Martin (1992: 222):
Concessive consequential relations on the other hand are realised through a number of distinctively internal conjunctions. Nevertheless, nonetheless and still function as the concessive counterparts of consequently, hence and in conclusion. In addition there is a set of internal concessives oriented to objections which may be conceded (admittedly, of course and needless to say) or dismissed (in any case, at any rate, anyhow and anyway).
 These are not "distinctively internal conjunctions". They are conjunctive Adjuncts that function textually by marking textual transitions by construing cohesive expansion relations between messages — relating the realisation of figures, not propositions or proposals.
 In SFL theory:
- nevertheless, nonetheless and still typically construe a concessive causal-conditional relation;
- consequently and hence typically construe a general causal-conditional relation; and
- in conclusion may construe a summative clarifying relation (elaboration, not enhancement) or an internal conclusive temporal relation (enhancement, but not causal-conditional).
 As the word 'objections' suggests, the metafunctional perspective being taken here is interpersonal, rather than textual (Martin's logical).
 In SFL theory:
- admittedly typically functions interpersonally as a comment Adjunct (persuasive: concession) rather than textually as a conjunctive Adjunct;
- of course typically functions interpersonally as a comment Adjunct (asseverative: natural or obvious) rather than textually as a conjunctive Adjunct; and
- needless to say typically functions interpersonally as a comment Adjunct (asseverative: obvious) rather than textually as a conjunctive Adjunct.
 In SFL theory, in any case, at any rate, anyhow and anyway typically construe a dismissive clarifying relation (elaboration, not enhancement).
Conclusion: The proposed (logical) opposition between conceded and dismissed objections — a subtype of Martin's internal concessive consequentials — is actually an opposition between comment Adjuncts (interpersonal) and conjunctive Adjuncts of elaboration (textual).