@misc{Lexicon of Arguments, title = {Quotation from: Lexicon of Arguments – Concepts - Ed. Martin Schulz, 28 Mar 2024}, author = {Thiel,Christian}, subject = {Infinity}, note = {I 59 Infinity/Thiel: to the "potentiality" of the election one does not have to march up all basic numbers in their "actuality". Even if finiteness occurs in a certain sense in infinity, not every sentence about finiteness is normally a special case of sentences about infinity. I 60 For example, study whether there might be a series of properties of the basic numbers, similar to the series of basic numbers themselves. To do this, we have to distinguish between properties and forms of expression through which we represent them. Here is a one-digit form of statement: For example, the property of being an even number. By means of a tally list I 60 ...+ Question: whether in any arithmetically suitable language the forms of statements representing a property of basic numbers can be arranged in a series: Cantor Diagonal Procedure/Thiel: There will be infinitely many such forms of statements. We would have the infinite series Aq(m), A2(m), A3(m), ... I 62 ... the statement form "~An(n)" represents a well-defined property of basic numbers, as long as we only have a series like the one above. In this series, however, no logically equivalent statement form to the newly constructed statement form can occur, and in particular no statement form itself! Thiel I 157 Infinite/Thiel: Example "There are infinitely many prime numbers". To capture this sentence it is of course not sufficient to formulate "There is one more prime number for each prime number". For this would also apply if 2 and 3 were the only prime numbers! What is meant, however, is that there is always at least one different to them to any number of primes. I 158 In another way, it is much easier to indicate this, namely by means of an order relation. (m)(En) (mF. Waismann. I 164 These discussions show the conflict between two views of infinity: Property or process. >Infinite/Cantor.}, note = { T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 }, file = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=527330} url = {http://philosophy-science-humanities-controversies.com/listview-details.php?id=527330} }