By Hallvard Lillehammer, D. H. Mellor
The Cambridge thinker Frank Ramsey died tragically in 1930 on the age of 26, yet had already proven himself as some of the most extraordinary minds of the 20th century. in addition to groundbreaking paintings in philosophy, quite in common sense, language, and metaphysics, he created smooth determination idea and made large contributions to arithmetic and economics. In those unique essays, written to commemorate the centenary of Ramsey's delivery, a exclusive overseas group of members supply clean views on his paintings and express its ongoing relevance to present-day issues.
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Extra resources for Ramsey's Legacy (Mind Association Occasional Series)
And a nice logic emerges. For example, modus ponens is valid: demonstrably, if p(A) is high and p(B given A) is high, p(B) is high. On the other hand, there are the counter-examples to strengthening of the antecedent, to transitivity, and to contraposition, which are now well known. ( Note: the logic is for sentences in which the conditional, if it occurs, occurs as a main connective. ) Robert Stalnaker was also impressed by Ramsey’s footnote, and by Adams’s work. His project in the late 1960s was to fill the gap noted by Adams: to find a proposition such that the probability of its truth is measured in Ramsey’s and Adams’s way (see Stalnaker 1968, 1970).
It is easy to prove the following: it is impossible that the improbability of the conclusion should exceed the sum of the improbabilities of the premises (where improbability is one minus probability). Thus, arguments which necessarily preserve truth, necessarily preserve probability in the sense that there can be no more improbability in the conclusion than there is in all the premises together. So, in a twopremise valid argument each of whose premises gets a probability of 99%, the worst-case scenario for the conclusion is that it gets 98%.
For instance, I judge that it’s 90% likely that Jane won’t be offered the job, 10% likely that she will, 1% likely that she will be offered and decline, 9% likely that she will be offered and accept. I think it’s 10% likely that she will decline if she is offered the job, while the probability of the corresponding material implication is 91%. This would appear to rule out that conditionals are material implications. If conditionals were material implications, we should judge them to be probable when the material implication is probable.