How to find an attractive solution to the liar paradox

The general thesis of this paper is that metasemantic theories can play a central role in determining the correct solution to the liar paradox. I argue for the thesis by providing a specific example. I show how Lewis’s reference-magnetic metasemantic theory may decide between two of the most influential solutions to the liar paradox: Kripke’s minimal fixed point theory of truth and Gupta and Belnap’s revision theory of truth. In particular, I suggest that Lewis’s metasemantic theory favours Kripke’s solution to the paradox over Gupta and Belnap’s. I then sketch how other standard criteria for assessing solutions to the liar paradox, such as whether a solution faces a so-called revenge paradox, fit into this picture. While the discussion of the specific example is itself important, the underlying lesson is that we have an unused strategy for resolving one of the hardest problems in philosophy

And so on: two theories of regress arguments in philosophy

This PhD dissertation is on infinite regress arguments in philosophy. Its main goals are to explain what such arguments from many distinct philosophical debates have in common, and to provide guidelines for using and evaluating them. Two theories are reviewed: the Paradox Theory and the Failure Theory. According to the Paradox Theory, infinite regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is settled, or the statement that discussions are settled only if there is an agreed-upon criterion to settle them). According to the Failure Theory, infinite regress arguments can be used to demonstrate that a certain solution fails to solve an existentially or universally quantified problem (e.g. to demonstrate that a certain solution fails to settle all discussions, or that it fails to settle even one discussion). In the literature, the Paradox Theory is fairly well-developed, and this dissertation provides the Failure Theory with the same tools

Considering the Harmonic Sequence "Paradox"

Blavatskyy (2006) formulated a game of chance based on the harmonic series which, he suggests, leads to a St Petersburg type of paradox. In view of the importance of the St Petersburg game to decision theory, any game which leads to a St Petersburg type paradox is of interest. Blavatskyy’s game is re-examined in this article to conclude that it does not lead to a St Petersburg type paradox.Keywords: St Petersburg paradox; harmonic series; harmonic series paradoxes; decision theory and games of chance; decision theory paradoxes; expected values.

A Quantum-like Model of Selection Behavior

In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach that employs the state representation specific to quantum theory, which has the mathematical framework beyond the classical probability theory. We show that our quantum approach can clearly explain the famous examples of anomalies for the expected utility theory, the Ellsberg paradox, the Machina paradox and the disparity between WTA and WTP. Further, we point out that our model mathematically specifies the characteristics of the probability weighting function and the value function, which are basic concepts in the prospect theory

Composite Prospect Theory: A proposal to combine ‘prospect theory’ and ‘cumulative prospect theory’

Evidence shows that (i) people overweight low probabilities and underweight high probabilities, but (ii) ignore events of extremely low probability and treat extremely high probability events as certain. The main alternative decision theories, rank dependent utility (RDU) and cumulative prospect theory (CP) incorporate (i) but not (ii). By contrast, prospect theory (PT) addresses (i) and (ii) by proposing an editing phase that eliminates extremely low probability events, followed by a decision phase that only makes a choice from among the remaining alternatives. However, PT allows for the choice of stochastically dominated options, even when such dominance is obvious. We propose to combine PT and CP into composite cumulative prospect theory (CCP). CCP combines the editing and decision phases of PT into one phase and does not allow for the choice of stochastically dominated options. This, we believe, provides the best available alternative among decision theories of risk at the moment. As illustrative examples, we also show that CCP allows us to resolve three paradoxes: the insurance paradox, the Becker paradox and the St. Petersburg paradox.Decision making under risk; Composite Prelec probability weighting functions; Composite cumulative prospect theory; Composite rank dependent utility theory; Insurance; St. Petersburg paradox; Becker.s paradox