Lewisian the are irreducible entities. It should be noted

Modal Realism is a well known theory whereby it is claimed that possible
objects are concrete and are equivalently as real as we are or as the bed you
sleep on. It is noted that the most prevalent of these possible objects are
worlds, which he says are maximally spatiotemporally related fusions of
concrete objects (1986: 69:81). Lewis’ three doctrines explain his views upon
the existence of possible worlds, saying they exist and are alike our real
world. His second doctrine describes the possible worlds as having the same
sort of things as our actual world, however, differing in content. This ultimately
brings us to his third doctrine which states that worlds cannot be reduced to
something more basic, as the are irreducible entities. It should be noted that
all possibilists accept the view that merely possible, non-actual entities
exist. The LMR is ontologically and ideologically parsimonious and has been categorized
as being an economical theory.  Lewis’ ontology
can be identified and separated into two categories, with the first being concrete
objects and the second; classes.


strongest argument in favour of modal realism is reductionism, which has been
taken to be a main strength of LMR. Despite LMR being a very controversial
theory to accept, Lewis’ account of possible worlds provides us with a logical
analysis of possibility and necessity, a view taken by Theodore Sider (2003:14).

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Looking through the analysis of possible worlds of modality, it can only be
considered reductive, as Sider states, if the notion of truth in possible
worlds is non-modal; with it depending upon the ontological status of possible worlds
(2003:8). As Lewis is able to distinguish the idea of possible worlds from
others of the same kind it makes his argument reductive, whereas if he wasn’t able
to distinguish then it wouldn’t be. As aforementioned, Lewis is able to
distinguish possible worlds from the actual world by defining possible worlds
spatiotemporally. Lewis is able to reduce modality by separating the modern
interest towards possible worlds from it. Reductionism is viewed as the most
favoured argument in support of LMR since it overlooks modal claims, which are
considered to cause conundrums.

LMR is
considered an extremely convincing and solid theory to follow, however, it is
not exempt from criticisms. A key objection comes from actualism, with the main
objective coming from the actualist point of view that Lewis’ ontology is an
incoherent argument. Sider recounts this objection in his book, ‘Reductive Theories of Modality’, noting
the objection is directed towards the existence of Lewis’ possible worlds
(2003:17). The objection is as follows that it is incomprehensible to suggest
the existence of absolutely anything being non actual. From an actualist point
of view, they are positing that the LMR’s possible worlds and accepting of
existing things as non actual to be a very illogical as the term actual is a
term that loosely means everything. Sider takes the actualist view that if one
is to accept the possibility of Lewis’ world existing then it would be included
in actuality and wouldn’t relate to possibility and necessity (2003:17). The
actualists criticism can be upheld as showing that the reductionist argument
may not be the strongest for LMR.