Considering views about the relation between the mental and the physical as distinguished first by whether or not mental entities are identical with physical entities, and second by whether or not there are strict psychophysical laws, we arrive at a fourfold classification: (1) nomological monism, which says there are strict correlating laws, and that the correlated entities are identical (this is usually called type physicalism); (2) nomological dualism, which holds that there are strict correlating laws, but that the correlated entities are not identical (parallelism, property dualism and pre-established harmony); (3) anomalous dualism, which holds there are no laws correlating the mental and the physical, that the substances are ontologically distinct, but nevertheless there is interaction between them (i.e. Cartesian dualism); and (4) anomalous monism, which allows only one class of entities, but denies the possibility of definitional and nomological reduction.
Davidson put forth his theory of anomalous monism as a possible solution to the mind–body problem.
However, according to anomalous monism, events cannot be so explained or predicted as described in mental terms (such as "thinking", "desiring" etc.
His original position, as expressed in Actions and Events, was that event-individuation must be done on the basis of causal powers.
Rather, "the turning on of the light-switch" also involves "the illumination of the room", "the alerting of the burglar in the kitchen", etc...
Davidson says that the causal event, in such a case, is the particular reason that caused the action to occur.
Davidson originally assumed the validity of this principle but, in more recent years, he felt the need to provide a logical justification for it.
This means that while the generalization ((M1 & M2) → P1) is justifiable ceteris paribus, it cannot be fully expanded into a more detailed law such as (P2 & P3 & M1 & M2 & M3) → P1.
Davidson defended the cause-law principle by revising Curt John Ducasse's (1926) attempt to define singular causal relations without appealing to covering laws.
Davidson turns this around and asks if it is not the case that our notions of change do not, rather, appeal to a foundation of laws.
Hence, it could be argued that what we view as change is theory-dependent and presupposes a background notion of laws.
This principle arises out of two further doctrines which Davidson espoused throughout his life: the normativity of the mental and semantic holism.
Vincenzo Fano provides an illustration of the point that holism of the mental generates anomalism.
To do this, we must assume a set of laws concerning the interaction between the table and the measuring apparatus: the length of the table doesn't vary significantly during the measurement, length must be an additive quantity, "longer than" must be an asymmetric, transitive relation and so forth.
.... As Fano states it, "this process would seem like a regressus ad infinitum, if it weren't that
We ask ourselves if Thomas, who has recently been betrayed by his girlfriend Ffion, believes that it is possible that the relationship can continue.
The way we can find out the answer to this question is simply by asking Thomas if he believes it is possible.
At this point, we think we have a definitive confirmation of the fact that Thomas believes that the relation must be interrupted, since he reflected on the matter before answering.
So we return to our original hypothesis on the basis that Thomas is angry and therefore confuses his desires and his beliefs.
This is a physical predicate F. We can call the attribution of Thomas' belief that the relationship cannot continue m. From Fx, we cannot deduce mx.
There is no law of nature under which events fall when they are described according to the order in which they appeared on the television news.
When the earthquake caused the Church of Santa Maria dalla Chiesa to collapse, there is surely some physical law(s) which explains what happened, but not under the description in terms of the event on Channel 7 at six p.m. causing the events on Channel 8 at six fifteen.
But if we describe the event as "the two French and green things caused the scale to move to the two-pound mark", then while this is true, there is no lawlike relation between the greenness and Frenchness of the pears and the pointers moving to the two-pound mark.
On this basis, we can formulate the generalization that Honderich calls 'the Nomological Character of Causally-Relevant Properties'.
But if we accept the first two claims of the argument for AM, along with the idea of the causal efficacy of the mental, and the Principle of Causally-Relevant properties, then the result is a denial of anomalous monism because there are indeed psycho-physical lawlike connections.
On the other hand, if we wish to retain the principle of the anomalism of the mental then we must reject causal efficacy and embrace epiphenomenalism.
Davidson has responded to such arguments by reformulating anomalous monism and has defended the improved version in Thinking Causes.
He points out that the defect in the so-called epiphenominalism problem lies in its confusion of the concept "by virtue of" (or necessary for) with the idea of an event's being responsible for another.
But the action of placing pears on a scale can have many different effects; it can attract the attention of a customer, for example.