The etymology of the word ἀδελφός is "from the collative a ..., denoting unity, and delphús (n.f.), a womb."1 So the chief idea is as BDAG and other lexicons state,2 that of a true brother or sister coming from the same mother (parents).3
However, as you noted, the word can be used in a variety of figurative, yet still physical relation extensions beyond this, and is found so used in Scripture:
- Of fellow Israelites roughly in age of the speaker (Act 7:2)4
- Of Moses in his relation to all the rest of Israel (Act 7:23)
- Of fellow human beings (Mt 5:22)
So usage indicates that the term could be used to make reference to any type relationship considered as uniting of one to another, considered in a more intimate way. This accounts for the even more figurative uses for communities of believers, etc.
A term more explicit of a cousin or other more distant type relation would be συγγενής, which BDAG has as:5
- belonging to the same extended family or clan, related, akin to ...
- belonging to the same people group, compatriot, kin
And then as was mentioned in a comment, ἀνεψιός is more explicitly a "cousin" (found only in Col 4:10, and the LXX in Num 36:11),6 or perhaps "nephew."7
It could not be ruled out completely on lexical grounds that a cousin could be referred to by the term ἀδελφός, since one could refer to any extended family relation by such a term (as the Jews did of one another). But that conclusion could only be made effectively if the context pointed to such a use, since the term clearly is that of a true brother (or sister) when referring to near family relations. This is even more so since there were words that could have been used to express a more explicit cousin (or more distant kin) relation.
A number of contextual points favor the basic meaning in Mt 13:55-56.
- It can be ruled out that the Jews are using the term in the broader sense of being Jewish, as they are not saying "Is this not our brother," but specifically tying Jesus to an explicit group of people.
- The naming of the individuals would seem out of place if a mere reference to cousins was in view. Rather, they are making an argument of an intimate connection to specific individuals that they know are closely related, but unlearned to the level that Jesus was demonstrating.
- The reference to both father and mother would make it an odd jump to cousin as the meaning for a term that is normally brother/sister; which joins to the next point...
- Spiros Zodhiates notes a significant observation (emphasis added):8
The Hebr. word ʾāch (251) encompassed more distant relatives (Gen.
14:16; 29:12, 15); therefore, some argue that this ought to be taken
into consideration where brothers and sisters of the Lord Jesus are
referred to (Matt. 12:46, 47; 13:55; Mark 3:31, 32; 6:3; Luke 8:19,
20; John 2:12; Acts 1:14). However, the only passage where the
brothers of Jesus are not conjoined with His mother is John 7:3, 5,
10. The conjoined mention of the mother of Jesus appears to imply that children of the same mother are meant.
The contextual evidence points so clearly to meaning real brothers and sisters that one has to have a clear bias against such to even consider it to be otherwise in this passage.
Conclusion of Meaning in Context of Mt 13:55-56
That the term ἀδελφός could generally be used of a cousin (or even more distant relative) seems apparent from usages. However, contextually, one could almost not make a more poignant statement of true brotherhood than the text in Matthew 13 (and other texts noting these individuals); only a presupposed bias against such a view would cause one to ignore that evidence.
1 Spiros Zodhiates, The Complete Word Study Dictionary: New Testament (Chattanooga, TN: AMG Publishers, 2000), #80.
2 Gerhard Kittel, Geoffrey W. Bromiley, and Gerhard Friedrich, eds. Theological Dictionary of the New Testament (Grand Rapids, MI: Eerdmans, 1964), 1:144, states: "In the NT ἀδελφός and ἀδελφή denote either 'physical brotherhood' in the strict sense or more generally the 'spiritual brotherhood' of Israelites or Christians." James Swanson, Dictionary of Biblical Languages with Semantic Domains: Greek (New Testament) (Oak Harbor: Logos Research Systems, Inc., 1997), #81, states: "1. brother, male sibling ... 2. fellow believer ... 3. fellow Jew ... 4. fellow countryman ... 5. neighbor."
3 Note that a half-brother or half-sister from the same mother would qualify as a true ἀδελφός by even the etymological definition. However, that would be limiting the definition too much, since if two individuals shared the same father but not the same mother, the term is still used (for example, all the sons of Israel were ἀδελφοὶ, even though many had a different mother from the others.
4 Stephen begins his address in Act 7:2 with "Men—brethren and fathers—listen" (my translation of
Ἄνδρες ἀδελφοὶ καὶ πατέρες, ἀκούσατε; a number of major translations omit translating Ἄνδρες, "men," probably considering it redundant, since there is no variant in the manuscripts there). An observation I make from this passage is that the distinction Stephen draws by stating both brethren and fathers indicates to me that even though the term ἀδελφοὶ could be used of all men of Israel in relation to their "brother" Stephen, that here he is using it more as a term indicating a lesser subset of those more his age, and using the term πατέρες ("fathers") to distinguish some honor to men older than he (how much older I don't know—probably about a generation). So at least in direct address situations, the Jews perhaps did not use ἀδελφός (or equivalent Semitic term) when addressing one deemed to be their elder, instead using πατήρ ("father") in its more figurative sense.
5 William Arndt, Frederick W. Danker, and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago: University of Chicago Press, 2000), s.v. συγγενής.
6 BDAG, s.v. ἀνεψιός.
7 Zodhiates, #431.
8 Zodhiates, #80.