Friday, 15 December 2017

Pageviews by Countries

Graph of most popular countries among blog viewers
EntryPageviews
United States
802
Australia
331
Russia
220
United Arab Emirates
112
France
36
United Kingdom
23
Germany
20
Poland
19
Ireland
15
Brazil
10

Sunday, 10 December 2017

The Location(s) Of Phonology In Fawcett's Model

Fawcett (2010: 40n):
The Cardiff Grammar recognizes that it is only items that require expression in segmental phonology (which includes inherent word stress). One effect of this is that the two major aspects of phonology — intonation and segmental phonology — are treated as two separate components. They may look like one component when you view language 'from below', but if you look at intonation and segmental phonology 'from above', i.e., from the viewpoint of the meaning potential of the system networks, and if you then ask how meanings are realized in language, it becomes clear that the two are very different from each other: intonation realizing meanings directly, while segmental phonology does not. 

Blogger Comments:

[1] 'Inherent word stress' is not a feature of segmental phonology;  but see [2].

[2] The main theoretical disadvantage of treating intonation and segmental phonology as "two separate components" is that it omits rhythm from the model, since 'inherent word stress' is insufficient to account for the rich diversity of speech rhythms and the lexicogrammatical distinctions they realise.  The inclusion of rhythm is necessary for the modelling of intonation, since tone groups are realised by feet, and the ictus of each foot identifies the elements of potential tonic prominence, which in turn identifies the focus of New information.

[3] This misunderstands Halliday's 'trinocular perspective'.  It not possible to look at language 'from below', because there is no level of symbolic abstraction below language.

[4] To be clear, looking at phonology 'from above' means looking at it in terms of its function in various contexts (Halliday 2008: 141), as the expression of some content (Halliday & Matthiessen 1999: 504).

[5] To be clear, looking at 'how meanings are realised' — i.e. in terms of its various modes of expression — is looking at 'meaning from below' (Halliday 2008: 141).

[6] The claim here is:
  • if you view meaning in terms of how it is realised,
  • (then) it becomes clear that intonation realises meaning directly while segmental phonology does not.
This is not a reasoned argument, since no reasons are provided in support of the conclusion.  It is merely a bare assertion that has been dressed up to look like reasoning through the use of a conditional relation.  The advantages and disadvantages of such a model, to the theory as a whole, need to be both identified and supported by reasoned argument.

Sunday, 3 December 2017

Modelling Content And Expression As The Same Level Of Symbolic Abstraction

Fawcett (2010: 39-40n):
There is a difference from Halliday's model in the way in which the term "form" is being used here. He uses "form" in a sense that includes (1) grammatical structures and items and (2) lexical items, but not intonation or punctuation. However, the Cardiff model of language integrates intonation and punctuation with syntax and lexis as the co-realizations of the meaning potential of the language, so that these too are regarded as types of 'form'. The effect is that intonation is not treated as 'below' the level of syntax and items, but as a parallel form of realization.

Blogger Comments:

[1] To be clear, it is grammatical units, not grammatical structures, that correspond to grammatical form in Halliday's model; that is, the compositional rank scale of clause, group/phrase, word and morpheme.  Grammatical structures, on the other hand, are function structures: i.e. function not form.

[2] To construe grammatical form and phonological/graphological form as the same level of symbolic abstraction is to construe content and expression as the same level of symbolic abstraction.  The distinction between content and expression is the major distinction of all semiotic systems.

[3] Here again Fawcett misleads by strategically confusing 'meaning' as a level of symbolic abstraction with 'meaning potential', the entire language conceived as a resource for making meaning (semogenesis).

Sunday, 26 November 2017

What Fawcett Means By 'Form'

Fawcett (2010: 39):
We turn now to the level of form — and it is at this level that we require a theory of syntax. The term "form" is used here in a wider sense than that in "Categories" (or indeed any of Halliday's later writings) because it includes, as well as syntax and grammatical and lexical items, components for intonation or punctuation (depending on whether the medium is speech or writing). This is an approach to the concept of 'form' that looks at language 'from above', i.e., intonation and punctuation are here considered to be types of 'form' because, like syntax and items, they directly realize meanings.

Blogger Comments:

[1] To be clear, in Fawcett's model, content (syntax and grammatical and lexical items) and expression (intonation or punctuation) are located at the same level of symbolic abstraction.  The distinction between content and expression, as different levels of symbolic abstraction, is the fundamental distinction in semiotic systems.

[2] This misunderstands Halliday's 'trinocular' perspective.  On the SFL model, to look at language 'from above' means observing in terms of its function in various cultural contexts.  Halliday (2008: 141):
When we are observing and investigating language, or any other semiotic system, our vision is essentially trinocular. We observe the phenomenon we want to explore — say, the lexicogrammar of language — from three points of vantage. We observe it from above, in terms of its function in various contexts. We observe it from below, in terms of its various modes of expression. And thirdly, we observe it from its own level: from within, or from round about, according to whether we are focussing on the whole or some of its parts.
On the other hand, it is not possible to look at form 'from below' — i.e. as the content of some expression — because form is the lowest level of symbolic abstraction.  There is no lower level from which to look at form.  Halliday & Matthiessen (1999: 504):
A stratified semiotic defines three perspectives, which (following the most familiar metaphor) we refer to as ‘from above’, ‘from roundabout’, and ‘from below’: looking at a given stratum from above means treating it as the expression of some content, looking at it from below means treating it as the content of some expression, while looking at it from roundabout means treating it in the context of (i.e. in relation to other features of) its own stratum.

Sunday, 19 November 2017

What Fawcett Means By 'Instances Of Meaning'

Fawcett (2010: 39):
Since there is a potential at the level of meaning, we should logically expect that there will also be instances at this level — and indeed there are. On each traversal of a system network, a set of semantic features is collec[t]ed, and the grammar then makes a copy of these, which is called a selection expression. There are two reasons for collecting the features as a set. The first is that they constitute the systemic description — and so, I would argue, the semantic description — of that unit in the text-sentence that is generated. The second is that the realization rules (to which we shall come in a moment) need to be able to refer to the whole set of the selected features, because many of the rules require two or more features to have been co-selected in order to 'fire', i.e., to be triggered into operation.

Blogger Comments:

This continues the discussion of Figure 4 (p36):


[1] On the SFL model, a traversal of a system network entails the selection of features, not the collection of them.  The notion of the grammar making a copy of collected features is not a model of humans engaged in the instantiation of texts, but a model of text generation by computer.

[2] This reason does not support the notion of collecting features, since the selecting of features, by itself, constitutes a "systemic description" of the instance.

[3] This "need" arises as a consequence of conceiving of a grammar as a flow chart between modules in which system networks and realisation rules are separated as two different levels of symbolic abstraction: system as 'semantic potential' and realisation rules as 'form potential'.  In SFL theory, the instantiation of systemic potential, at a given level of symbolic abstraction (stratum), involves both the selection of features and the activation of realisation statements.

For three internal inconsistencies in Fawcett's model see On 'The Main Components Of A Systemic Functional Grammar'.

Sunday, 12 November 2017

Misrepresenting Halliday On Meaning Potential

Fawcett (2010: 38-9):
First, our model of language has, at the level of meaning, a component that specifies the meaning potential of the language — as Halliday has aptly named it (e.g., Halliday 1970:142). This is the core of a systemic functional grammar, and it consists of a vast system network of choices between meanings. In other words, the system networks model the language's potential at the level of meaning. Figure 1 in Appendix A introduces a simple system network for 'things', thus exemplifying the standard way of representing a system network in diagram form. 

Blogger Comments:

[1] This again misrepresents Halliday in order to give credence to Fawcett's model in which all system networks are located at the level of meaning.  For Halliday, 'meaning potential' is the entire language system, not merely the systems at the semantic level of symbolic abstraction (stratum).

[2] The system network of Figure 1 in Appendix A (below):
  • confuses features (singular, plural) with what are specified by the synthesis of the most delicate features (water, bread etc.);
  • confuses the semantics of things with the grammar of nouns (mass vs count, singular vs plural);
  • confuses experiential 'thing' with both interpersonal deixis (near vs un-near) and textual cohesion (recoverable).

Sunday, 5 November 2017

What Fawcett Means By 'Meaning'

Fawcett (2010: 38):
Now let us consider the term "meaning', as used in Figure 4. Throughout this chapter I have been careful to use to use the term "meaning" rather than "semantics" — even though I have happily used it elsewhere as the label for this level of language. Many systemic functional linguists (including Halliday in most of his writings) are understandably reluctant to use the term "semantics", because of the conceptual baggage that it brings with it from other disciplines and, within linguistics, from other theories of language. The types of 'meaning' that are covered in SFL by the system networks of TRANSITIVITY, MOOD, THEME and so one are much more comprehensive than the sense in which the term "semantics' is used by many linguists and philosophers. Nonetheless Halliday has till fairly recently allowed himself to use "semantic" (as a modifier) to refer to phenomena at this level of 'meaning'. And some systemic functional linguists — including Halliday himself in his important paper 'Text as semantic choice in social contexts" (1977/78) and myself — have regularly used the term "semantics" in the systemic functional sense of 'meaning potential'. We have done so because it is one way of expressing the theory's important claim that all of the different types of meaning covered by the system networks have to be included in any adequate theory of 'meaning', if only because the various sub-networks of TRANSITIVITY, MOOD, THEME and the others are partially interdependent on each other. SFL offers a particularly rich and powerful way to model the level of 'meaning' in language, and I have always felt it right to refer to this level of language by the term "semantics". Thus, in Figure 4.1 would be happy to replace "choice between meanings" by "semantic choices" and "meaning' features" by "semantic features".

Blogger Comments:

[1] This is misleading in a way that favours Fawcett's own position. It is Fawcett, not Halliday, who locates these systems at the level of meaning. In SFL, the system networks of TRANSITIVITY, MOOD, THEME are systems of wording (lexicogrammar), not meaning (semantics).  That is, they are posited as being of a lower level of symbolic abstraction than meaning — they realise meaning.

[2] Again, this is misleading in a way that favours Fawcett's own position of locating Halliday's grammatical systems at the level of meaning.  Halliday uses 'semantic' to refer to the stratum of meaning, with 'text' as the highest unit at that level of symbolic abstraction, and uses 'meaning potential' to refer to the theoretical construal of language as system.

[3] The argument here is:
  • reason: because the more delicate metafunctional systems of the clause are partially interdependent on each other
  • result: the meanings "covered" (realised) by the metafunctional systems of the clause have to be included in any adequate theory of 'meaning'.
It can be seen that this is a non-sequitur.  The latter does not follow from the former.  The partial interdependence of the more delicate metafunctional systems of clause is not itself a reason for the inclusion of all such systems in a theory of 'meaning' — any more than the "non-interdependence" would be.

[4] Rhetorically, this non-sequitur is presented as part of Fawcett's argument for locating Halliday's clause systems in semantics, rather than lexicogrammar.

[5] This is potentially misleading.  For Fawcett, modelling the level of 'meaning' is to interpret the metafunctional systems of the clause as semantic systems.  On the SFL model, on the other hand, modelling the level of meaning is modelling it as a higher level of symbolic abstraction (stratum) than all lexicogrammatical systems — not just those of the clause.  On the SFL model, the grammar not only realises the semantics, but makes possible the type of meaning that is only found in a tri-stratal semiotic system (i.e. language).

[6] Feeling that something is right is mere opinion, not reasoned argument.

Sunday, 29 October 2017

What Fawcett Means By 'Lexicogrammar'

Fawcett (2010: 37-8):
In using the term "lexicogrammar" here, then, I am starting from the concept that a grammar is a 'model of language' (which is not the way that Halliday uses the term "grammar") and I am then incorporating into it, by prefixing it with "lexico", Halliday's important point that 'lexis' must be integrated with 'syntax' (or 'grammar') in any such model. But I have to point out that this is a hybrid term that does not correspond to Halliday's normal use of the term "lexicogrammar" — and, having made the point that the model must include lexis (and indeed intonation and punctuation), I shall normally use the shorter term "grammar" in the rest of the book, when referring to the concept of a model of the sentence-generating component of language.

Blogger Comments:

[1] To be clear, for Fawcett, a grammar is a model of language in which lexis is integrated with syntax — hence "lexicogrammar" — and which also includes intonation and punctuation.  When normally using the term 'grammar', however, he is only referring to the sentence-generating component.

[2] Halliday uses the term 'grammar' as shorthand for 'lexicogrammar' (wording), and locates its systems on a level of symbolic abstraction (stratum) between semantics (meaning) and phonology (sounding).  For Halliday, it is the grammar that construes (intellectually constructs) the semantics.  Halliday & Matthiessen (2014: 22, 10):
Grammar is the central processing unit of language, the powerhouse where meanings are created …
The clause is the central processing unit in the lexicogrammar — in the specific sense that it is in the clause that meanings of different kinds are mapped into an integrated grammatical structure.
[3] This is potentially misleading, since, for Halliday, syntax is not equivalent to grammar, but merely one aspect of it — modelled as the rank scale.

Sunday, 22 October 2017

Misrepresenting Halliday On 'Form'

Fawcett (2010: 37):
However, there is a problem about using the term "lexicogrammar" (or indeed "grammar") in a sense that includes the level of meaning. The problem is that Halliday has explored two different positions on the issue of what we might call 'levels of meaning', and when he uses the term "lexicogrammar" it is typically in a sense where it is equated with the level of form, such that this is in a relationship of realisation to the level of "semantics". (See Sections 4.6 to 4.9 of Chapter 4 for a full account of Halliday's two positions, and for the reasons why I think that his first position is greatly preferable.)

Blogger Comments:

[1] This is misleading in a way that supports Fawcett's stance.  Even before developing Systemic Functional Grammar, Halliday (2006 [1961]: 39) defines his theoretical levels as follows:
The primary levels are form, substance and context. The substance is the material of language: phonic (audible noises) or graphic (visible marks). The form is the organisation of the substance into meaningful events: meaning is a concept, and a technical term, of the theory. The context is the relation of the form to non-linguistic features of the situations in which language operates, and to linguistic features other than those of the item under attention: these being together “extratextual” features.
With the development and substantial elaboration of Systemic Functional Grammar, Halliday (1985) distinguishes between function and form on the lexicogrammatical stratum, with form modelled as the rank scale, from clause to morpheme, and with the choice of rank as the entry condition to the functions available at that rank.  In later editions, as if to answer misunderstandings like those of Fawcett, Halliday & Matthiessen (2014: 49) explain:
Being a ‘functional grammar’ means that priority is given to the view ‘from above’; that is, grammar is seen as a resource for making meaning — it is a ‘semanticky’ kind of grammar. But the focus of attention is still on the grammar itself.
[2] Fawcett's "full" account will be examined in detail in the critiques and clarifications of Sections 4.6 to 4.9 of Chapter 4.

Sunday, 15 October 2017

What Fawcett Means By 'Grammar'

Fawcett (2010: 37):
At this point I should clarify the sense in which I am using the terms "grammar" and "meaning". Let us take "grammar" first, since it is used in the caption for Figure 4. In "Categories", "grammar" was the name of a subcomponent of the level of form, but here its meaning has been extended in two ways. The most obvious is that a grammar now includes a level of meaning as well as a level of form. Thus a 'grammar' is essentially a model of the sentence-generating component of a full model of language and its use. The second extension — which is less obvious — is that the term "grammar" is regularly used as a short form for "lexicogrammar".

Blogger Comments:

[1] Contrary to the implication, this "extension" of the meaning of 'grammar' to 'lexicogrammar' is not Fawcett's.  It appears in Categories of the Theory of Grammar (Halliday 1961), where lexis is conceived as most delicate grammar.  Halliday (2004 [1961]: 54):
The theoretical place of the move from grammar to lexis is therefore not a feature of rank but one of delicacy.  It is defined theoretically as the place where increase in delicacy yields no further systems;

[2] To be clear, Fawcett stratifies grammar into meaning and form, whereas Halliday locates meaning in semantics, and distinguishes between grammatical functions and grammatical forms (the rank scale).  Crucially, it is the distinction between semantics and lexicogrammar that allows Halliday to account for grammatical metaphor in his model.

Fawcett
Halliday
(lexico)grammar
meaning
meaning
semantics
function
lexicogrammar
form
form

Sunday, 8 October 2017

Fawcett's Introduction Of The Term 'Instance'

Fawcett (2010: 36n):
In the past SF linguists have usually referred to instances as "instantiations". But since we need the term "instantiation" to refer to the relationship between the 'potential' and the 'instances' that it generates, as here, it is preferable to use a different term for the 'product' of the 'process' of instantiation. Hence my introduction here of the term "instance". Note that some SF linguists (e.g., Matthiessen & Bateman 1991) have used the term "actualisation" in place of "instantiation". One reason for preferring "instantiation"' to "actualisation" is the fact that English has the corresponding noun "instance", which can be used to distinguish the 'product' from the 'process'. It is this pair of terms, then, that is used in the present theory.

Blogger Comments:

This is misleading.  The term 'instance' was "introduced" in Categories Of The Theory Of Grammar (Halliday 1961: passim), and many subsequent publications, such as Halliday (1978 [1974]: 40), Halliday (1977: 54) and Halliday (1987:152).

Sunday, 1 October 2017

On 'The Main Components Of A Systemic Functional Grammar'

Fawcett (2010: 36):
The diagram in Figure 4 brings together these two pairs of concepts to define the four components that are essential for modelling any semiotic system. It provides a framework for thinking about language in terms of (1) the potential and (2) the many possible instances of that potential, and to do so at the two levels of (a) meaning and (b) form. The four components of the model are defined by the intersections of these two pairs of concepts. 

Blogger Comments:

On the one hand, Figure 4 presents a flow chart for text generation by computer, not a systemic functional model of grammar.  It is also inconsistent with SFL theory in that it presents the architecture of the theory in terms of interactions between modules instead of relations along dimensions; see Halliday & Webster (2009: 231).

On the other hand, Figure 4 is internally inconsistent.  Firstly, the 'potential' column presents realisation rules as the form that realises the system of meaning.  To be consistent with the level of meaning, the level of form would need to be a 'system network of choices in form'.  To be consistent with SFL theory, the realisation rules would need to be located in the system of meaning.

Secondly, the 'instance' column presents structure as the form that realises features of meaning.  That is, it presents the axial relation between paradigm (features) and syntagm (structure) as a stratal relation between meaning and form.

Thirdly, the 'form' row presents structure as an instance of realisation rules as potential.  That is, it presents the axial relation between paradigm (realisation rules) and syntagm (structure) as a relation of instantiation between potential and instance.

Any theoretical advantages afforded by such inconsistencies need to be demonstrated, and their value weighed against their consequences for the theoretical architecture as a whole.

Sunday, 24 September 2017

Multiple Misrepresentations Of Halliday In A Footnote

Fawcett (2010: 35n):
Halliday often writes in a way that implies that the reason why human languages are more complex than many other semiotic systems is that grammar 'intervenes' between meanings and phonological and graphological forms (e.g., Halliday 1996:29), whereas it does not in simpler systems (such as a traffic light system). One difficulty about this view is that he also sees the grammar as having its own 'meaning potential' inside it, and this gives us a model in which the 'meanings' of the higher semantic level are detached, as it were, from their realisations in forms, such that they have to be mapped first onto the meanings within the grammar (or 'lexicogrammar', as Halliday prefers to call it). I take a different view, as this book shows, in that I regard the level of meanings within the 'lexicogrammar' as the key level of linguistically-realised meaning, such that it is realised in any one of (1) syntax, (2) intonation or punctuation (depending on the medium of discourse) and (3) items(Notice that it is only one of these, namely items, to which the supposed 'third level' of segmental phonology/graphology is relevant, and this fact raises serious questions about its traditional status as a 'level of language'.) In my approach, therefore, any 'higher' meaning — such as those that Halliday includes under the umbrella concept of 'grammatical metaphor'is to be accounted for by one or other of several different concepts. See Fawcett (1993) for a brief indication of some of these, and Fawcett & Huang (in preparation) for a much fuller picture. Many of the concepts introduced in this footnote will be amplified in later parts of this book.

Blogger Comments:

[1] Halliday does not imply this, he is quite explicit about it. Halliday & Matthiessen (2014: 25):
The ‘content’ expands into two, a lexicogrammar and a semantics (cf. Halliday, 1984a; Halliday & Matthiessen, 1999). This is what allows the meaning potential of a language to expand, more or less indefinitely.
The stratification of content makes grammatical metaphor possible, and it this, chiefly, that 'allows the meaning potential of a language to expand, more or less indefinitely'.  This is why the inability of Fawcett's model to account for grammatical metaphor is such a serious shortcoming.

[2] This is a bizarre misunderstanding.  For Halliday, the system of language is meaning potential — the potential to make meaning (semogenesis).   Halliday & Matthiessen (2014: 48, 76, 601):
Language has evolved as a fully systemic semiotic system: it is possible to posit and describe the overall meaning potential for a given language, interpreting this meaning potential as an aggregate of registerial subpotentials. … 
The functional categories provide an interpretation of grammatical structure in terms of the overall meaning potential of the language. … 
Logogenesis pertains to the entire meaning potential of a language – all the strata and all the metafunctions.

[3] This misunderstands stratification.  Meanings are modelled as a higher level of abstraction than the forms of wording.  There are no "meanings within the grammar"; the wordings of grammar realise the meanings of semantics.

[4] Halliday "prefers" the term lexicogrammar because the stratum encompasses both lexis and grammar, related systemically along the scale of delicacy.

[5] This is not a different view to Halliday's; it is merely different from Fawcett's misunderstanding of Halliday.  Halliday sees lexicogrammar as the dynamo of language, and as the source of the type of meanings that differentiate language from other (bi-stratal) semiotic systems.  Halliday & Matthiessen (2014: 22):
Grammar is the central processing unit of language, the powerhouse where meanings are created …
[6] This misrepresents the SFL hierarchy of stratification, which distinguishes meaning (semantics) from wording (lexicogrammar) as different levels of symbolic abstraction.  Grammatical functions (wordings) are congruent (agree) with semantic functions (meanings) in the absence of grammatical metaphor.

[7] This blurs the distinction between two distinct realisation relations in SFL theory.  On the one hand, grammatical functions are realised in the grammatical forms of the rank below; e.g. clause functions are realised by groups ± phrases.  On the other hand, the realisation of grammar in phonology or graphology is an interstratal relation.

[8] This confuses realisation with delicacy.  In SFL theory, lexical items are the synthesis of the most delicate features of the systems of lexicogrammar.  They do not "realise" grammatical functions because lexis and grammar are of the same level of symbolic abstraction (wording).

[9] Here Fawcett presents his own misunderstanding of the place of lexis in SFL theory as a challenge to modelling some of the systems of the expression plane as a lower level of symbolic abstraction than lexicogrammar.

[10] This misrepresents Halliday's notion grammatical metaphor, which is not 'higher meaning', but an incongruent realisation of meaning (semantics) in wording (lexicogrammar).  Grammatical metaphor is an integral part of semogenesis, and the inability of Fawcett's model to account for it is a very serious shortcoming indeed.

[11] The promised concepts to account for grammatical metaphor are said to be in:
Fawcett, Robin, 1993. "Language as program: a reassessment of the nature of descriptive linguistics". Language Sciences 14.4. 623-57. 
Fawcett, Robin, & Huang, Guowen, in preparation. Explaining Enhanced Theme (the 'Cleft' Construction): a Test Case for Systemic Functional Linguistics - and Every Theory of Language. London: Continuum. 
The latter publication is still, apparently, "in preparation" in 2017, but there is:
Huang, G.-W. (2003). Enhanced theme in English: Its structures and functions. Taiyuan: Shangxi Education Publishing House.
However, the abstract of Fawcett (1993), at least, makes no mention of grammatical metaphor:
The purpose of this paper is to challenge one of the basic tenets of linguistics. The traditional view is that it is the business of linguists to describe language and languages—and/or to theorise about it and them. It is essentially a view of language as an object. While I remain solidly based in linguistics, I draw here on my experience in natural language processing (i.e. of putting English in computers as part of a model of a communicating mind) as I advocate the view that it is more insightful to view language not as object, but as procedure, as process, as program. Note that ‘program’ has no final ‘me’ to signify the sense of ‘computer program’. 
I invite you to come with me on an exploration of what is involved when someone produces (‘generates’) a sentence, to show why I advocate a model of language that is not static, but dynamic. The model is also, I shall argue, essentially generative (in the sense of ‘productive’) rather than interpretive. Thus a program whose essential design is as it is to enable it to run in one direction—i.e. to turn meanings into sounds—is consulted as the person trying to understand a text attempts the converse task. This is not just ‘to turn sound into meaning’, but to turn the performer's sounds back into the performer's meanings. Hence the logical priority of generation over interpretation. 
In this new view of language as program, it is no longer possible to draw a clear line between the material of linguistics and the algorithms that determine how we choose between linguistic options; one needs a more complete framework, which is inevitably also more complex, e.g. as described here.

[12] If any of the "concepts introduced in this footnote" are "amplified in later parts of this book", each will be noted on this blog, and cross-referenced to this post.