The Celts: a culture or a language family — does the distinction matter?
The question of whether ancient Athens was genuinely democratic or a democracy with fundamental exclusions — of women, enslaved people, resident foreigners (metics), and non-citizens — is both a legitimate historical question and a sometimes anachronistic one.
The exclusions were large. Women — roughly half the free population — had no political rights. Enslaved people — perhaps a third of the population — were not citizens. Metics — free residents without citizen status, who might have lived in Athens for generations — paid taxes, served in the military, and contributed to Athenian cultural life (Aristotle was a metic) but could not vote or own land. Citizenship was restricted to those born of two Athenian citizen parents after Pericles' citizenship law of 451 BC.
From one perspective, the Athenian 'democracy' was really a democratic system for about 15-20% of the population, embedded in a profoundly unequal society. From another perspective, it was the most participatory political system that had ever existed for the people it included — and the question of who counts has been contested in every democracy since.
The more historically interesting question might be how Athenians themselves thought about these exclusions. The sources suggest that the citizenship boundary was largely taken for granted rather than philosophically defended — Aristotle's defense of 'natural slavery' and his account of female inferiority are rationalizations of existing practice rather than founding principles. The genuine innovations — sortition, pay for jury service, direct legislation by assembly — were aimed at equalizing participation among the included, not at expanding inclusion.