|Abstract||In principle, a proof can be any sequence of logical deductions from axioms and previously-proved statements that concludes with the proposition in question. This freedom in constructing a proof can seem overwhelming at ﬁrst. How do you even start a proof? Here’s the good news: many proofs follow one of a handful of standard templates. Proofs all diﬀer in the details, of course, but these templates at least provide you with an outline to ﬁll in. We’ll go through several of these standard patterns, pointing out the basic idea and common pitfalls and giving some examples. Many of these templates ﬁt together; one may give you a top-level outline while others help you at the next level of detail. And we’ll show you other, more sophisticated proof techniques later on. The recipes below are very speciﬁc at times, telling you exactly which words to write down on your piece of paper. You’re certainly free to say things your own way instead; we’re just giving you something you could say so that you’re never at a complete loss.|
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
|Through your library||Only published papers are available at libraries|
Similar books and articles
Peter Pagin (1994). Knowledge of Proofs. Topoi 13 (2):93-100.
R. B. J. T. Allenby (1997). Numbers and Proofs. Copublished in North, South, and Central America by John Wiley & Sons Inc..
Carlo Cellucci (2008). Why Proof? What is a Proof? In Giovanna Corsi & Rossella Lupacchini (eds.), Deduction, Computation, Experiment. Exploring the Effectiveness of Proof, pp. 1-27. Springer.
Marvin R. G. Schiller (2013). Granularity Analysis for Mathematical Proofs. Topics in Cognitive Science 5 (2):251-269.
Andrzej Wiśniewski (2004). Socratic Proofs. Journal of Philosophical Logic 33 (3):299-326.
Joram Hirshfeld (1988). Nonstandard Combinatorics. Studia Logica 47 (3):221 - 232.
Duccio Luchi & Franco Montagna (1999). An Operational Logic of Proofs with Positive and Negative Information. Studia Logica 63 (1):7-25.
Ryo Takemura (2013). Proof Theory for Reasoning with Euler Diagrams: A Logic Translation and Normalization. Studia Logica 101 (1):157-191.
Felix Mühlhölzer (2006). "A Mathematical Proof Must Be Surveyable" What Wittgenstein Meant by This and What It Implies. Grazer Philosophische Studien 71 (1):57-86.
Mateja Jamnik, Alan Bundy & Ian Green (1999). On Automating Diagrammatic Proofs of Arithmetic Arguments. Journal of Logic, Language and Information 8 (3):297-321.
Edwin Coleman (2009). The Surveyability of Long Proofs. Foundations of Science 14 (1-2):27-43.
Konstantine Arkoudas & Selmer Bringsjord (2007). Computers, Justification, and Mathematical Knowledge. Minds and Machines 17 (2):185-202.
David Sherry (2009). The Role of Diagrams in Mathematical Arguments. Foundations of Science 14 (1-2):59-74.
Carlo Cellucci (1985). Proof Theory and Complexity. Synthese 62 (2):173 - 189.
Sorry, there are not enough data points to plot this chart.
Added to index2010-12-22
Total downloads1 ( #291,386 of 722,826 )
Recent downloads (6 months)0
How can I increase my downloads?