Rejecting the idea that mental phenomena would be different to physical phenomena, makes it possible to accept both other premises:
Mental phenomena can cause physical phenomena.
Every physical phenomenon has a physical cause.
But what does it mean that mental phenomena are identical to physical phenomena?
Classical Type Physicalism
A first version of modern identity theories was presented by U. T. Place in his famous article “Is Consciousness a Brain Process?” from 1956. Here, Place is arguing for mental states being physical states, using an “is of composition” instead of an “is of definition”. This distinction – originally being worked out by Bertrand Russell – can easily be illustrated by an easy statement like “fish are animals”. Here, clearly an “is of compisition” is being used, since all fish are animals but not all animals are fish. In other words, fish are a subset of animals. Analogous, Place argues that conscious states are brain states but not all brain states are conscious states.
J. J. C. Smart in his article “Sensations and Brain Processes” is arguing in a slightly different way relating to identity. His hypothesis is somewhat bolder and more in the direction of an “is of composition” type of identity claim between mental and physical states. In Frege’s terms, statements about mental states and statements about physical states according to Smart have the same reference, but another sense, as they are referring to the same ontological entity but differ in the kind of referring to it. Both Place and Smart emphasize that the logic of the mental sphere is different from the logic of the physical sphere and therefore cannot be reduced to each other. So, it can be stated that though their identity theories are ontologically reductive, they are not linguistically reductive.
Token Physicalism: Anomalous Monism
The classical type physicalist theories received quite some criticism. A notable argument introduced by Hilary Putnam in 1967 is “multiple realizability”, the idea that the same mental states – e.g. pain – can be produced by vastly different physical states, a fact that seems apparent when looking at the quite different nervous system architecture of various animals of which we all assume to feel pain. Defending identity theory against such criticism, Donald Davidson in his notably article “Mental Events” framed what he called anomalous monism. He criticies Place and Smart for not distinguishing between type and token. According to Davidson, single, mental events (token) have effects on the physical world, but no strict laws between types of mental and physical events exist.