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@user6726 has a great explanation of feature matrices in which s/he writes:

There are two related questions about features in connection with matrices in pre-autosegmental generative phonology: are the featural elements of a segment ordered, and are they value-attribute pairs, or just values? The way matrices are typically presented in papers suggests that within the segment, there is no ordering to the features, thus [+cons,-son,-cont] is not distinct from [+cons,-cont,-son] or any of the other permutations: features are "simultaneous" within the segment; this also implies that features are pairings of name and specification. An alternative interpretation of the representation is that a segment is an ordered collection of values only, e.g. [+,-,-,+...] where value 1 refers to "consonantal", value 2 refers to "sonorant" and so on. The "matrix of unordered value-attribute pairs" can be easily translated into a "matrix of ordered values" – provided that the set of features is part of universal grammar. This was the claims for the phonetic features of SPE, but there are also diacritic features, and it was noted in SPE (fn 1 p. 390) that there is an unlimited set of diacritic features. In light of the fact that the total set of features is not fixed and varies between languages, a segment has to be interpreted as being composed of a collection of value-attribute pairs, in which case the feature specifications would be unordered (ordering would be superfluous).

While this is a tremendous explanation of questions which were, at the time, crucial to understanding feature matrices, I have trouble understanding the logical reasoning that lead to the conclusion in bold at the end.

Why is it the case, that in this framework, a segment must be interpreted as a collection of value-attribute pairs?

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The underlying issue is what / how much information is necessary to characterize a segment. The background assumption is the Jakobsonian one that every segment is defined in terms of a collection of features = descriptive attributes and values associated with the attributes (we usually say the values are "plus and minus" but in fact values have included plus, minus, "plus-and-minus", 0, u, m as well as numbers). The answer to the "what structure" question then depends on the nature of the feature set.

If there is a fixed set of features for language where all and only those features are present in all languages, then a segment can be defined as a set of pairs "value, attribute", without ordering of those features. They can also be defined as an ordered list of values (without attributes), where the attribute can be projected from the order -- e.g. the first attribute is interpreted as "consonantal", the second as "sonorant" and so on. Thus [æ] could be simply (-,+,+,-,+....), and the interpretation "the third segment is [+low]" would derive from a modular arithmetic computation based on the 57th value in an utterance being "+".

A third possibility would be to have ordered value-attribute pairs i.e. (-cons,+son,+syl...): however, having both ordering and attributes is redundant – one can be supplied on the basis of the other, so there is no reason to use both (therefore, one doesn't -- it's either ordering, or value-attribute pairs). This is a classical application of Occam's Razor, that there is no evidence (given the assumption that features are value, attribute pairs) that the grammatical faculty also includes ordering of features.

The foregoing assumes, however, that the set of features is universally fixed. That assumption was made in SPE phonology for the set of phonetic features, but it was not assumed for the remaining features. There is an unlimited supply of arbitrary non-phonetic features, including both letter diacritics (X,Y,D...) and rule features ([rule37]). This thwarts the modular arithmetic computation, because the 57th value might be a phonetic feature of the second segment in one language, or a rule feature of the first segment in another language, and so on. Given the conclusion that the set of features is not universally predetermined, then the ordering of the features also cannot be predetermined, so there can be no universal scheme for interpreting a list of bare values. In that case: the only alternative is that features are value, attribute pairs (and furthermore ordering of features would be redundant, since the attribute part provides the necessary information that allows a feature matrix to be physically interpreted).

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  • So, if I can paraphrase: 1) non-phonetic features impede a modular, arithmetic computation, so therefore 2) the set of features is not universally predetermined, and accordingly 3) there is no universal scheme for interpreting a list of bare values, ergo 4) features are comprised of unordered sets of value-attribute pairs (i.e. Matrices). Is this accurate? – Teusz Sep 19 '16 at 5:47
  • Wait a minute, I must have got that wrong - specifically 4), above because you write "If there is a fixed set of features for language where all and only those features are present in all languages, then a segment can be defined as a set of pairs "value, attribute", without ordering of those features." This contradicts 3). – Teusz Sep 19 '16 at 5:51
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    Well 2 is primary, 1 is a consequence of 2 and 3 follows from 1: 1-3 dispose of ordered bare value theory, leaving the alternative, 4. – user6726 Sep 19 '16 at 15:19

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