I am not quite sure how we’ve got on to Zeno’s Dichotomy Paradox — the one about never arriving if your every stride is half the length of the previous one — but Richard Stoneman is using a handful of Turkish nuts to help to explain it.

It is late morning off Turkey’s remote and lovely Dilek Peninsula, and Stoneman, the resident lecturer on our small-group archaeology and ancient history cruise, illustrates his point by arranging pistachios across the rear-deck table (among the glasses of chilled local Doluca wine) of our 25m gulet.

Romantic gulets, with their oversized bowsprits and high galleon sterns, have long been the signature craft of the Turkish Riviera. The difference is that where they once freighted the local citrus crop to the great markets at Izmir and Antalya, today’s fleets have been adapted for leisure cruising, successfully combining all manner of holiday functions, from floating villa (fully staffed, with sunbeds and swimming), offshore transportation and restaurant to, in this case, al fresco lecture hall.

Southwest Turkey tends to conjure visions of bars and nightclubs, banana boats and foam parties, but the extraordinary classical heritage of this deeply indented, mountain-backed coast — Homer, St Nicholas and Alexander the Great, three of the Seven Wonders, a dizzying wealth of other ancient sites, claims to cultural firsts from town planning to pornography — has long drawn another kind of visitor.

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It’s typical that Stoneman’s pre-lunch talk is taking place at Mycale, where the Greeks in 479BC followed up triumphs at Marathon and Salamis to finally send the Persians packing and thereby confirm the survival of Western civilisation.

On-hand lecturers such as Stoneman, a Greek- speaking classics Fellow and expert on Alexander, serve this erudite, often senior breed by giving daily talks and enriching gulet-based itineraries with their insights and knowledge. That brings us back to Zeno, a near contemporary of the earliest Greek philosophers, the so-called Pre-Socratics, who first flourished at Miletus and elsewhere along this coast in the 6th century BC.

It’s not hyperbole, then, when our hosts label this two-week itinerary — taking in the early Classical mindset at sites such as Miletus, Ephesus, Bodrum and Rhodes and a great deal besides — “The Origins of Western Thought”.

We are ten guests when we arrive at the port of Kusadasi. Our stately vessel awaits us, complete with wood-panelled cabins, en suite bathrooms, spacious decks and a courteous, approachable three-man crew.

We dine on deck; the ship’s cook serves freshly prepared meze — salads of aubergine and chilli, stuffed peppers, filo pastry boreks filled with feta cheese — followed by chicken kebabs and salad. With all this and the abundant wine, it’s no time before we discover just how like-minded we are. A convivial atmosphere descends, as settled as the warm September skies.

A minibus arrives after breakfast, a reminder that the gulet cannot deliver us to every site on the itinerary. We’re heading for Ephesus, its harbour long since silted, after a visit to the site’s museum at nearby Selcuk. It’s here that local guides take over, as the regulations insist; Stoneman, who remembers how St Paul was nearly lynched while addressing the crowds at the theatre in Ephesus, is happy to play second fiddle.

At the best-preserved ancient site in Turkey we follow a raised, transparent walkway, newly opened this year, through the recently excavated hillside homes of what was surely a favoured Ephesus postcode.

Here, the astonishingly intact interiors, with magnificent floor mosaics and wall frescoes set between ornate marble panels, provide an exquisite glimpse of privileged domesticity in the ancient world. We return to the gulet after a brief visit to the Temple of Artemis, where a few column stubs sticking out of a marsh constitute a widely acknowledged let-down. The truth is that we have seen enough wonders not to let this one, for all its upper-case credentials, disappoint us.

We cast off the next morning and head south through the dramatically narrow strait that separates Turkey from the birthplace of Pythagoras, the Greek island of Samos. There is time now not only for talk — of oracles and triremes — but also for sunbathing, snoozing and dusting down that essential gulet item, the backgammon board.

The local wind, the meltem, gets up in the afternoon so we are pleased to anchor in a sheltered bay near Altinkum. Some of us swim, others snorkel, from the boat. I lower the gulet’s kayak into the sea and mosey round the bay in the late light. Over dinner all sorts of accomplishments begin to emerge; an American, Jo Ann, demonstrates an impressive knowledge of the night sky. “It’s the time of year for meteor showers in Perseus,” she says.

This sort of knowledge is one of the great benefits of learned company, and I cash in during the early hours, dragging myself on deck to see shooting stars cause brief flashes, white on black, above the masthead.

A big day awaits us, beginning with Didyma, where a magnificent oracular temple stands, at once tumbledown but unfinished. It’s partly ruin, partly late-stage building site, with the vertical scores where the round columns were to have been fluted serving only to highlight the sense of achievement.

Then there is the silt-stranded city site of Miletos, where the early philosophers, Thales among them, first sensed natural processes, not merely capricious gods, at work around them. And at lovely Priene, set amid pine-clad hills above the Meander Valley, a gleeful Stoneman falls upon ancient signs inscribed in the walls.

“Temple Street,” he translates, and for a moment we are in the 4th century BC, around the time when Alexander visited the city en route to conquering the East.

The days pass, the crew busy scrubbing decks, shelling borlotti beans or fixing us drinks, while we laze and learn, journeying south and east into ancient Caria. There is Bodrum, where the great tomb of Mausolus was once accounted a Wonder, and Knydos, with its lovely waterside theatre, where vast crowds once gathered to admire, even lust over, Praxiteles’ famous nude statue of Aphrodite. We dig out our passports to take in Rhodes before returning to Turkey at Kaunos, the gorgeously sited city on the banks of the bird-rich Dalyan River.

There have been “moments”, of course; passing bouts of seasickness, tummy complaints, a briefly flooded cabin, sites so extensive as to deter some heat-weakened group members. The overall view of this beautiful coast, however, as rich in Turkish hospitality as it is in history, is of enchantment.

Time passes too fast for our liking. And that brings us back to Zeno, he of the halving strides, and to our hopes that our journey’s end may never arrive.

Need to know

Westminster Classic Tours (020-8286 7842, www.westminsterclassictours.com) has a 13-night “The Origins of Western Thought” tour departing on September 20. The cost of £2,600pp (based on two sharing) includes full board but not flights, visa (£10 on arrival) or crew tips. Flights are through Tulip Holidays (020-8211 0001, www.tulipholidays.com ) for about £335 return.

Further information Turkish Tourist Office (020-7839 7778, www.gototurkey.co.uk).

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