Frege (§5) Begriffsschrift, Chapter 1 (Geach transl.), ‘Conditionality’, summary

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Gottlob Frege

Begriffsschrift, Chapter 1
(Geach transl.)

§5 Conditionality

Brief Summary:
Frege explains how to notate in his system a conditional judgment. B implies A would look like:

Summary

[Frege is providing a notation system for describing conceptual relations. He will now look at conditional judgments (if .. then …). Let’s first recall their truth table.

p,   q | p => q
T,  T |     T
T,  F |     F
F,  T |     T
F,  F |     T

As you can see, the conditional is false when the antecedent is true but the consequent is false.]

Frege will now describe the notation for conditional judgments. He has us consider contents A and B. [In the conventional truth table formulation above, p, which precedes q alphabetically, is what implies q. If in the following formulation by Frege we in like manner make A imply B, then I cannot explain what he is saying. According to Jean-Yves Béziau in “A History of Truth Values,” (p.257) this should be interpreted as B implies A, and since that works, we will go with it. So we could make the table now:

A,  B | B => A
T,  T |     T
T,  F |     T
F,  T |     F
F,  F |     T

]

Frege writes:

If A and B stand for possible contents of judgment (§ 2), we have the four following possibilities:
(i) A affirmed, B affirmed;
(ii) A affirmed, B denied;
(iii) A denied, B affirmed;
(iv) A denied, B denied.

stands for the judgment that the third possibility is not realized, but one of the other three is. (5, red type mine)

[So because we are not affirming the antecedent while denying the consequent, this is valid, and so it can take the vertical judgment line.] But if we deny the truth of this consequence relation [and thus say it is invalid] then we must be affirming the antecedent while denying the consequent, and it will not receive the vertical line, even though its conceptual content is still expressible in this notation:

But we will consider that the above judgment is affirmed, and Frege will emphasize three points on this matter:

1) A is to be affirmed. [note that in the truth tables that when the consequent is affirmed, it does not matter whether or not the antecedent is affirmed or denied, as both produce valid judgments].

A is to be affirmed.- In this case the content of B is quite indifferent. Thus, let ⊢ A mean: 3 x 7 = 21; let B stand for the circumstance of the sun's shining. Here only the first two cases out of the four mentioned above are possible. A causal p. 6] connexion need not exist between the two contents. (5)

2) B is to be denied. [Notice in the truth table that when the antecedent is denied, that it does not matter what we say of the consequent; both cases will produce true judgments]

In this case the content of A is indifferent. E.g. let B stand for the circumstance of perpetual motion's being possible, and A for the circumstance of the world's | being infinite. Here only the second and fourth of the four cases are possible. A causal connexion between A and B need not exist. (5-6)

3) We may form the judgment

without knowing whether A and B are to be affirmed or denied. [This would be the case for example in a situation where if B holds then A would as well, but we do not know whether or not either is holding in actuality.] In such a case, we may formulate the conjunction with ‘if’.

'if the Moon is in quadrature with the Sun, then she appears semicircular.' The causal connexion implicit in the word 'if' is, however, not expressed by our symbolism; although a judgment of this sort can be made only on the ground of such a connexion. For this connexion is something general, and as yet we have no expression for generality. (6)

Frege then explains the individual lines of the notation for the conditional judgment. We already know that the vertical on the far left is the judgment stroke for the conceptual content of the conditional.

[We begin with B implies A. Then we turn that into a judgment, B implies A is a fact, and in the notation add the left-most vertical line to the rest of the symbol.] The vertical line connecting A and B is the conditional stroke.

[It says perhaps, the condition for B is A (or A conditions B), thus if you have B, you will also have A, or, B implies A.] The horizontal line to the left of the conditional stroke is the content stroke for the conceptual content of the conditional itself.

He writes: “any symbol that is meant to relate to the content of the expression as a whole will be attached to this content-stroke” (6). [The content stroke of the conditional perhaps says, the given lower subcontent is conditioned by the upper, but not yet judging that ‘it is a fact’.] The horizontal line between A and the conditional stroke is the content stroke of A, and likewise for B.

 

Frege, Gottlob. “Begriffsschrift (Chapter 1)”. Transl. P.T. Geach. In Translations from the Philosophical Writings of Gottlob Frege. Eds. P.T. Geach and Max Black. Oxford: Basil Blackwell, 1960, second edition (1952 first edition).

Jean-Yves Béziau. “A History of Truth Values.” In Logic: A History of Its Conceptual Contents. Dov M. Gabbay, Francis Jeffry Pelletier, and John Woods, eds. Amsterdam / London: North Holland (Elsevier), 2012

Frege (§4) Begriffsschrift, Chapter 1 (Geach transl.), summary

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Gottlob Frege

Begriffsschrift, Chapter 1
(Geach transl.)

§4

Brief Summary:

Frege examines different modifications to judgments, such as negation and necessary/possible modalities, and emphasizes his point that there is a conceptual content in judgments which is not affected by such logical variations.

Summary

[Frege is providing a notation system for describing conceptual relations. He previously distinguished the conceptual content, which is the basic meaning of a proposition (regardless of its subject-verb arrangement, and it is determined by its inferential behavior) from the judgment, which is this conceptual content plus ‘… is a fact’.] Since ‘… is a fact’ is not what would be universal or particular, these terms refer to contents and not to judgments.

The same holds for negation. [It seems that for Frege negation is not taking the proposition in quotes and speaking of it in a metalanguage and denying its truth in that metalanguage. Rather it seems that negation will have to at least on the level of the judgment itself involve a negation of the contents.] In fact, whether or not a content can be negated tells us if it can be a possible content of a judgment. (4)

The same thing holds good for negation. Thus, in an indirect proof one says ‘suppose the segments AB and CD were not equal.’ There is a negation involved here in the content: the segments AB and CD not being equal; but this content, though suitable matter for judgment, is not presented in the shape of a judgment. Negation thus attaches to the content, no matter whether this occurs in the shape of a judgment or not. I therefore hold it more suitable to regard negation as a mark of a possible content of judgment.
(4)

Later in this work Frege will support this claim he now gives: “The distinction of judgments into categorical, hypothetical, and disjunctive seems to me to have a merely grammatical significance.” (4)

Apodeictic judgments “indicate the existence of general judgments from which the proposition may be inferred,” while assertoric judgments do not (4). But if we say that a judgment is necessarily so [meaning that it is apodeictic] that will not change its content, and thus it will have no bearing on our current task of providing a conceptual notation.

When someone makes a possible [assertoric] judgment, they are refraining from judgment [judging the truth of the claim] and they are indicating that they are “not acquainted with any laws from which the negation of the proposition would follow”; otherwise they are “saying that the negation of the proposition is in general false.”(5a) This second case is called ‘a particular affirmative judgment’, and an example is ‘a chill may result in death’ [because the claim, ‘a chill may not result in death’ is generally (but not necessarily) false]. An example of the first case where the speaker is unacquainted with “any laws from which the negation of the proposition would follow” could be: ‘It is possible that the Earth will one day collide with another celestial body’ [because the speaker cannot think of a reason why this might be false] (5).

 

 

Frege, Gottlob. “Begriffsschrift (Chapter 1)”. Transl. P.T. Geach. In Translations from the Philosophical Writings of Gottlob Frege. Eds. P.T. Geach and Max Black. Oxford: Basil Blackwell, 1960, second edition (1952 first edition).

 

 

Frege (§3) Begriffsschrift, Chapter 1 (Geach transl.), summary

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Gottlob Frege

Begriffsschrift, Chapter 1
(Geach transl.)

§3

Brief Summary:

Often in logic we might distinguish the subject and what predicates it. Frege does not make this distinction in his own system of concept notation. This is because he recognizes a conceptual content which can be expressed with different subjects, as by inverting to a passive voice. For example, “the Greeks defeated the Persians at Plataea” and “the Persians were defeated by the Greeks at Plataea” have the same conceptual content but opposing subjects. The only real subject and predicate in his system are the conceptual content (in the form of a proposition) and the predicate, ‘… is a fact’, for example: ‘the violent death of Archimedes at the capture of Syracuse is a fact.’ This predicate is what his ⊢ symbol stands for.

Summary

[Frege is providing a notation system for describing conceptual relations.] In Frege’s notation system, we do not make the classical distinction in logic between a subject and a predicate. Frege provides his justification for this interesting decision. [I do not understand Frege’s formulation in the following, but it seems he is saying that given two propositions with different content, that content may either have the same power of inferential productivity as the other or it may have different inferential productivity (or maybe, the same or different inferential life), meaning that what each content implies is functionally isomorphic on the level of their inferential behavior. “the Greeks defeated the Persians at Plataea” and “the Persians were defeated by the Greeks at Plataea” literally have different contents and perhaps connotationally have slightly different contents. However, when we look at how inferences made by each interact with other judgments we see that they are inferentially similar. A possible counter-example might be “the Persians defeated the Greeks at Plataea” and “the Greeks defeated the Trojans at Troy” also have distinguishable contents, but in terms of their implications they are very different. But please interpret the following for yourself:]

A distinction of subject and predicate finds no place in my way of representing a judgment. In order to justify this, let me observe that there are two ways in which the content of two judgments may differ; it may, or it may not, be the case that all inferences that can be drawn from the first judgment when combined with | p. 3] certain other ones can always also be drawn from the second when combined with the same other judgments. The two propositions ‘the Greeks defeated the Persians at Plataea’ and ‘the Persians were defeated by the Greeks at Plataea’ differ in the former way; even if a slight difference of sense is discernible.
(2-3)

[The difference between “the Greeks defeated the Persians at Plataea” and “the Persians were defeated by the Greeks at Plataea” might be something like a connotational difference but not something conceptual. They both conceptually have the same content, and this was established by Frege as being a matter of their sharing the same inferential life.]

Now I call the part of the content that is the same in both the conceptual content. Only this has significance for our symbolic language; we need therefore make no distinction between propositions that have the same conceptual content.
(3)

[Perhaps what Frege is doing with the prior examples is showing how the same conceptual content can be expressed in sentences with different subjects.]

When people say ‘the subject is the concept with which the judgment is concerned,’ this applies equally well to the object. Thus all that can be said is: ‘the subject is the concept with which the judgment is chiefly concerned.’
(3)

In language, word order might matter, but conceptually it need not.

In my formalized language there is nothing that corresponds; only that part of judgments which affects the possible inferences is taken into consideration. Whatever is needed for a valid inference is fully expressed; what is not needed is for the most part not indicated either; no scope is left for conjecture. 
(3)

In Frege’s system, there is one basic predicate all conceptual content take in propositions, and that is ‘… is a fact’. This is the meaning of the ⊢ in his system.

In this I follow absolutely the example of the formalized language of mathematics; here too, subject and predicate can be distinguished only by doing violence to the thought. We may imagine a language in which the proposition ‘Archimedes perished at the capture of Syracuse’ would be expressed in the following way: ‘the violent death of Archimedes at the capture of Syracuse is a fact.’ You may if you like distinguish subject and predicate even here; but the subject contains the whole p. 4] content, and the only purpose of the predicate is to present this in the form of a judgment. Such a language would have only a single predicate for all judgments, viz. ‘is a fact.’ We see that there is no question here of subject and predicate in the ordinary sense. | Our symbolic language is a language of this sort; the symbol ⊢ ­ is the common predicate of all judgments.
(3-4)

Frege, Gottlob. “Begriffsschrift (Chapter 1)”. Transl. P.T. Geach. In Translations from the Philosophical Writings of Gottlob Frege. Eds. P.T. Geach and Max Black. Oxford: Basil Blackwell, 1960, second edition (1952 first edition).

 

 

Frege (§2) Begriffsschrift, Chapter 1 (Geach transl.), “Judgment”, summary

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Gottlob Frege

Begriffsschrift, Chapter 1
(Geach transl.)

§2
Judgment

Brief Summary:

In Frege’s conceptual notation system, ⊢ is the sign used for a judgment such that

could for example mean “unlike magnetic poles attract one another.”

Summary

[Frege is providing a notation system for describing conceptual relations.] The sign used for judgment is ⊢

“This stands to the left of the sign or complex of signs in which the content of the judgment is given” (1d)

[The whole sign itself seems to represent a whole judgment or proposition. The horizontal line seems to just be for the ideas in the judgment, and by adding the vertical line we seem to be indicating that certain ideas are predicated to certain subjects. For,] by omitting the vertical line, we are left with a ‘mere complex of ideas’. So if we take

to mean, “unlike magnetic poles attract one another,” then

will only “produce in the reader the idea of the mutual attraction of unlike magnetic poles.”

[Frege seems to be saying that this mere complex of ideas can then be developed into a fuller judgment perhaps by adding to it (qualifying it) with expressions such as ‘the circumstance that’ or ‘the proposition that’. I suppose this would mean it would produce something like in this example ‘the circumstance that unlike magnetic poles mutually attract…’ and then something would be inferred by this by implication, but I am not sure. Please interpret the following sentences for yourself:]

it will be intended just to produce in the reader the idea of the mutual attraction of unlike magnetic poles-so that, e. g., he may make inferences from this thought and test its correctness on the basis of these. In this case we qualify the expression with the words 'the circumstance that' or 'the proposition that.'
(2)

Some contents cannot be made into judgments merely by adding the ⊢ in front of them. One example is the idea of ‘house’.

 

[Frege then goes on to further distinguish the horizontal from the vertical line. You will have to interpret the following for yourself, but the main idea seems to be that the horizontal line is for the contents whose logical relations are not inherently specified and the vertical is for the judgment that predicates or otherwise relates those contents.]

As a constituent of the sign ⊢ the horizontal stroke combines the symbols following it into a whole; assertion, which is expressed by the vertical stroke at the left end of the horizontal one, relates to the whole thus formed. The horizontal stroke I wish to call the content-stroke, and the vertical the judgment-stroke. The content-stroke is also to serve the purpose of relating any sign whatsoever to the whole formed by the symbols following the stroke. The content of what follows the content-stroke must always be a possible content of judgment.
(2)

Frege, Gottlob. “Begriffsschrift (Chapter 1)”. Transl. P.T. Geach. In Translations from the Philosophical Writings of Gottlob Frege. Eds. P.T. Geach and Max Black. Oxford: Basil Blackwell, 1960, second edition (1952 first edition).

 

Frege (§1) Begriffsschrift, Chapter 1 (Geach transl.), “Explanation of the Symbols”, summary

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Gottlob Frege

Begriffsschrift, Chapter 1
(Geach transl.)

§1
Explanation of the Symbols

Brief Summary:

In Frege’s conceptual notation system, letters will stand for variables and express conceptual generality while other symbols will have specific values.

Summary

[Frege begins with the idea of the general theory of magnitude, which seems to refer to mathematics, also known to be a science of quantity]. He says there are two types of symbols in the general theory of magnitude. The first type are letters which represent either indeterminate numbers or indeterminate functions. [If we were only dealing with specific numbers and equations made of them, then we would be finding the validity of or proving just these specific formulations like 2 + 2 = 4. However, if we wanted to articulate more general observations about how quantities relate, then we would need to not refer to specific values.] The indeterminateness of these terms and functions allows us to “express by means of letters the general validity of propositions; e.g.: (a+b)c = ac + bc.” The other kind of symbol includes individual ones each with their own specific meaning; for example: +, –, √ , 0, 1, 2, 3, and so on. (1)

Although these symbols are used normally in mathematics (general theory of magnitude), Frege will use this distinction between types of symbols more generally “in the wider domain of pure thought” (1). [Like the first category of variables and like the second category of specific meanings for symbols:]

Accordingly, I divide all the symbols I use into those that can be taken to mean various things and those that have a fully determinate sense. The first kind are letters, and their main task is to be the expression of generality. For all their indeterminateness, it must be laid down that a letter retains in a given context the meaning once given to it.
(1)

Frege, Gottlob. “Begriffsschrift (Chapter 1)”. Transl. P.T. Geach. In Translations from the Philosophical Writings of Gottlob Frege. Eds. P.T. Geach and Max Black. Oxford: Basil Blackwell, 1960, second edition (1952 first edition).

.

Frege, Begriffsschrift, Chapter 1 (Geach transl.), Entry Directory

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Gottlob Frege

Begriffsschrift, Chapter 1 (Geach transl.)

§1. Explanation of the Symbols

§2. Judgment

§3 [untitled]

§4 [untitled]

§5. Conditionality

§6 [untitled]

§7 Negation

§8 Equality of Content

§9 The Function

§10 [untitled. function notation]

§11 Generality 

§12 [untitled. combinations of structures]

Frege, Gottlob. “Begriffsschrift (Chapter 1)”. Transl. P.T. Geach. In Translations from the Philosophical Writings of Gottlob Frege. Eds. P.T. Geach and Max Black. Oxford: Basil Blackwell, 1960, second edition (1952 first edition).




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Begriffsschrift

 

Begriffsscrift, Chapter 1 (Geach transl.)

 

 

“Function and Concept”

 

Frege, “Function and Concept”, summary

 

 

“On Concept and Object”

 

Frege. “On Concept and Object”, summary

 

 

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Frege “On Sense and Reference”, summary

 

 

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Priest (1.1) One, ‘The Illusion of Simplicity”

 

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Summary of

Graham Priest

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

Part 1: Unity

Ch.1: Gluons and their Wicked Ways

1.1 The Illusion of Simplicity

Brief Summary:

As we perceive, think, and react emotionally to one thing or another, ‘oneness’ must be a basic structure of our thought and experience. But trying to understand it philosophically wraps us into many complicated conceptual problems, so the seeming simplicity of the notion of ‘one’ is illusory.

 

Summary

 

Oneness is one of the most very basic structures of our thought and experience, as we are often thinking, perceiving, and reacting emotionally to some one thing or another. We must have some fundamental grasp of what it means for something to be just one thing. And of all the simple philosophical concepts, including being, existence through time, identity, intentionality, and so on, ‘one’ seems to be the simplest concept and the most fundamental because it is “embroiled in all of the them” (5). But when we try to think about it, we find ourselves wrapped up in difficult conceptual problems.

Answering the question ‘what does it mean to be one?’ draws us into a number of interlocking problems. Priest now turns to one of them: “how, if an object has parts, these cooperate to produce a unity—one thing” (5).

 

 

 

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

Priest (P11) One, ‘And so . . .’, summary

 

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Summary of

Graham Priest

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

Preface

P.11 And so . . .

Brief Summary:

Priest’s book is based on three unorthodox philosophical concepts: dialetheism, noneism, and the non-transitivity of identity. But as we will see, these ideas mutually support one another, and there was never sufficient cause to consider them heretical in the first place.

 

Summary

 

Priest’s book is build upon three ‘heresies’:

the book draws on two views that are contemporary heresies: dialetheism and noneism. Indeed, it adds a third to the picture, in the form of the non-transitivity of identity. Some may think that only ill can come from compounding heresy upon heresy. Personally, I do not see it that way. The orthodoxies on these matters were never as rationally grounded as their adherents like to pretend. Moreover, in the present context, the three heresies, far from adding to each others’ woes, interlock and support each other in fundamental | ways. And in doing so, they open up a perspective of the world that is forever closed to those with the blinkers of orthodoxy.
(xxvii-xxviii)

Priest then goes on to thank schools and other institutes and as well many people who helped make the book possible. These people include Jay Garfield, Yasuo Deguchi, Amber Carpenter, Sarah Brodie, Maureen Eckert, Ricki Bliss, Dave Ripley, Naoya Fujikawa, two anonymous referees for Oxford University Press, Eric Steinhardt, and Peter Momtchiloff.

 

 

 

 

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

Priest (P10) One, ‘Buddhist Philosophy II: China’, summary

 

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Summary of

Graham Priest

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

Preface

P.10 Buddhist Philosophy II: China

Brief Summary:

In China and Japan, Buddhism changes by means of the influence of other schools like Confucianism and Daoism and also by original contributions of Chinese and Japanese Buddhists, including Fazang and Dōgen.

 

Summary

 

Buddhist ideas in China diverged notably from their Indian origins (xxv).

They were influenced by Confucianism and Daoism. Confucianism comes from Confucius’ Lunyu (Analects), and Daoism from the Dao De Jing of Laozi and the Zhuangzi of Zhuangzi. Daoism had more influence on Buddhism than Confucianism did.

According to Daoism, there is a principle behind the flow of events, the Dao; and the Daoist sage is someone who does not cling, but “goes with the flow” of the Dao. (xxvi)

In China, Buddhism was misunderstood until good translations became available around the 4th century AD. What came to prominence were Chinese forms of Mahāyāna Buddhism. (xxvi)

Of these schools, the most philosophically sophisticated was the Huayan school, which provided a view of the world as made of interpenetrated and co-encoding phenomenal objects.

Philosophically the most sophisticated was Huayan (Skt: Avataṃsaka; Eng: Flower Garland), named after the sūtra which it took to be most important. The founder of the school is traditionally taken to be Tuxun | (557–640 AD), but philosophically more important is Fazang (643–712 AD), who parlayed the Indian notion of emptiness into a picture of the world in which all phenomenal objects interpenetrate and mutually encode each other.
(xxvi-xxvii)

In the 9th century AD, the Huayan school fades out and is absorbed into the Chan school, which was interested in practical more than theoretical matters.

A distinctive feature of the school is that enlightenment can be sudden, and occurs with a conceptually unmediated, and therefore indescribable, encounter with ultimate reality (Buddha nature).
(xxvii)

 

In the eight century Buddhist ideas enter Japan.

Perhaps the most important period in Japanese Buddhism was the thirteenth century AD, when thinkers such as Dōgen (1200– 1253 AD) imported Chan, or Zen, as it is called there. When it entered Japan, Buddhism encountered the indigenous animistic view, Shinto. Shinto certainly coloured Japanese Buddhism, but it did not have a profound impact in the way in which the indigenous Chinese ideas had done, the general perception being that Shinto and Buddhism are quite compatible.
(xvii)

 

 

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

Priest (P9) One, ‘Buddhist Philosophy I: India’, summary

 

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Summary of

Graham Priest

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

Preface

P.9 Buddhist Philosophy I: India

Brief Summary:

Buddhist philosophy saw most of its development between 500 BC and 1200 AD primarily in India but spreading to other parts of Asia. One of its principle concepts is emptiness, understood either (or both) as emptiness of self-existence or of mind-independence.

 

Summary

 

The final part of the book deal with Buddhist philosophy, so here in the preface Priest will provide some background to prepare us for that section.

Priest first tells us a bit of the history and the basic principles of Buddhist philosophy. Indian thinker Siddhārtha Gautama, the historical Buddha (circa 563 to 483 BC) created the Four Noble Truths for contending with the difficulties of the human condition. Later a cannon of Buddhist writings emerged, called the Tripitaka. It contains the sūtras, the discourses of the historical Buddha. Among its principle ideas in the Tripitaka is that we are collections of changing parts.

The foundations of Buddhist philosophy were laid by the historical Buddha, the Indian thinker Siddhārtha Gautama. (The word ‘Buddha’ itself is an honorific, like ‘Christ’, and simply means ‘the awakened one’.) His exact dates are uncertain, but a traditional chronology gives them as 563 to 483 BC. He enunciated principles often called the Four Noble Truths. These diagnose what one might call the human condition: an unhappiness-causing attachment to things in a world of impermanence (anitya) and interdependence (pratītyasamutpāda); they then give a recipe for what to do about it. Buddhist thought developed for the next several hundred years, until a canon of writings emerged: the Tripitaka (Three Baskets). One of these comprised the sūtra: discourses featuring the historical Buddha. Another was the vinaya, the rules for monastic living. The third was the abhidharma (higher teachings). A principal concern of this was to provide a taxonomy of things in the world and their parts. Thus, a person is just a collection of changing and interacting, mental and physical, parts (skandhas). Most objects of experience are of a similar kind, though this is not the way in which things appear. That is conventional reality (saṃvṛti-satya), as opposed to the ultimate reality (aramārtha satya) of the way that things actually are. Naturally, a number of different schools of Buddhist thought developed in this period. Only one of these now survives: Theravāda (Doctrine of the Elders).
(xxiv)

Then around the turn from BC to AD, a new sort of sūtra emerged called the Prajñāpāramitā Sūtras, which were concerned with being ethical to all sentient creatures.

Around the turn of the Common Era, a new class of sūtras started to appear: the Prajñāpāramitā (Perfection of Wisdom) Sūtras. (These include the most famous, short and cryptic, Heart Sūtra.) They initiated a new kind of Buddhism: Mahāyāna (the Greater Vehicle). The new Buddhism differed from the old in ways both ethical and metaphysical. The older Buddhism was concerned with individuals liberating themselves from the human condition. Someone on this path was an arhat (worthy one). By contrast, according to Mahāyāna, the ethical path was to help all sentient creatures liberate themselves. People who had dedicated themselves to do this were said to be on the Bodhisattva (enlightened being) Path. In Mahāyāna, compassion (karunā) therefore became the central virtue.
(xxiv)

The central metaphysical concept of Buddhism is emptiness. there are two schools of thought on this concept. One sees the emptiness as lacking self-existence, the other sees it as being empty of mind-independence. (xxv)

In India Buddhist philosophy continued to develop primarily at the university of Nālandā up through the first millennium. (xxv)

Theravāda Buddhism spread southeast to Sri Lanka, Burma, and Thailand, and Mahāyāna to Afghanistan, China, and Tibet. Moslem invasions wiped Buddhism out of India and Afghanistan, and consequently many Indian Buddhist texts were lost and exist only in translation. (xxv)

 

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

Priest (P8) One, ‘Characterization’, summary

 

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

 

Summary of

Graham Priest

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

Preface

P.8 Characterization

Brief Summary:

When we characterize something, we mean that were it a real thing it would have its ascribed properties. But if it does not exist in the actual world, it can be misleading to say that its characterization is true, even though technically it is, because it might imply the fictional thing is true as well. One solution is to think in terms of impossible and possible worlds, with the actual world as one of the possibles. We would say that a thing with a certain characterization may not exist on our world but does on some other. That way we eliminate the problem of implying the fictional thing truly exists in the actual world, while still affirming the truth of its characterization.

 

Summary

 

When we characterize a non-existent entity, we are saying that the characterization holds even though the thing bearing it may not exist.

Consider the first woman to land on the Moon in the twentieth century. Was this a woman; did they land on the Moon? A natural answer is yes: an object, characterized in a certain way, has those properties it is characterized as having (the Characterization Principle). That way, however, lies triviality, since one can characterize an object in any way one likes. In particular, we can characterize an object, x, by the condition that x = x∧A, where A is arbitrary. Given the Characterization Principle, A follows.
(xxii)

To add clarity to this issue in our discussion of dialetheism, Priest will construe the matter using the concepts of possible and impossible worlds. Some worlds are possible, others impossible. The actual world, @, is one of the possible worlds.

 

 

In dialetheism, certain contradictions in the actual world are true. But if contradiction does not indicate the impossibility of a world, then what does? Priest says that an impossible world is one with different logical laws than our own, and truth is relativized for each world [on some impossible world, what is true there depends on its particular logical system.]

One might wonder, therefore, what makes a world impossible. Answer: an impossible world is one where the laws of logic are different from those of the actual world (in the way that a physically impossible world is a world where the laws of physics are different from those of the actual world). Given the plurality of worlds, truth, truth conditions, and so on, must be relativized to each of these. That is a relatively routine matter.
(xxiii)

Priest then explains how characterization can be described in this context of worlds. [My interpretation is imperfect, so I invite better ones to the passage that I quote below. It seems he is saying something like the following.  Recall from the previous section how instead of the existential quantifier, Priest proposed the particular quantifier G as in GxPx meaning ‘some x is such that Px’. This was so that we do not imply the existence of x, which may be a non-existent entity. It seems now we are thinking of objects not in terms of existence or non-existence but rather as existence on one or another world, perhaps on an impossible one. Priests also says that by using paraconsistent logic well, we can say that each thing with its designating characterization is possible on some world. So we can speak of things as if they do exist, but the question is, ‘where?’ So instead of  G Priest uses ε as in εxPx, meaning ‘an x such that Px’. It seems to be then implying its existence but being indefinite about which world it exists on. Priest writes: “Hence, we know that if GxPx is true at @, so is P(εxPx); but if not, P(εxPx) is true at at least some world.” I cannot with certainty interpret what this means, but it seems to be saying that if it is true that there is some object with property P in the actual world, then it is also true that indeed a thing with property P has that property P (the ‘indeed’ is my best interpretation of the first P in the formulation, as if the redundancy is an affirmation of its existence). Please interpret this paragraph for yourself:]

If we characterise an object in a certain way, it does indeed have the properties it is characterized as having; not necessarily at the actual world, but at some world (maybe impossible). Specifically, suppose we characterize an object as one satisfying a certain condition, Px. We can write this using an indefinite description operator, ε, so that εxPx is ‘an x such that Px’. Given that we play our paraconsistent cards right, for any condition, Px, this is going to be satisfied at some worlds. If @ is one such, the description denotes an object that satisfies the condition there. If not, just take some other world where it is satisfied, and some object that satisfies it there.The description denotes that. Hence, we know that if GxPx is true at @, so is P(εxPx); but if not, P(εxPx) is true at at least some world. Thus, consider the description εx(x is the first woman to land on the Moon in the twentieth century). Let us use ‘Selene’ as a shorthand for this. Then we can think about Selene, realize that Selene is non-existent, and so on. Moreover, Selene does indeed have the properties of being female and of landing on the Moon—but not at the actual world. (No existent woman was on the Moon in the twentieth century; and no non-existent woman either: to be on the Moon is to have a spatial location, and therefore to exist.) Selene has those properties at a (presumably possible) world where NASA decided to put a woman on one of its Moon flights.
(xxiii)

[Note, the G and U (G and U) above should look like:

  ]

 

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