Abstract
This paper defends a counterexample to Modus Tollens, and uses it to draw some conclusions about the logic and semantics of indicative conditionals and probability operators in natural language. Along the way we investigate some of the interactions of these expressions with knows, and we call into question the thesis that all knowledge ascriptions have truth-conditions. A probabilistic dynamic semantics for probability operators, conditionals, and acceptance attitudes is developed around the idea of representing the common ground of a conversation as a set of probability spaces.
Highlights
A marble is selected at random and placed under a cup
I take it that the probability operators likely and probably are synonyms, so I will use them interchangeably
Since it is just a special case of Modus Tollens (MT), it is a counterexample to the claim that MT is a generally valid pattern
Summary
Are three possible replies to our counterexample. The first reply is that I have misrepresented the logical form of (P1). We should be clear about the nature of this burden It would be one thing if we could detect some semantic difference between these two allegedly logically possible scopal orders, and declare that intuitively, the scopal order in (P1) is obligatorily probably, →. This style of argument certainly works in principle.. In this sentence there are two logically possible scopal orders for the interpretation of probably and the quantifier everyone, each of which would yield a (truthconditionally) different reading of the sentence. If things are not equal here, we are owed some account why
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
