Context and question: The ultimate substantive legacy of Principia Mathematica is mixed. It is generally accepted that Kurt Godel's incompleteness theorem of 1931 definitively demonstrated that for any set of axioms and inference rules proposed to encapsulate mathematics, there would in fact be some truths of mathematics which could not be deduced from them, and hence that Principia Mathematica could never achieve its aims. However, Godel could not have come to this conclusion without Whitehead and Russell's book. In this way, Principia Mathematica's legacy might be described as its key role in disproving the possibility of achieving its own stated goals. But beyond this somewhat ironic legacy, the book popularized modern mathematical logic and drew important connections between logic, epistemology, and metaphysics.
Godel couldn't have come to his conclusion without what book?
Answer: Principia Mathematica
Context and question: Borders Books, started in Ann Arbor, was opened by brothers Tom and Louis Borders in 1971 with a stock of used books. The Borders chain was based in the city, as was its flagship store until it closed in September 2011. Domino's Pizza's headquarters is near Ann Arbor on Domino's Farms, a 271-acre (110 ha) Frank Lloyd Wright-inspired complex just northeast of the city. Another Ann Arbor-based company is Zingerman's Delicatessen, which serves sandwiches and has developed businesses under a variety of brand names. Zingerman's has grown into a family of companies which offers a variety of products (bake shop, mail order, creamery, coffee) and services (business education). Flint Ink Corp., another Ann Arbor-based company, was the world's largest privately held ink manufacturer until it was acquired by Stuttgart-based XSYS Print Solutions in October 2005. Avfuel, a global supplier of aviation fuels and services, is also headquartered in Ann Arbor. Aastrom Biosciences, a publicly traded company that develops stem cell treatments for cardiovascular diseases, is headquartered in Ann Arbor.
What is the name of the complex located on 217 acres just northeast of the city?
Answer: unanswerable
Context and question: The country is a significant agricultural producer within the EU. Greece has the largest economy in the Balkans and is as an important regional investor. Greece was the largest foreign investor in Albania in 2013, the third in Bulgaria, in the top-three in Romania and Serbia and the most important trading partner and largest foreign investor in the former Yugoslav Republic of Macedonia. The Greek telecommunications company OTE has become a strong investor in former Yugoslavia and in other Balkan countries.
What is Greece a significant producer of within the EU?
Answer:
agricultural