Explanatory coherence

Thagard has proposed that many cognitive functions, including perception, analogy, explanation, decision-making, planning etc., can be understood as a form of (maximum) coherence computation.

Thagard (together with Karsten Verbeurgt) put forth a particular formalization of the concept of coherence as a constraint satisfaction problem.^[11][12] The model posits that coherence operates over a set of representational elements (e.g., propositions, images, etc.) which can either fit together (cohere) or resist fitting together (incohere).

If two elements p and q cohere they are connected by a positive constraint ${\displaystyle (p,q)\in C^{+}}$, and if two elements ${\displaystyle p}$ and ${\displaystyle q}$ incohere they are connected by a negative constraint ${\displaystyle (p,q)\in C^{-}}$. Furthermore, constraints are weighted, i.e., for each constraint ${\displaystyle (p,q)\in C^{+}\cup C^{-}}$ there is a positive weight ${\displaystyle w(p,q)}$.

According to Thagard, coherence maximization involves the partitioning of elements into accepted (${\displaystyle A}$) and rejected (${\displaystyle R}$) elements in such a way that maximum number (or maximum weight) of constraints is satisfied. Here a positive constraint ${\displaystyle (p,q)}$ is said to be satisfied if either both ${\displaystyle p}$ and ${\displaystyle q}$ are accepted (${\displaystyle p,q\in A}$) or both ${\displaystyle p}$ and ${\displaystyle q}$ are rejected (${\displaystyle p,q\in R}$). A negative constraint ${\displaystyle (p,q)}$ is satisfied if one element is accepted (say ${\displaystyle p\in A}$), and the other rejected (${\displaystyle q\in R}$).

Philosophy of science

Thagard worked on the demarcation problem in philosophy of science. Faced with the failure of verifiability and falsifiability, what he called "post positivist depression",^[13]: 114 he proposed in 1978 a criterion to define pseudoscience, with the broader goal being rescuing science from the relativism of Feyerabend and Rorty. According to Thagard's criterion, "A theory which purports to be scientific is pseudoscientific if and only if":

1. It has been less progressive than alternative theories over a long period of time, and faces many unsolved problems; but
2. The community of practitioners makes little attempt to develop the theory towards solutions of the problems, shows no concern for attempts to evaluate the theory in relation to others, and is selective in considering confirmations and disconfirmations.^[14][15]

However, in 1988, Thagard wrote that this proposal should "be abandoned," because it had two flaws. Firstly it was hopeless to attempt to find necessary and sufficient conditions for pseudoscience in general, and secondly, the criterion was too soft on astrology which it was specifically meant to brand as pseudoscience.^[13]: 168 Nonetheless, Thagard, didn't completely abandon his criterion, but instead incorporated it into his new solution to the demarcation problem, which he called "Profile of Science and Pseudoscience", a collection of psychological, historical and logical characteristics, against which a discipline could be compared and categorized as either science or pseudoscience. This process, though not "strict necessary or sufficient", could fulfill the normative goals of science, or what Thagard prefers to call "Natural philosophy", by relying "on descriptions of how everyday and scientific reasoning actually works."^[13]: 114

^[13]: 170

He describes the Aristotelian realist philosophy of mathematics as "the current philosophy of mathematics that fits best with what is known about minds and science."^[16]