Combinators,lambda-terms and proof theory by Soren Stenlund

By Soren Stenlund

The purpose of this monograph is to provide a number of the simple principles and leads to natural combinatory good judgment and their functions to a couple issues in facts conception, and likewise to provide a few paintings of my very own. many of the fabric in bankruptcy 1 and three has already seemed in my notes creation to Combinatory good judgment. it seems that the following in revised shape because the presentation in my notes is wrong in numerous respects.

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In that case angels 42 God, Mind, and Logical Space are not redundant when considering their existence-relative-to-theregions-that-depict-them-as-existing, and our analysis is consistent with this insight. 3 Nested logical space As was apparent when discussing, in Chapter 1, the way to account for the conflict between certain philosophical positions that disagree about logical space itself, our notion of Logical Space has both a horizontal dimension and a vertical one. By vertical dimension I mean the fact that Logical Space is nested, that is, it contains levels that represent mutually exclusive canonical logical spaces at lower or more basic levels.

However, when it comes to empty proper names, the Russellian approach has some counterintuitive consequences. The only true sentence involving an empty proper name, NN, according to that approach is the negative existential, that is the statement that NN does not exist. But some other sentences are also, intuitively, true. For instance: “Sherlock Holmes is smarter than George W. Bush”, or “Sherlock Holmes is a Arthur Conan Doyle’s invention”. These statements, as asserted by a speaker, s, are translated as follows, respectively: (18) r s (r ≠ s & r x x = h & s y y = b & S xy) (19) r s (r ≠ s & r x x = h & s y y = d & I xy) Sxy means “x is smarter than y”, and Ixy means “x is y’s invention”.

For instance, “Superman” typically connotes a superhuman, and also refers to such a superior human. Other examples include “Spiderman”, “Jack the Ripper”, “The Evening Star” and various nicknames whose connotations indicate a property that the bearer instantiates, for example “Bigmouth”. Another category of informative proper 38 God, Mind, and Logical Space names is what Gareth Evans introduced as descriptive names; these are names introduced via a definite description, for example the fictional “Zip”, which is introduced in language as “the actual inventor of the zip”, or the real-world example of “Neptun”, which in 1845 Leverrier introduced as “the planet that is responsible for the irregularities of Uranus”.

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