Shores. Jc Beall’s Current and Potential Impact on the Continental Philosophy of Non-Classical Logics (Author Manuscript)

by Corry Shores

 

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In accordance with the archiving and open access policies of Springer Nature, I am making a PDF of the Author Manuscript (AM) available here on my personal website.

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at:

http://dx.doi.org/10.1007/s44204-023-00071-5

To access the final published version, please reach the publisher using that link or contact the author at corryshores@gmail.com or through Research Gate.

 

 

Corry Shores

Jc Beall’s Current and Potential Impact on the Continental Philosophy of Non-Classical Logics

 

PDF LINK

 

 

 

 

Shores, Corry. “Jc Beall’s Current and Potential Impact on the Continental Philosophy of Non-Classical Logics.” Asian Journal of Philosophy 2, no. 1 (2023): 1–12. doi:10.1007/s44204-023-00071-5.

https://link.springer.com/article/10.1007/s44204-023-00071-5

http://dx.doi.org/10.1007/s44204-023-00071-5

 

Research Gate link:

https://www.researchgate.net/publication/370444805_Jc_Beall%27s_current_and_potential_impact_on_the_continental_philosophy_of_non-classical_logics_in_the_Asian_Journal_of_Philosophy

Shores. Logic of Gilles Deleuze: Basic Principles. Announcement and Preview

 

by Corry Shores

 

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Announcement and Preview of

 

Corry Shores

 

The Logic of Gilles Deleuze:

Basic Principles

[Publisher’s book-webpage]

 

 

 

 

 

My book on Deleuze’s logic is now in press. A preview of the table of contents, acknowledgments, and introduction is available here:

https://www.academia.edu/44372079/The_Logic_of_Gilles_Deleuze_Basic_Principles

 

The publisher offers a preview of the first chapter here:

https://bloomsburycp3.codemantra.com/viewer/5f4e5a6fdc0e82000176fab1

 

 

Here is the publisher’s webpage for the book:

https://www.bloomsbury.com/us/the-logic-of-gilles-deleuze-9781350062252/

 

And here is an Amazon.com link:

The Logic of Gilles Deleuze: Basic Principles (Bloomsbury Studies in Continental Philosophy)

 

 

 

I thank a number of people in the acknowledgements (also see below). But here on this blog post I want to especially thank readers of this blog who have helped me on the book and supported me throughout the process, including Clifford Duffy, Terrance Blake, and Scott Wollschleger.

 

 

 

Full Acknowledgements:

This book was first made possible by Roland Breeur, who recommended me to the person who became one of my main editors, Liza Thompson. Much of what I know about philosophy and how it should be conducted, I learned from Prof. Breeur. And Liza, along with my other editors, Frankie Mace and Lucy Russell, have extended to me an incredible amount of generosity with the scheduling for the book. It never would have made it without their help, so I thank you all very much.

The basic content of the book was first made possible by the participants and organizers of the 2014 Paraconsistent Reasoning in Science and Mathematics conference at Ludwig Maximilian University: Peter Verdée, Holger Andreas, David Ripley, Graham Priest, Diderik Batens, Fenner Tanswell, Marcos Silva, Bryson Brown, Hitoshi Omori, Heinrich Wansing, Andreas Kapsner, Cian Chartier, Franz Berto, Itala Maria Loffredo D’Ottaviano, Zach Weber, João Marcos, Luis Estrada-González, Nick Thomas, Maarten McKubre-Jordens, Maria Martinez, Diego Tajer, and Otávio Bueno. They graciously allowed me to present, despite being quite incapable with logic, and they afterward did much to help me begin my project. Peter Verdée and Holger Andreas edited an edition of the proceedings for Springer, and they were kind enough to include my paper in it, the text of which is partly used here. I thank everyone for getting me started in non-classical logics, which still I love to this day.

I could not have written this book without the enduring, loving support of my wife, Gülben Salman. Her sacrifices and efforts are the reason I was able to do all the work necessary here. As a philosopher herself, she also made substantial contributions throughout the whole compositional process, and I cannot thank her enough. Gülben, I dedicate this book to you. I also thank Yasin Ceylan, Aziz Fevzi Zambak, Deniz Yılmaz Zambak, Aret Karademir, Hikmet Ünlü, Bolkar Özkan, Scott Wollschleger, Kurt Ozment, Samet Bağçe, Karen Vanhercke, Vykintas Baltakas, along with my family, Patricia, Ebbie Victor, Fatma, Hasan, Ebbie Paul, Brandon, Aimee, Mandy, Austin, and Joseph for the companionship, support, and advice they gave me all throughout.

Certain parts specifically benefited from help I received from other scholars. Oğuz Akçelik reviewed the logic parts (and any mistakes are mine). Many of the cinema parts (Chapters 4, 7, 8) were made possible by the guidance and teaching of Ahmet Gürata. The section on Plato in Chapter 8 was improved with Hikmet Ünlü’s expert assistance, and his instruction in Ancient Greek proved indispensable for working through the Stoic material in Chapter 5. Dorothea Olkowski taught me about intuitionism and its importance in Deleuze’s philosophy, so all of Chapter 6 was made possible by her writings and comments, and also she reviewed and made suggestions on most of Chapter 5. Roland Breeur’s work on imposture influenced much of what I write on the Falsifier in Chapter 8, and he reviewed and made suggestions for both Chapters 7 and 8. Along the way, I also received help with interpretation, sourcing, and translation from Antoine Dolcerocca, Terence Blake, Clifford Duffy, Roger Vergauwen, Julie Van der Wielen, Griet Galle, Iain McKenzie, Guillaume Collet, and Steven Spileers. Meriç Aytekin contributed much to the sourcing in Chapter 2, and Çi̇si̇l Vardar, to Chapter 1. At the beginning stages, my project benefitted from the comments provided by anonymous referees and from Ronald Bogue. I am very grateful to them. And I have taken great inspiration from the work of Jeffrey Bell, who has pioneered this particular field of study and whose advice I deeply appreciate. I am also heavily indebted to the archivists, transcribers, and translators (listed in the bibliography, but let me here mention Richard Pinhas) who have made Deleuze’s courses accessible. I thank everyone mentioned here so very much.

And many of the logic parts were improved through my correspondences and conversations with Graham Priest. His philosophy is the original inspiration for this book, and he has been nothing but the most generous and supportive toward this project. I thank him for patiently and thoroughly answering all of my questions about his writings and ideas. The philosophical world is so much better because of him, and I will always be deeply grateful.

I also could not have completed this book without the support and understanding of my colleagues at the Middle East Technical University: Halil Turan, Barış Parkan, Murat Baç, David Grünberg, Ayhan Sol, Samet Bağçe, Elif Çırakman, Mehmet Hilmi Demir, Aziz Fevzi Zambak, Fulden İbrahimhakkıoğlu, Yasin Ceylan, Teo Grünberg, Ahmet İnam, Ertuğrul Rufayi Turan, Refik Güremen, James Griffith, Selma Aydın Bayram, Dilek Başar Başkaya, Ercan Erkul, Gülizar Karahan Balya, Hikmet Ünlü, Erdinç Sayan, and Tahir Kocayiğit. (Ayhan Sol helped me especially with freeing up my scheduling for more time to write.)

Many students in my classes and seminars have contributed ideas and insights to this book, including: Bolkar Özkan, Gürkan Kılınç, Ilgın Aksoy, Yıldırım Bayazit, Faik Tekin Asal, Ekin Demirors, Hazal Babur, Tanayça Ünlütürk, Aybüke Aşkar, Meli̇ke Başak Yalçın, Ulaş Murat Altay, Sedef Beşkardeşler, Toprak Seda Karaosmanoğlu, İlkyaz Taşdemir, Çınar Uysal, Handan Ağirman, Tunahan Akbulut, Yasemin Karabaş, Aybüke Aşkar, Mahsasadat Shojaei, Umut Kesi̇kkulak, Ayşe Pekdiker, Seyran Sam Kookiaei, Atakan Botasun, Esra Saçlı, Firuza Rahimova, Sona Mustafayeva, İrem Kayra Özdemir, Erkan Özmacun, Ezel Ortaç, Rada Nur Ergen, and Yiğit Baysal. I thank all of you for your interest in these topics, for your original philosophical thinking, and for helping me interpret the texts.

And finally, I thank the following publishers and journals who granted me permission to reprint texts and figures (and additionally, I thank their blind referees, who helped me improve the articles):

Tijdschrift voor Filosofie / Peeters Publishers. (“The Primacy of Falsity: Deviant Origins in Deleuze.” TijdschriftVoorFilosofie 81 (2019): 81–130).

Routledge. (“Affirmations of the False and Bifurcations of the True: Deleuze’s Dialetheic and Stoic Fatalism.” In Deleuze and Guattari’s Philosophy of Freedom: Freedom’s Refrains, edited by Dorothea Olkowski and EftichisPirovolakis, 178–223. New York: Routledge, 2019.)

Springer. (“Dialetheism in the Structure of Phenomenal Time.” In Logical Studies of Paraconsistent Reasoning in Science and Mathematics, edited by Holger Andreas and Peter Verdée, 145-157. Cham, Switzerland: Springer, 2016.)

Deleuze and Guattari Studies / Edinburgh University Press. (“In the Still of the Moment: Deleuze’s Phenomena of Motionless Time.” Deleuze Studies 8, no. 2 (2014): 199–229.)

 

 

Shores, Corry. The Logic of Gilles Deleuze: Basic Principles. London: Bloomsbury, 2020.

[Publisher’s book-webpage]

 

 

 

 

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Priest (CBS) “Dialectic and Dialetheic,” collected brief summaries

 

by Corry Shores

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Collected Brief Summaries for

 

Graham Priest

 

“Dialectic and Dialetheic”

 

 

Introduction:

Dialectics Requires Dialetheism

 

Priest will argue that Hegel’s and Marx’s dialectics were based on dialetheia, that is, on true contradiction.

 

 

1

Why It Is Necessary to Argue This

 

Many scholars argue that Marx’s and Hegel’s dialectics involve a non-logical notion of contradiction or that contradiction is conceptual and does not obtain in reality. Priest, however, will argue that the logical sense of contradiction is fundamental to their philosophies of dialectic.

 

 

 

2

The Argument Against this Interpretation

 

The main argument against reading Hegel and Marx as dialetheists is that it goes against the basic restriction of classical logic that you cannot have contradictions. But this restriction is based on an assumption and is thus not a necessary one.

 

 

 

3

Dialetheic Logic

 

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.

 

 

 

4

Motion: An Illustration

 

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.

 

 

 

5

The History of Hegel’s Dialectic

 

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.

 

 

 

6

Contradiction in Hegel’s Dialectic

 

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].

 

 

 

7

Contradiction in Marx’s Dialectic

 

 

 

8

Identity in Difference

 

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.

 

 

 

9

Dialectics and Epistemology

 

 

 

10

Conclusion

 

 

 

 

 

 

Priest, Graham. “Dialectic and Dialetheic.” Science & Society 53, no. 4 (1990): 388–415.

 

 

 

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Priest (CBS) Logic: A Very Short Introduction, collected brief summaries

 

by Corry Shores

 

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[The following collects the brief summaries for Priest’s book. The directory of entries without the summaries is found here:

http://piratesandrevolutionaries.blogspot.com/2015/07/entry-directory-priest-logic-very-short.html

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Collected Brief Summaries for:

 

Graham Priest

 

Logic: A Very Short Introduction

 

 

Preface

 

Logic is an ancient discipline that was revolutionized in the 20th century with mathematical techniques and is currently very useful in information and computational sciences. This book will give a brief, broad, and non-technical overview.

 

 

Ch.1

Validity: What Follows from What?

 

“Logic is the study of what counts as a good reason for what, and why” (Priest, 1). An inference draws a conclusion from premisses (or from a premiss). It is valid if the conclusion follows from those premisses. It is deductively valid if it necessarily follows, that is, if no other conclusion could possibly follow, and it can be determined as such when “there is no situation in which all the premisses are true, but the conclusion is not.” An inductively valid inference is based on reasoning given in the premisses, yet other conclusions could also follow instead.

 

Ch.2

Truth Functions – Or Not?

 

Our intuitions about the validity of inferences are often correct, but sometimes they are misleading. One such case is the inference: q, ¬q / p, for example, “The Queen is rich,” “The Queen is not rich,” therefore “Pigs can fly”. Since the conclusion seems logically unrelated, we might erroneously think it is an invalid inference. By rendering these sentences into symbols and computing their truth values, we can see that there is no instance when the premisses are true and the conclusion not-true (false), and thus indeed it is valid. But since there is no situation where both the premisses can be true anyway, it is called vacuously valid. We also learn the truth tables for negation, disjunction, and conjunction, which are based on the truth conditions for these operations. If a sentence is true, then its negation is false, and vice versa. A disjunction is true only if at least one disjunct is true. And a conjunction is true only if both conjuncts are true. But conjunctions and disjunctions in English do not always map perfectly onto these truth tables.

 

 

 

Ch.3

Names and Quantifiers: Is Nothing Something?

 

When we speak of things, we might refer to some specific thing by name, like if we say, “Marcus came to the party”. In this case, what we are saying refers just to this one named person or thing. Or we might speak broadly and universally of all of a group of things, like if we said, “everyone came to the party”. In this case, what we say of the people or things applies to all of them. Or, we might refer to some thing, but without designating it specifically with a name, like when we say, “Someone came to the party”. Here we are saying something about a person or thing, but we are not specifying which one. When we want to speak of some thing or another, as in, “someone is happy,” we could use the existential quantifier and formulate this as, ∃x xH, meaning, there is some x such that x is happy. Or if we wanted to say, “Everyone is happy,” we could write ∀x xH, meaning, for all x, x is happy. Note that from just one quantified sentence an inference can be drawn. For example, if all people are happy, then there is some person who is happy. By using quantification, we can settle debates in mathematics and philosophy.

 

 

Ch.4

Descriptions and Existence: Did the Greeks Worship Zeus?

 

A definite description specifies a thing satisfying certain conditions, for example, “the man who first landed on the Moon”. Descriptions can be formulated symbolically by the use of variables that are predicated. The overall formulation takes the form ιxc_x. Here, the ιx means, “the object x, such that…”, and the c_x gives the conditions specifying the object. In our example we could write ιx(xM & xF) to mean, “the object x such that x is a man and x first landed on the Moon”. Furthermore, we may treat the whole description as something that can take predicates, and we can use Greek letters to stand for the whole description, thus possibly making the above formulation simply μ. This abbreviation will help us examine the validity of the Characterization Principle (CP), which is used in the Ontological Argument for God. We describe God as having a variety of properties that specify God, with the final one being “exists”: ιx(xP₁ & … & xP_n). The CP says that a thing characterized by certain properties in fact has those properties, and thus the whole described thing is predicated by the properties given in the description. Symbolically this involves substituting all cases of x in the description with that description itself. In this formulation we would get: ιx((xP₁ & … & xP_n)P₁ & … & (xP₁ & … & xP_n)P_n), which in part says that the object that is omniscient etc., and exists, is in fact omniscient, etc., and does really exist. Using the Greek letters we can render the above substitution as: γP₁ & … & γP_n. But there is an important rule this argument breaks, namely that any predication to a non-existing entity is false. If there is a God, then the predication that God exists is true; but if there is no God in reality, then this predication is false. This means that for the argument to work, it must assume the truth of its conclusion at the outset, and is thus invalid. Yet there are cases where this rule does not apply, for example in instances of fictional entities like Greek gods whose properties can rightly be predicated to their description even though the thing described does not exist.

 

 

Ch.5

Self Reference: What is this Chapter About?

 

Paradoxical and otherwise problematic instances of self-reference lead us to suspect that we have more options than the following two: 1) a sentence can be just true, or 2) a sentence can be just false. Consider the “liar” sentence, ‘This sentence is false.’ If it is true, then it is false; but if it is false, then it is true. Either way, it’s truth-value will contradict what it says its truth-value is. So we have option 3) a sentence can be both true and false. Or consider the “liar cousin” sentence, ‘This sentence is true.’ Normally the terms in such a declarative sentence refer to things or situations by which we may determine the truth or falsity of the statement, that is to say, whether or not the indicated situation holds in reality or not. So if we say, “this chair is red,” we look to the indicated chair and its color, and we determine if the sentence is true or not. However, the terms in “this sentence is true” does not point us to such a determining situation, since we are only able to make two equally viable assumptions about its truth value, namely, that it is either true or that it is false; but, we have no way to make the determination one way or another, since it will always be consistent with what it says of itself under both assumptions. It would seem that we have no grounds that would allow us to determine whether it is true or false, and thus we have option 4) a sentence may be neither true nor false. The classical assumptions 1 and 2 lead us to conclude certain inferences are valid when our intuitions say otherwise. For example, “The Queen is rich,” “The Queen isn’t rich,” therefore, “Pigs can fly” (q, ¬q/p). Our intuitions tell us this seems invalid. But by just using assumptions 1 and 2, it is valid, since structurally speaking there is no situation where the premises are true and the conclusion is false. For, the premises can never all be true anyway. However, under the new assumptions, particularly that sentences can be both true and false, q, ¬q/p can be valid, if q is both true and false and p just false. For, q is at least true and ¬q is also at least true. However, our intuitions tell us that q∨p, ¬q/p is valid, but the new assumptions deem it invalid. Yet, perhaps it only seems intuitively valid if we forget that there are exceptional situations where sentences can be both true and false. There are other problems with the assumptions. When we assume that the liar cousin, “This sentence is true,” is neither true nor false, that means it cannot be true, but it says of itself that it is true. And while we might go along with saying that “This sentence is false” is both true and false, we might not feel the same way about “This sentence is not-true”. Here, we might conclude that it is both true and not-true (and not just true and false), which is a stronger contradiction that we may not want to accept.

 

 

Ch.6

Necessity and Possibility: What Will be Must be?

 

We can modify a statement of fact to indicate whether or not the referenced state of affairs is possibly the case or necessarily so. Modal logic allows us to deal with these modifications formally. Suppose “it will rain” is p. We write, “Possibly it will rain” as ⋄p, and we write “necessarily it will rain” as ◻p. Unlike truth-functional operators (like negation and conjunction), these modal operators do not alter the truth values of statements in a mechanically consistent way. To formally examine modally modified sentences, we think of there being other possible worlds about which we may make the same statements of fact, and these statements may be true or false depending on which alternate possible world it is in. In one possible world, it does rain tomorrow. But in another, it will not. We say something is possible when in at least one other world this state of affairs is false. However, no matter what possible world we conceive of, in all of them, if it rains, then fluid is falling. Such things which cannot be otherwise, when for example they are governed by fixed laws of physics, are considered necessarily true; for, in every other possible world they are true. We can diagram these possible world situations using boxes. In one box we give the statements of fact and their truth values for one situation or world (this world for example), and in other boxes we give the statements and their values for the other possible worlds. This helps us see which statements are necessarily true or false in one world and which are possibly so. This manner of formulation helps with certain debates, for example, it allows us to see that Aristotle’s argument for fatalism is fallacious. The argument makes us think that there is nothing we can do now to change the future, and also, that there is nothing in the past that we can regret or feel responsible for. The reasoning is as follows. If it is true that something will happen, then it will happen no matter what. But if it is false that something will happen, it will fail to happen no matter what. Either way, whatever happens occurs no matter what. By formulating this using modal logic, we see that it infers something incorrectly. There is a difference between the following two claims: 1) it is necessarily the case that if it is true that tomorrow I will get in an accident, then I will get in an accident, and 2) if it is true that if I will get in an accident, then I will necessarily get in an accident. If we just look at the semantic references, both formulations seem to have the same meaning. But on the level of their logical structure they are making different claims, and also structurally the second claim cannot be derived from the first, which is what is needed for the argument to hold. Aristotle’s fatalist argument would want you to believe that in every possible world you will get in an accident tomorrow, which is not so. It even acknowledges that the opposite could happen. However, there is a way to twist this fatalist argument a bit to remove that fallacy, and we may wonder whether or not this modification provides a valid argument for fatalism. We first say that there is nothing we can do now to change the past. This implies that states of affairs in the past are irrevocably true and statements about those situations are necessarily true. Now, suppose we do get in an accident tomorrow. This means it is true now if we say that we will. Suppose further that we said it yesterday also. We can say now that in the past it was true that we will get in an accident tomorrow. This means that it is irrevocably true that in the past we will get into an accident, and thus it is necessarily true that we will.

 

 

Ch.7

Conditionals: What’s in an If?

 

Conditionals are of the form, “if a then c,” or a→c. The first term is the antecedent, and the second, the consequent. Conditionals are false only if the antecedent is true and the consequent false, and they are true for all other value assignments. But there are many difficulties regarding conditionals, and some of which call into question the universal applicability of these value-assignments. For example, according to the truth table for conditionals, when the antecedent is false, then the whole conditional is true, regardless of whether or not the consequent is true. This means that the following two conditionals should both be true: “If Italy is part of France, Rome is in France” and “If Italy is part of France, Beijing is in France”. But intuitively, the second one seems false. So conditionals are not truth-functional, since a lot depends on the meanings of the terms. In order to evaluate them, we can use possible worlds, like with modal operators: “the conditional a→c is true in some situation, s, just if c is true in every one of the possible situations associated with s in which a is true; and it is false in s if c is false in some possible situation associated with s in which a is true.” Since Rome is by definition in Italy, that means in no possible world would it not be in France, were Italy to be in France. So that is why the first sentence is true. However, since Beijing is by definition a city in China and not a city of Italy, then in some possible worlds Beijing will not be in France, were Italy to be in France. And that is why the second sentence is false. Another problem with conditionals has to do with ¬(a&¬c), which has the same truth table as a→c, and in fact is called the material conditional and is symbolized as a⊃c. But although we might think that we can infer a→c from ¬(a&¬c), this is not in fact a valid inference, and we can show this using the possible worlds analysis. The important difference between a→c and ¬(a&¬c) is that a→c involves the relevance of a to c, where there is no such relevance implied in ¬(a&¬c). For this reason we can think of situations where a→c will be false but ¬(a&¬c) will technically true, thereby invalidating the inference. There are other cases too of inferences using conditionals that seem valid, and yet there are troubling counter-examples that call their validity into question.

 

 

Ch.8

The Future and the Past: Is Time Real?

 

We can use tense logic to analyze the validity of inferences that are based on statements referring to different moments in time. We first think of a one-dimensional series of situations arranged in their proper chronological sequence. We then think of statements of fact. They may or may not be true for one temporalized situation or another. Suppose a statement h is true only for the temporally situated moment s₀. This statement refers to an instantaneous state of affairs, like the moment the first bullet entered Czar Nicolas’ heart. It will be false for all situations coming before and after that temporalized situation, since the event did not happen at those other moments. However, at a succeeding moment in the future, we can say truly that the event happened in the past. And likewise for a preceding moment in the past, we can say it will be happening in the future. We use the modifier P for past (“it was the case that”) and F for future (“it will be the case that”). So in moment s₁, Ph is true, and for moment s_-1, Fh is true. We can further designate temporal relations by compounding the modifiers. PPh would apply h to a situation coming before some other situation that is already in the past. FPh would apply h then to some situation coming after some other situation that is already in the past. Now, P and F refer to some determinate situation in the past or future. We can instead refer to all future situations with the modifier G (“it is always Going to be the case that”) and all past ones with the modifier H (“it Has always been the case that”). We can also make a model  for this tense logic by arranging in sequence a number of s’s, placing s₀ in the middle, and counting up and down the subscripts on both sides. This allows us to evaluate inferences based on tense modifiers. One example is McTaggart’s argument against the reality of time. If time is real, then the past and future are real, and thus they do not present logical contradictions. We then consider a sentence that is true just for the situation at one time-point. This means it did not happen in two temporally distinct time-points, and thus it did not happen both in the past and in the future: ¬(Ph&Fh). However, time flows, and so before it happened, it was in the future, and after it happened, it was in the past: Ph&Fh. The concepts of past and future present a contradiction, and thus time is unreal. One may object to the second formulation and say that it pretends that, for one situation that is located at one time point, the event can be both in the past and in the future. So to clarify the problem, we might then compound the modifiers and write ¬(PPh&FFh) to mean that the event did not happen at some determinate point coming before another in the past and at the same time happen at some determinate point coming after another in the future. Those following McTaggart’s reasoning can then say that still, because of the flow of time, PPh will be true and FFh was true, and thus, in contradiction with the prior, negated conjunction, PPh&FFh. But, by using the tense-logic model, we can display visually that the McTaggart argument is mistaken. There is never a singular temporalized situation where both terms in the past&future parings are true. Nonetheless, as this is a model that spatializes the flow of time, it might not be adequate for dealing with this argument about time’s non-spatial flow.

 

 

Ch.9

Identity and Change. Is Anything Ever the Same?

 

Over time, something’s properties might change. But it might either keep its identity or it might take on another one altogether. This presents a difficulty for philosophy and logic, especially since identity is a foundational concept in our thinking. We first distinguish objects and their properties, and we note that the properties may be variable while the objects remain constant. The ‘is’ of predication (x is red, or Rx) is different from the ‘is’ of identity (x is y, or x=y). However, Leibniz’s Law [of indiscernibles] uses properties to define identity. If two things share the same properties, then they are identical, and vice versa. This is a useful law in most applications, as for example when we use it for substituting terms in algebra. There are some other instances that at first seem to cast doubts on the applicability of the law, but these cases can be shown in the end to be mistaken for other reasons. However, there is one case that presents a big problem for the Law. We assume that identical things always were and always will be identical. When an amoeba A splits into amoebae B and C, then A has transformed into two other things in the sense of it having taken on new guises. This means that before the split, B and C  were identical to A and thus were identical to each other. However, after the split they are non-identical. This contradicts the assumption that things that are identical always are so.

 

 

Ch.10

Vagueness: How Do You Stop Sliding Down a Slippery Slope?

 

A thing can change gradually over time. A true statement about that thing’s status at the beginning can later be false at the end of the development. But in many cases, it is not clear when exactly during that development the status changes without ambiguity. “Jack is a child” is true when Jack is very young and not true when Jack is old; but, when precisely in his young adult years does it cease being entirely true and instead “Jack is an adult” becomes entirely true? This issue is related to sorites paradoxes. Consider that “Jack is a child” is true at the beginning, and “If Jack is a child at the beginning, then he is still a child one second later” also is probably also true. That means by modus ponens, “Jack is a child one second later” is true. Using this same sort of reasoning, we can then conclude that Jack is a child two seconds later, and so on, meaning that he never ceases being a child. (We reiterate the structure, taking the affirmed prior conclusion that Jack is still a child in the  succeeding second, and use it as a premise in an argument of the same structure, allowing us to conclude he is a child in yet the next succeeding second, and so on infinitely).  One solution to these issues is to use fuzzy truth values. We can say for example that when he is 3 years old, the statement “Jack is a child” has a full truth value of 1. At 9 years “Jack is  child” has a truth value of 0.75. At 14 years, 0.5. At 19 years, 0.25. And at 24 years, 0. And when we apply truth functional operators to statements with  values between 1 and 0, we can determine the different resulting fuzzy values. Also, we can say that an inference is valid when both the conclusion and the premises meet a certain minimum level of truth value, which is determined by the actual context to which the statements apply. What we find then is that the sorites paradox does not hold when we use this fuzzy system. [For, in order for the modus ponens inference to work in all steps, we will need the minimum value to be 0 (in order to accommodate the final transitional step), which is too low to be meaningful.] Also, fuzzy values do not clear up the situation entirely, because we have the same problem when we need to determine precisely at what point the values change from 1 to something less than 1.

 

 

 

 

 

 

 

 

 

Priest, Graham. Logic: A Very Short Introduction. 1st ed. Oxford: Oxford University, 2000.

Priest (7.7) An Introduction to Non-Classical Logic, ‘Truth-value Gluts: Paradoxes of Self-reference,’ 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]

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[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

 

7.

Many-Valued Logics

 

7.7

Truth-value Gluts: Paradoxes of Self-reference

 

 

 

 

Brief summary:

(7.7.1) We will now consider paradoxes of self-reference as motivation for advocating for truth-value gluts. (7.7.2) One paradox of self-reference is the liar’s paradox. For example, ‘this sentence is false’. “Suppose that it is true. Then what it says is the case. Hence it is false. Suppose, on the other hand, that it is false. That is just what it says, so it is true. In either case – one of which must obtain by the law of excluded middle – it is both true and false” (129). (7.7.3) Another paradox of self-reference is Russell’s Paradox: “Consider the set of all those sets which are not members of themselves, {x; x ∉ x}. Call this r. If r is a member of itself, then it is one of the sets that is not a member of itself, so r is not a member of itself. On the other hand, if r is not a member of itself, then it is one of the sets in r, and hence it is a member of itself. In either case – one of which must obtain by the law of excluded middle – it is both true and false. “ (7.7.4) There are many such arguments that come to a conclusion of the form A∧¬A, and supposing they are sound, that makes the conclusions true and thus means there really are truth-value gluts. (7.7.5) We will now examine briefly a couple claims that these paradoxical arguments are not sound. (7.7.6) Objection 1: All self-referential sentences are meaningless. Reply 1: But, there are many such meaningful sentences, like, ‘this sentence has five words’. (7.7.7) Objection 2: The liar sentence is neither true nor false. Thus our logical assumptions remove excluded middle, and we cannot develop the argument as, “either it is true or false; if false, then thus; if true then false; thus ...”. For, now we have a third situation, that it is neither. (7.7.8) Reply 2: “Extended Paradoxes” still present a contradiction. For example: “This sentence is either false or neither true nor false”. If true, it is either false or neither value. Either way, it is not true, which contradicts our assumption that it is true. If it is either false or neither valued (meaning that it is not true), then its value is what it claims to be, and thus it is true, which contradicts what we assumed. Reply 3: Some paradoxes of self-reference, like Berry’s paradox, do not invoke the law of excluded middle.

 

 

 

 

 

 

 

Contents

 

7.7.1

[Paradoxes of Self-Reference as Motivation for Gluts]

 

7.7.2

[The Liar’s Paradox]

 

7.7.3

[Russell’s Paradox]

 

7.7.4

[These Paradoxes of Self-Reference as Showing Truth-Value Gluts]

 

7.7.5

[Turning to Claims that the Paradoxes are not Sound]

 

7.7.6

[Objection 1: Self-Referential Sentences Are Meaningless. Reply 1: Not So in Many Cases]

 

7.7.7

[Objection 2: The Liar Sentence Is Neither True nor False]

 

7.7.8

[Reply 2: Extended Paradoxes Still Produce Contradiction. Reply 3: Not All Paradoxes of Self-Reference Invoke the Law of Excluded Middle]

 

 

 

 

Summary

 

 

7.7.1

[Paradoxes of Self-Reference as Motivation for Gluts]

 

[We will now consider paradoxes of self-reference as motivation for advocating for truth-value gluts.]

 

[In the previous section 7.6, we examined a motivation for arguing for truth-value gluts, namely, inconsistent laws. We consider now another motivation: paradoxes of self-reference. There are both old and modern ones.]

A second argument for the existence of truth-value gluts concerns the paradoxes of self-reference. There are many of these; some very old; some very modern. Here are a couple of well-known ones.

(129)

[contents]

 

 

 

 

 

 

7.7.2

[The Liar’s Paradox]

 

[One paradox of self-reference is the liar’s paradox. For example, ‘this sentence is false’. “Suppose that it is true. Then what it says is the case. Hence it is false. Suppose, on the other hand, that it is false. That is just what it says, so it is true. In either case – one of which must obtain by the law of excluded middle – it is both true and false” (129).]

 

[(ditto)]

THE LIAR PARADOX: Consider the sentence ‘this sentence is false’. Suppose that it is true. Then what it says is the case. Hence it is false. Suppose, on the other hand, that it is false. That is just what it says, so it is true. In either case – one of which must obtain by the law of excluded middle – it is both true and false.

(129)

[contents]

 

 

 

 

 

 

7.7.3

[Russell’s Paradox]

 

[Another paradox of self-reference is Russell’s Paradox: “Consider the set of all those sets which are not members of themselves, {x; x ∉ x}. Call this r. If r is a member of itself, then it is one of the sets that is not a member of itself, so r is not a member of itself. On the other hand, if r is not a member of itself, then it is one of the sets in r, and hence it is a member of itself. In either case – one of which must obtain by the law of excluded middle – it is both true and false. “]

 

[(ditto) (See  section P.6 of One and ch.5 of Logic: A Very Short Introduction.)]

RUSSELL’S PARADOX: Consider the set of all those sets which are not members of themselves, {x; x ∉ x}. Call this r. If r is a member of itself, then it is one of the sets that is not a member of itself, so r is not a member of itself. On the other hand, if r is not a member of itself, then it is one of the sets in r, and hence it is a member of itself. In either case – one of which must obtain by the law of excluded middle – it is both true and false.

(129)

 

[contents]

 

 

 

 

 

 

7.7.4

[These Paradoxes of Self-Reference as Showing Truth-Value Gluts]

 

[There are many such arguments that come to a conclusion of the form A∧¬A, and supposing they are sound, that makes the conclusions true and thus means there really are truth-value gluts.]

 

[(ditto)]

These (and many others like them) are both prima facie sound arguments, and have conclusions of the form A∧¬A. If the arguments are sound, the conclusions are true, and hence there are truth-value gluts.

(129)

[contents]

 

 

 

 

 

 

7.7.5

[Turning to Claims that the Paradoxes are not Sound]

 

[We will now examine briefly a couple claims that these paradoxical arguments are not sound.]

 

[(ditto)]

Many people have claimed that the arguments are not, despite appearances, sound. The reasons given are many and complex; let us consider, briefly, just a couple.

(129)

[contents]

 

 

 

 

 

 

7.7.6

[Objection 1: Self-Referential Sentences Are Meaningless. Reply 1: Not So in Many Cases]

 

[Objection 1: All self-referential sentences are meaningless. Reply 1: But, there are many such meaningful sentences, like, ‘this sentence has five words’.]

 

[(ditto)]

Some have argued that any sentence which is self-referential, like the liar sentence, is meaningless. (Hence, such sentences can play no role in logical arguments at all.) This, however, is clearly false. Consider: ‘this sentence has five words’, ‘this sentence is written on page 129 of Part I of An Introduction to Non-Classical Logic’, ‘this sentence refers to itself’.

(129)

[contents]

 

 

 

 

 

 

7.7.7

[Objection 2: The Liar Sentence Is Neither True nor False]

 

[Objection 2: The liar sentence is neither true nor false. Thus our logical assumptions remove excluded middle, and we cannot develop the argument as, “either it is true or false; if false, then thus; if true then false; thus ...”. For, now we have a third situation, that it is neither.]

 

[The second objection is the most popular one. It says that the liar sentence is neither true nor false. This means that we cannot appeal to the law of excluded middle (because it is no longer the case that the sentence is either true nor false. How did we use it previously? I am not really sure. Maybe it goes like this, but I am guessing. We have the sentence, “this sentence is false.” Then we say, “Either it is true or it if false. If it were true, then it is false, and if it is false, then it is true. Either way, it is both true and false.” So maybe, the argument works by having the original proposal that it is either true or false. And maybe the idea now is that were it neither value, then the law of excluded middle does not hold, and so we cannot start off with the assumption “Either it is true or it is false; if true ...”. Or maybe we can start it that way, but it cannot end that way, because we have the third possibility to assess, that it is neither, meaning that we cannot further derive another value from it in addition to it being neither. I am not sure.) “Thus, the paradoxes of self-reference are sometimes used as an argument for the existence of truth-value gaps, too” (129).]

The most popular objection to the argument is that the liar sentence is neither true nor false. In this case, we can no longer appeal to the law of excluded middle, and so the arguments to contradiction are broken. (Thus, the paradoxes of self-reference are sometimes used as an argument for the existence of truth-value gaps, too.)

(129)

[contents]

 

 

 

 

 

 

7.7.8

[Reply 2: Extended Paradoxes Still Produce Contradiction. Reply 3: Not All Paradoxes of Self-Reference Invoke the Law of Excluded Middle]

 

[Reply 2: “Extended Paradoxes” still present a contradiction. For example: “This sentence is either false or neither true nor false”. If true, it is either false or neither value. Either way, it is not true, which contradicts our assumption that it is true. If it is either false or neither valued (meaning that it is not true), then its value is what it claims to be, and thus it is true, which contradicts what we assumed. Reply 3: Some paradoxes of self-reference, like Berry’s paradox, do not invoke the law of excluded middle.]

 

[(ditto)]

This suggestion does not avoid contradiction, however, because of ‘extended paradoxes’.³ Consider the sentence ‘This sentence is either false or neither true nor false.’ If it is true, it is either false or neither. In both cases it is not true. If, on the other hand, it is either false or neither (and so not true), then that is exactly what it claims, and so it is true. In either case, therefore, it is both true and not true.

(130)

3. Moreover, and in any case, not all of the paradoxical arguments invoke the law of excluded middle. Berry’s paradox, for example, does not.

(130)

[contents]

 

 

 

 

 

 

 

From:

 

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

 

 

 

 

 

 

 

.

 

Priest (7.6) An Introduction to Non-Classical Logic, ‘Truth-value Gluts: Inconsistent Laws,’ 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

 

7.

Many-Valued Logics

 

7.6

Truth-value Gluts: Inconsistent Laws

 

 

 

 

Brief summary:

(7.6.1) We will now examine philosophical motivations for advocating for multi-valued logics with truth-value gaps or gluts. (7.6.2) In this chapter subsection, Priest will elaborate on the issue of inconsistent laws. (7.6.3) For example, consider if long ago there were the laws {1} that no aborigines have the right to vote, but {2} all property-holders have that right. At the time it was unthinkable for aborigines to own property, but later in history they do. Thus in the legal system, later on in history, aborigines both have and do not have the right to vote. (7.6.4) In cases of insistent laws, normally they are rectified to make them consistent. Nonetheless, they will remain inconsistent for some time until that change will be made. (7.6.5) Priest next considers a possible objection, namely, that such seemingly contradictory laws are actually consistent, because there is always some other law that clarifies which of the two contradicting laws takes precedent; “for example lex posterior (that a later law takes precedence over an earlier law), or that constitutional law takes precedence over statute law, which takes precedence over case law. One might insist that all contradictions are only apparent” (128). (7.6.6) Priest’s reply to this objection is that while it may be that in actual fact there are many cases where additional laws dissolve the apparent legal contradiction, in principle it is still possible, as for example were both laws made at the same rank.

 

 

 

 

 

Contents

 

7.6.1

[Philosophical Motivations for Multi-Valued Logics]

 

7.6.2

[The Topic: Inconsistent Laws]

 

7.6.3

[An Example of Inconsistent Laws: Aborigine Land-Owners

 

7.6.4

[The Temporary Persistence of Inconsistent Laws]

 

7.6.5

[Objection: Other Laws are Always in Place to Clarify the Law that Takes Precedent]

 

7.6.6

[Reply: This Holds in Fact but not in Principle]

 

 

 

 

 

 

 

Summary

 

 

7.6.1

[Philosophical Motivations for Multi-Valued Logics]

 

[We will now examine philosophical motivations for advocating for multi-valued logics with truth-value gaps or gluts.]

 

[We are dealing with 3-valued logics, which have the truth values 1, 0, and i  (true, false, and indeterminate; see Nolt’s Logics section 15.2). We examined two pairings of 3-valued logics. The first pairing, K₃ and Ł₃, regards the value i as having the sense of neither true nor false (see section 7.3), and the second pairing, LP and RM₃, regard i as meaning both true and false (see section 7.4). (I am not sure how that distinction of their sense comes about from the semantics. My best guess is that it has something to do with the fact that for K₃ and Ł₃, the designated value is 1, and for LP and RM₃ it is 1 or i. So maybe if we think of validity as truth preservation, then to have i as a designated value means that it has at least some 1 in it, and when it is not a designated value means it has no 1 in it. I am just wondering aloud.) In the following sections we will consider some philosophical motivations for advocating for either truth-value gaps or gluts. The motivations for gaps will be denotation failure and future contingents. The motivations for gluts will be inconsistent laws and paradoxes of self reference. But Priest notes some other motivations for gluts that we will not examine here, namely: “the state of affairs realised at an instant of change; statements about some object in the border-area of a vague predicate; contradictory statements in the dialectical tradition of Hegel and Marx; statements with predicates whose criteria of application are over-determined; and certain statements about micro-objects in quantum mechanics” (128). See In Contradiction chapter 11 and 12 for inconsistency and motion, and see “Dialectic and Dialetheic” for contradiction in Hegel and Marx.]

Let us now turn to the issue of the philosophical motivations for many-valued logics and, in particular, the 3-valued logics we have met. Typically, the motivations for those logics that treat i as both true and false (a truth-value glut), like LP and RM₃, are different from those that treat i as neither true nor false (a truth-value gap), like K₃ and Ł₃. Let us start | with the former. We will look at two reasons for supposing that there are truth-value gluts.²

(127-128)

2. Other examples of truth-value gluts that have been suggested include the state of affairs realised at an instant of change; statements about some object in the border-area of a vague predicate; contradictory statements in the dialectical tradition of Hegel and Marx; statements with predicates whose criteria of application are over-dertermined; and certain statements about micro-objects in quantum mechanics.

(128)

[contents]

 

 

 

 

7.6.2

[The Topic: Inconsistent Laws]

 

[In this chapter subsection, Priest will elaborate on the issue of inconsistent laws.]

 

[In section 4.8.3, Priest gave an example where a contradiction of laws does not create a logical “explosion” entailing everything.

Another example: pieces of legislation are often inconsistent. To avoid irrelevant historical details, here is an hypothetical example. Suppose that an (absent-minded) state legislator passes the following traffic laws. At an unmarked junction, the priority regulations are:

(1) Any woman has priority over any man.

(2) Any older person has priority over any younger person.

(We may suppose that clause 2 was meant to resolve the case where two men or two women arrive together, but the legislator forgot to make it subordinate to clause 1.) The legislation will work perfectly happily in three out of four combinations of sex and age. But suppose that Ms X, of age 30, approaches the junction at the same time as Mr Y, of age 40. Ms X has priority (by 1), but has not got priority (by 2 and the meaning of ‘priority’). Hence, the situation is inconsistent. But, again, it would be stupid to infer from this that, for example, the traffic laws are consistent.

(p.75, section 4.8.3)

In this chapter subsection, Priest will elaborate on this matter of inconsistent laws.]

The first concerns inconsistent laws, and the rights and obligations that agents have in virtue of these. We have already had an example of this in 4.8.3 concerning inconsistent traffic regulations.

(128)

[contents]

 

 

 

 

7.6.3

[An Example of Inconsistent Laws: Aborigine Land-Owners]

 

[For example, consider if long ago there were the laws {1} that no aborigines have the right to vote, but {2} all property-holders have that right. At the time it was unthinkable for aborigines to own property, but later in history they do. Thus in the legal system, later on in history, aborigines both have and do not have the right to vote.]

 

[(ditto)]

Here is another example. Suppose that in a certain (entirely hypothetical) country the constitution contains the following clauses:

(1) No aborigine shall have the right to vote.

(2) All property-holders shall have the right to vote. We may suppose that when the law was made, the possibility of an aboriginal property-holder was so inconceivable as not to be taken seriously. Despite this, as social circumstances change, aborigines do come to hold property. Let one such be John. John, it would appear, both does and does not have the right to vote.

(128)

[contents]

 

 

 

 

7.6.4

[The Temporary Persistence of Inconsistent Laws]

 

[In cases of insistent laws, normally they are rectified to make them consistent. Nonetheless, they will remain inconsistent for some time until that change will be made.]

 

[(ditto)]

Of course, if a situation of this kind comes to light, the law is likely to be changed to resolve the contradiction. The fact remains, though, that until the law is changed the contradiction is true.

(128)

[contents]

 

 

 

 

7.6.5

[Objection: Other Laws are Always in Place to Clarify the Law that Takes Precedent]

 

[Priest next considers a possible objection, namely, that such seemingly contradictory laws are actually consistent, because there is always some other law that clarifies which of the two contradicting laws takes precedent; “for example lex posterior (that a later law takes precedence over an earlier law), or that constitutional law takes precedence over statute law, which takes precedence over case law. One might insist that all contradictions are only apparent” (128).]

 

[(ditto)]

One way that one might object to this conclusion is as follows. The law contains a number of principles for resolving apparent contradictions, for example lex posterior (that a later law takes precedence over an earlier law), or that constitutional law takes precedence over statute law, which takes precedence over case law. One might insist that all contradictions are only apparent, and can be defused by applying one or other of these principles.

(128)

[contents]

 

 

 

 

7.6.6

[Reply: This Holds in Fact but not in Principle]

 

[Priest’s reply to this objection is that while it may be that in actual fact there are many cases where additional laws dissolve the apparent legal contradiction, in principle it is still possible, as for example were both laws made at the same time or they are of the same rank.]

 

[(ditto)]

It is clear, however, that there could well be cases where none of these principles are applicable. Both laws are made at the same time; they are both laws of the same rank, and so on. Hence, though some legal contradictions may be only apparent, this need not always be the case.

(128)

[contents]

 

 

 

 

 

 

 

 

 

From:

 

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

 

 

 

 

 

 

 

.

 

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]

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[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.

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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

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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)

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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.

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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.

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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.

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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.

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23. See Priest (2006).

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

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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.

 

 

 

 

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