In analytic philosophy, anti-realism is an
epistemological position first articulated
by British philosopher Michael Dummett.
The term was coined as an argument against
a form of realism Dummett saw as 'colorless
reductionism'.In anti-realism, the truth of
a statement rests on its demonstrability through
internal logic mechanisms, such as the context
principle or intuitionistic logic, in direct
opposition to the realist notion that the
truth of a statement rests on its correspondence
to an external, independent reality.
In anti-realism, this external reality is
hypothetical and is not assumed.Because it
encompasses statements containing abstract
ideal objects (i.e. mathematical objects),
anti-realism may apply to a wide range of
philosophic topics, from material objects
to the theoretical entities of science, mathematical
statement, mental states, events and processes,
the past and the future.
== Varieties ==
=== 
Metaphysical anti-realism ===
One kind of metaphysical anti-realism maintains
a skepticism about the physical world, arguing
either: 1) that nothing exists outside the
mind, or 2) that we would have no access to
a mind-independent reality, even if it exists.
The latter case often takes the form of a
denial of the idea that we can have 'unconceptualised'
experiences (see Myth of the Given).
Conversely, most realists (specifically, indirect
realists) hold that perceptions or sense data
are caused by mind-independent objects.
But this introduces the possibility of another
kind of skepticism: since our understanding
of causality is that the same effect can be
produced by multiple causes, there is a lack
of determinacy about what one is really perceiving,
as in the brain in a vat scenario.
The main alternative to this sort of metaphysical
anti-realism is metaphysical realism.
On a more abstract level, model-theoretic
anti-realist arguments hold that a given set
of symbols in a theory can be mapped onto
any number of sets of real-world objects—each
set being a "model" of the theory—provided
the relationship between the objects is the
same (compare with symbol grounding.)
In ancient Greek philosophy, nominalist (anti-realist)
doctrines about universals were proposed by
the Stoics, especially Chrysippus.
In early modern philosophy, conceptualist
anti-realist doctrines about universals were
proposed by thinkers like René Descartes,
John Locke, Baruch Spinoza, Gottfried Wilhelm
Leibniz, George Berkeley, and David Hume.
In late modern philosophy, anti-realist doctrines
about knowledge were proposed by the German
idealist Georg Wilhelm Friedrich Hegel.
Hegel was a proponent of what is now called
inferentialism: he believed that the ground
for the axioms and the foundation for the
validity of the inferences are the right consequences
and that the axioms do not explain the consequence.
Kant and Hegel held conceptualist views about
universals.
In contemporary philosophy, anti-realism was
revived in the form of empirio-criticism,
logical positivism, semantic anti-realism
and scientific instrumentalism (see below).
=== Semantic anti-realism ===
The term "anti-realism" was introduced by
Michael Dummett in his 1982 paper "Realism"
in order to re-examine a number of classical
philosophical disputes, involving such doctrines
as nominalism, Platonic realism, idealism
and phenomenalism.
The novelty of Dummett's approach consisted
in portraying these disputes as analogous
to the dispute between intuitionism and Platonism
in the philosophy of mathematics.
According to intuitionists (anti-realists
with respect to mathematical objects), the
truth of a mathematical statement consists
in our ability to prove it.
According to Platonic realists, the truth
of a statement is proven in its correspondence
to objective reality.
Thus, intuitionists are ready to accept a
statement of the form "P or Q" as true only
if we can prove P or if we can prove Q. In
particular, we cannot in general claim that
"P or not P" is true (the law of excluded
middle), since in some cases we may not be
able to prove the statement "P" nor prove
the statement "not P".
Similarly, intuitionists object to the existence
property for classical logic, where one can
prove
∃
x
.
ϕ
(
x
)
{\displaystyle \exists x.\phi (x)}
, without being able to produce any term
t
{\displaystyle t}
of which
ϕ
{\displaystyle \phi }
holds.
Dummett argues that this notion of truth lies
at the bottom of various classical forms of
anti-realism, and uses it to re-interpret
phenomenalism, claiming that it need not take
the form of reductionism.
Dummett's writings on anti-realism draw heavily
on the later writings of Ludwig Wittgenstein,
concerning meaning and rule following, and
can be seen as an attempt to integrate central
ideas from the Philosophical Investigations
into the constructive tradition of analytic
philosophy deriving from Gottlob Frege.
=== Scientific anti-realism ===
In philosophy of science, anti-realism applies
chiefly to claims about the non-reality of
"unobservable" entities such as electrons
or genes, which are not detectable with human
senses.One prominent variety of scientific
anti-realism is instrumentalism, which takes
a purely agnostic view towards the existence
of unobservable entities, in which the unobservable
entity X serves as an instrument to aid in
the success of theory Y and does not require
proof for the existence or non-existence of
X.
Some scientific anti-realists, however, deny
that unobservables exist, even as non-truth
conditioned instruments.
=== Mathematical anti-realism ===
In the philosophy of mathematics, realism
is the claim that mathematical entities such
as 'number' have an observer-independent existence.
Empiricism, which associates numbers with
concrete physical objects, and Platonism,
in which numbers are abstract, non-physical
entities, are the preeminent forms of mathematical
realism.
The "epistemic argument" against Platonism
has been made by Paul Benacerraf and Hartry
Field.
Platonism posits that mathematical objects
are abstract entities.
By general agreement, abstract entities cannot
interact causally with physical entities ("the
truth-values of our mathematical assertions
depend on facts involving platonic entities
that reside in a realm outside of space-time")
Whilst our knowledge of physical objects is
based on our ability to perceive them, and
therefore to causally interact with them,
there is no parallel account of how mathematicians
come to have knowledge of abstract objects.Field
developed his views into fictionalism.
Benacerraf also developed the philosophy of
mathematical structuralism, according to which
there are no mathematical objects.
Nonetheless, some versions of structuralism
are compatible with some versions of realism.
==== Counterarguments ====
Anti-realist arguments hinge on the idea that
a satisfactory, naturalistic account of thought
processes can be given for mathematical reasoning.
One line of defense is to maintain that this
is false, so that mathematical reasoning uses
some special intuition that involves contact
with the Platonic realm, as in the argument
given by Sir Roger Penrose.Another line of
defense is to maintain that abstract objects
are relevant to mathematical reasoning in
a way that is non causal, and not analogous
to perception.
This argument is developed by Jerrold Katz
in his 2000 book Realistic Rationalism.
In this book, he put forward a position called
realistic rationalism, which combines metaphysical
realism and rationalism.
A more radical defense is to deny the separation
of physical world and the platonic world,
i.e. the mathematical universe hypothesis
(a variety of mathematicism).
In that case, a mathematician's knowledge
of mathematics is one mathematical object
making contact with another.
== See also
