I have attempted to create a more rigorous definition of oceans and lakes. This definition allows for a consistent, geometrically grounded distinction between oceans and lakes. Rather than relying on ambiguous naming conventions, the classification becomes a matter of spherical geometry and enclosure.

Continents

According to Oxford, a "continent" is

any of the world's main continuous expanses of land (Europe, Asia, Africa, North and South America, Australia, Antarctica).

Presumably, Europe, Asia, Africa, North and South America, Australia and Antarctica are these supposed main continuos expanses of land. If a continuos expanse of land fails to find itself amongst this main set, then it finds itself relegated it undefined set of auxiliary or subordinate expanses of land.

Some of these continents connect to others. For example, Asia connects with Africa via Egypt, at Isthmus of Suez in the Sinai Peninsula. This forms Afro-Asia, a supercontinent. However, Asia also has a land border with Europe. Combined, they make Eurasia. The exact land divide between Europe and Asia is artificial of course. It is commonly defined by the Ural mountains in Russia, to the Black sea. The Black Sea is where Europe and Asia's border becomes maritime. Although, the two continents get very close to touching once more at the Bosporus Strait, which splits Turkiye into West (Thrace) and East (Anatolia). This is true despite the fact that the the Bosporus Strait is a channel from the Black Sea into the Sea of Marmara and the Dardanelles, and finally empties into the Aegean/​Mediterranean. If the Bosporus Strait were considered a tributary, then it would be considered a part of the land border (like as for the Ural River). But, technically, the Bosporus Strait is a just a narrow, salt-water "channel". Thus, it too is maritime.

For other continents such as Australia, they have no land borders with other continents. That is, they are completely surrounded by water. Australia finds itself surrounded by 3 distinct world oceans, namely the Indian Ocean, Southern/Antarctic Ocean and the Pacific Ocean. However, these Oceans connect with one another.

Lakes

Oxford purports that a lake is

a large area of water surrounded by land.

But one could argue that the World Ocean is surrounded by land. And the World Ocean is most certainly large. So, is the World Ocean in truth just a lake?

It feels as though the continents of the world are surrounded by the World Ocean, not the other way round. Lakes are surrounded by land, Oceans, it feels, should not. The World Ocean covers 71% of the Earth's surface area, so saying it is surrounded feels wrong. But is it?

What if the World Ocean covered only 49% of the Earth's surface? Would it be downgraded to only a lake? Surely not. It would still be the largest body of water.

One could retort that the World Ocean is surrounded by multiple continents, not by one landmass. Hence, if we define the World Ocean as the only large body of water contacting multiple landmasses, it becomes clearly distinguished from mere lakes.

However, this same definition would have the Nile river, which touches two different and separate parts of Africa in two the World Ocean.

So it seems a more precise definition is in order.

Before we attempt to define lakes and oceans rigorously, it's worth noting that geologists already tried. They use the term superocean to describe oceans that surround supercontinents, such as Panthalassa around Pangaea. This framing, however, is geochronological—it only works when the landmass happens to be unified. It’s binary and temporal. What about a definition that works today, independent of arbitrary continental definitions or geological epochs?

A Geometric Definition of a Lake

Let us propose a novel, geometric distinction between a lake and an ocean, based on the topology of enclosing boundaries and geodesic behavior on a sphere.

Suppose a body of water fully enclosed by any landmass (atoll, island, continent, etc.) which we shall call its enclosing boundary. Now, choose any two points \( A \) and \( B \) along this enclosing boundary. Between these two points, we shall define the geodesic that connect them.

A geodesic is

the shortest path between two points on a curved surface — on a sphere, this is a segment of a great circle (like the arc of the Earth's equator or a line of longitude).

Now consider that there is another arc joining \( A \) and \( B \) that takes the longer path around the globe. If the points are not antipodal, then this path is longer than the geodesic. We call this arc the exterior geodesic.

Importantly, this exterior geodesic cannot not at any point intersect our original body of water. Consider for example a concave body of water, say, a river forming an S shape. If the two points are chosen over two different twists of the river, then we might not be able to form an external geodesic. In this case, we must pick another \( A \) and \( B \) pair for which this doesn't occur.

We now define:

a lake is a body of water for which we may find an external geodesic which subtends an arc greater than or equal to \( 180^{\circ} \).

Let us now consider the so-called "World Ocean". For any two points \( A \) and \( B \) along the enclosing border (e.g., coastal regions of the continents), the longer geodesic connecting them typically traverses open ocean and spans at least \( 180^{\circ} \).

In contrast, consider the Caspian Sea, the largest inland body of water on Earth, and doubly, a misnomer, being considered a lake not a sea. For any two points along the Caspian Sea's shoreline, the external geodesic will typically be greater than \( 180^{\circ} \).

This distinction provides a mathematically grounded criterion to differentiate oceans from lakes.