 Another popular recent way of delineating the Aristotelian intuition of the semantic “insubstantiality” of logical expressions appeals to the concept of “pure inferentiality”. The idea is that logical expressions are those whose meaning, in some sense, is given by “purely inferential” rules. (See Kneale 1956, Hacking 1979, Peacocke 1987, Hodes 2004, among others.) A necessary property of purely inferential rules is that they regulate only inferential transitions between verbal items, not between extra-verbal assertibility conditions and verbal items, or between verbal items and actions licensed by those items. A certain inferential rule licenses you to say “It rains” when it rains, but it's not “purely inferential”. A rule that licenses you to say “A is a female whose husband died before her” when someone says “A is a widow”, however, is not immediately disqualified as purely inferential. Now, presumably in some sense the meaning of “widow” is given by this last rule together perhaps with the converse rule, that licenses you to say “A is a widow” when someone says “A is a female whose husband died before her”. But “widow” is not a logical expression, since it's not widely applicable; so one needs to postulate more necessary properties that “purely inferential” rules ought to satisfy. A number of such conditions are postulated in the relevant literature (see e.g. Belnap 1962 (a reply to Prior 1960), Hacking 1979 and Hodes 2004). However, even when the notion of pure inferentiality is strengthened in these ways, problems remain. Most often the proposal is that an expression is logical just in case certain purely inferential rules give its whole meaning, including its sense, or the set of aspects of its use that need to be mastered in order to understand it (as in Kneale 1956, Peacocke 1987 and Hodes 2004). However, it seems clear that some paradigmatic logical expressions have extra sense attached to them that is not codifiable purely inferentially. For example, inductive reasoning involving “all” seems to be part of the sense of this expression, but it's hard to see how it could be codified by purely inferential rules (as noted by Sainsbury 1991, pp. 316–7; see also Dummett 1991, ch. 12). A different version of the proposal consists in saying that an expression is logical just in case certain purely inferential rules that are part of its sense suffice to determine its extension (as in Hacking 1979). But it seems clear that if the extension of, say, “are identical” is determined by a certain set of purely inferential rules that are part of its sense, then the extension of “are identical and are not male widows” is equally determined by the same rules, which arguably form part of its sense; yet “are identical and are not male widows” is not a logical expression (see Gómez-Torrente 2002).