perhaps even more so, as that in the mind/body case.

(12)

[contents]

 

 

 

 

1.5.4

[The Failure of the Relational Interpretation of the Gluon on Account of the Bradley Regress]

 

[The relational interpretation of the gluon also fails because the thing’s relationality only presents itself as another entity needing yet another to explain its integration in the whole, and that new binding entity would need yet another, and so on.]

 

[Priest’s next point seems to be the following. We said in section 1.5.3 above that one problem with the relational interpretation of the gluon is that it posits an entity whose metaphysical compatibility with its parts is not easy to account for. Now we return to the Bradley regress. By positing the relationality as the binding, organizing element, we have only created another entity which calls for yet another binding entity to explain how it binds with the parts, and that new entity will need yet another, and so on. Priest may be saying something else or more, so let me quote:]

So it has to be the particular nature of the special object that is supposed to solve the problem. But how does it do so? To say that it just does do this – by its nature – is not to solve the problem; it is simply to name it. As Bradley puts it (speaking of the mind, but with considerations that apply quite generally):20

When we ask ‘What is the composition of [an object]’, we break up [that object], which comes to us as a whole, into units ... But since it is clear that these units by themselves are not all the ‘composition’, we are forced to recognize the existence of relations. But this does not stagger us. We push on with the conceptions we have brought to the work, and which of course can not be false, and we say, Oh yes, we have there more units, naturally not quite the same as the others, and – voilà tout. But when a sceptical reader, whose mind has not been warped by a different education, attempts to form an idea of what is meant, he is somewhat at a loss.

For when one invokes the object in question, one simply adds an extra element to the melange. If one is puzzled by the unity in the first case, one should be equally puzzled by the supposed unity in the second. Thus, for example, instead | of a plurality of physical parts of an object, we now have a plurality of [parts plus configuration]. Or more generally, we have the parts plus the relationship between them (or the action of the relation, or the fact that they are so related). How is this any better? This is exactly what the Bradley regress highlights.

(12-13)

20.

Bradley (1922), sect. 65. Here and throughout the book, all italics in quotations are original unless otherwise specified.

(12)

[contents]

 

 

 

 

1.5.5

[The Ontological Dependence Account of Unity and Its Failure]

 

[Another possible sort of account for unity is ontological dependence. One might claim that whenever the identity of the parts depends on the identity of the whole, that this very dependence itself is what accounts for the thing’s unity. But this fails as an account, because it does not yet explain how the parts cooperate to form a unity.]

 

[Priest now notes another way to account for the unity of an object. I may not summarize this properly, so it is best to skip to the quotation below. But let us follow the reasoning first. We first consider a pile of stones. Now, what gives the pile of stones its identity? To be a pile of stones means first that it is a pile, and thus a pile of things, and secondly it means that what it is a pile of are stones. In other words, the identity of a pile of stones depends entirely in the identity of its parts. But what about the identity of the stones, the parts of the pile? They would have the same identity as being whatever stone they are, independently of the pile they happen to be in. Were they in another pile or lying outside a pile, they would have the same identity. Next consider some person’s body. Each body part, like a hand, has (it seems from the text) an identity related to the owner. Priest writes: “We would not have that hand unless it were part of that body.” This means that the identity of the body part (being, it seems, individualized and identifiable by means of the body it belongs to) depends on the identity of the body it is a part of. (I am not sure if the body’s identity also depends on the parts’ identities or not.) Some use this notion to explain unity. They say that this dependence of the parts’ identities on the whole’s identity is what explains the unity of the thing. (Perhaps the insight here is the following, but this is a spontaneous guess, sorry. The parts have identities. That is something fundamental to them, maybe even what is most fundamental to them. Now, what is most fundamental to the parts is not something lying within them but rather is something lying in their belonging-together to the whole. The parts as such would not even exist were they not part of that whole (or at least they would be different things altogether). So we might think then of this dependence of the parts on the whole as being a fundamental “bond” they hold with each other; for without this bond, they would not be what they are. This “bond” would seem to be some fact of their “being” or some such metaphysical concept. To put it another way, we have established that the parts’ being, identity, existence, etc. stems from their being in the particular whole they are in. But that being in some particular whole is a matter of their particular relational combination with the other parts. Thus this very dependence on the whole for identity is at the same time the inter-relative bonding dependence of the parts. I am reaching.) Priest next explains why this notion of ontological dependence does not still account for unity. He says that this account only provides a description of some feature of unified things. What it cannot do, but needs to for such an account, is to explain how the parts interrelate so to compose a unified thing. (Philosophically speaking, I find this claim striking, but perhaps it is obvious. In philosophy, when we want to give an account of something, the question we ask is how. For example, to give an account of unity, we ask, how do the parts form the whole. What sort of an answer would satisfy such how questions? In the case of unity, we will find out as we go. But I suspect that it could involve identifying structural elements and describing both the structural features they have which play a role in forming the unity and also their manner of interaction or interrelation in that formation. In other words, we might need something more of a mechanical explanation, or an account or story that tells us, how it all works.)

A quite different possibility for explaining the unity of an object is one which appeals to the notion of (ontological) dependence. Consider a pile of stones and a person’s body. The former, it might be suggested, is not a true unity; the latter is. And what makes the difference is that the identity of the pile depends on the identity of its parts, the stones; whereas in the case of the body, it is the other way around: the identity of the parts depends on the identity of the whole. (We would not have that hand unless it were part of that body.) Thus, the thought continues, what explains the oneness of a partite genuine unity is the dependence of its parts on the whole. There will be much to be said about dependence in Part III of the book. For the moment, let us grant the claims about what depends on what. Even given these, the suggestion will not work. The fact that in a unity the natures of the parts depend on the nature of the whole in no way explains how they cooperate to form a unity. For all their dependence, the parts are still parts; and facts about identity do not bear on cooperation. Granted, the parts would not be the parts they are unless they were parts of the whole. But that hardly explains how it is that the various parts do what they do to create the whole. We know, by their nature, that they are parts of that whole; but how is it that they have this nature?

(13)

21. This possibility was suggested to me by Jonathan Schaffer. It is hinted at in his (2010b).

(13)

[contents]

 

 

 

1.5.6

[Priest’s Offer]

 

[There are a lack of conventional accounts of unity. Priest will propose a new one, which will involve modifications in our notion of identity.]

 

Priest now notes that unity could be one of those things that are impossible to explain and that thus we must just accept without further investigation. Priest says that we should not quit so fast, because if we are willing to modify certain concepts like identity, we can arrive upon a satisfactory account, which is what Priest will be doing.

One could, I suppose, be a quietist about the whole matter: one might just accept that one cannot provide an explanation. All one can say about the phenomenon is to aver, every time one walks past a united object, ‘there it goes again’. Perhaps one has to be a philosophical quietist about some things. But giving up without a fight is an untoward defeatism. And if a perfectly good explanation can be found, as I shall argue that it can, unwarranted. Of course, explanations always come at a cost—some kind of commitment; and the explanation I shall offer is no exception. The cost in this case is revising how it is we currently think that certain things, and especially identity, work. But such is to be expected in any conceptual advance.Thus, for several hundred years scientists had no account of how gravitational effects are transmitted. Everything has an instantaneous effect on everything else, and that is that. No explanation. Since Einstein, we now have an explanation; but the explanation has caused major revisions in our conceptions of space, time, matter. The cost of a revision may be entirely warranted.

(13)

[contents]

 

 

 

 

1.5.7

[The Causal Process Account of Unity and Its Failure]

 

[Accounts of unity that merely describe the causal processes that go into something’s generation or production, like a carpenter’s explanation of how to construct a table, satisfy to some extent the how curiosity we have for an account of unity. But they fall short for a number of reasons. {1} They do not explain the unity brought about but only the processes bringing it about. {2} They lack an explanation for what makes unifying causal processes different from non-unifying ones. And {3} they cannot explain the unity of abstract objects.]

 

Priest next discusses explanations of unity that are simply accounts of the causal processes that are needed for the unity to come about. He says that such explanation are not satisfactory. For, such explanations do not tell us about what the thing actually is as the unity that it is. It simply tells us how that unity comes into being. He gives the example of marriage. To explain how to get married tells us nothing about what marriage is. Also, not all causal processes produce unities [so to use causal processes as the basis of the account still requires an explanation of what makes these unifying causal processes different from those that do not produce unities.] And lastly, even if we were satisfied with such causal accounts, they would only work for explaining the unities of physical things and not of “abstract objects, such as propositions, pieces of music (types, not tokens), sets” (14).

Alternatively, one might suggest that no explanation in the pertinent sense is called for. What constitutes the unity of a table? Simply that I take a piece of wood and nail four legs to it in appropriate places. There is nothing more to be | said. This will not do, however. What we are being offered here is an explanation of how the unity came into being – the causal processes that brought it about. Now, explaining how something is brought about is not explaining what it is that has been brought about. To explain how to get married is not to explain what a marriage is. One who nails the legs to a table top in the appropriate way has indeed brought the table into existence by certain causal processes. But causal processes are going on all around us, and only some of them bring objects into existence. So what is it that one which does so, actually does? In any case, the suggestion, appealing as it does to causal processes, can account at best for the unity of things subject to such processes. It cannot account for the unity of abstract objects, such as propositions, pieces of music (types, not tokens), sets.

(13-14)

[contents]

 

 

 

 

1.5.8

[The Lack of Convenient Accounts of Unity]

 

[Thus, we do not have any easy ways to account for unity.]

 

Priest ends by saying, “There are no easy roads here” [for, we have seen all of our viable options, and none works well enough. Priest’s own suggestion is probably not an “easy” road either, as it will involve tweaking some fundamental concepts. But although it is not easy, at least it will work, unlike with our other options.] (14)

[contents]

 

 

 

 

 

Bibliography:

 

Priest, Graham. 2014. One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University.

 

 

Or if otherwise cited:

 

Bradley, F. H. (1922), The Principles of Logic, Oxford: Oxford University Press.

 

Schaffer, J. (2010b), ‘The Internal Relatedness of All Things’, Mind 119: 341–75.

 

 

 

 

 

.

16 Apr 2018

Priest (10.1) An Introduction to Non-Classical Logic, ‘Introduction [to ch.10 “Relevant Logics”], summary

 

by Corry Shores

 

[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

[Logic and Semantics, entry directory]

[Graham Priest, entry directory]

[Priest, Introduction to Non-Classical Logic, entry directory]

 

[The following is summary of Priest’s text, which is already written with maximum efficiency. Bracketed commentary and boldface are my own, unless otherwise noted. I do not have specialized training in this field, so please trust the original text over my summarization. I apologize for my typos and other unfortunate mistakes, because I have not finished proofreading, and I also have not finished learning all the basics of these logics.]

 

 

 

 

Summary of

 

Graham Priest

 

An Introduction to Non-Classical Logic: From If to Is

 

Part I:

Propositional Logic

 

10.

Relevant Logics

 

10.1

Introduction

 

 

 

 

Brief summary:

(10.1.1) In this chapter Priest will introduce relevant logics, which “are obtained by employing a ternary relation to formulate the truth conditions of →” and which can be made stronger by adding constraints to that ternary relation. (10.1.2) Also we will combine relevant semantics with the semantics of conditional logics “to give an account of ceteris paribus enthymemes” (188).

 

 

 

 

 

Contents

 

10.1.1

[Relevant Logics and Their Ternary Relation and Its Constraints]

 

10.1.2

[Combining Relevant and Conditional Semantics to Account for Ceteris Paribus Enthymemes]

 

 

 

 

 

 

Summary

 

10.1.1

[Relevant Logics and Their Ternary Relation and Its Constraints]

 

[In this chapter Priest will introduce relevant logics, which “are obtained by employing a ternary relation to formulate the truth conditions of →” and which can be made stronger by adding constraints to that ternary relation.]

 

In this chapter Priest will introduce us to relevant logics. He says that “These are obtained by employing a ternary relation to formulate the truth conditions of →” (188). Although the most basic relevant logic does not have any constraints on this ternary relation, stronger relevant logics can be obtained by adding constraints. [I am not certain, but a “stronger” system might mean that it has more valid formulas. But I could be completely wrong, sorry. See section 4.4.4 for more discussion.]

In this chapter we look at logics in the family of mainstream relevant logics. These are obtained by employing a ternary relation to formulate the truth conditions of →. In the most basic logic, there are no constraints on the relation. Stronger logics are obtained by adding constraints.

(188)

[contents]

 

 

 

 

10.1.2

[Combining Relevant and Conditional Semantics to Account for Ceteris Paribus Enthymemes]

 

[Also we will combine relevant semantics with the semantics of conditional logics “to give an account of ceteris paribus enthymemes” (188).]

 

[As I have not yet summarized anything from chapter 5, I will need to simply quote the next lines.]

We also see how these semantics can be combined with the semantics of conditional logics of chapter 5 to give an account of ceteris paribus enthymemes.

(188)

[contents]

 

 

 

 

 

From:

 

Priest, Graham. 2008 [2001]. An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University.

 

 

 

 

 

.