Document (#13511)

Author

Scheibe, E.

Title

Calculemus! : The problem of the application of logic and mathematics

Source

Knowledge organization. 23(1996) no.2, S.67-76

Year

1996

Abstract

Starting out from Descartes' and Leibniz' idea of a mathesis universalis the achievements of modern mathematics are divided into three major parts: the creation of algortihms, the invention of proofs, and the application of mathematics to the description of nature. This applicability has repeatedly been viewed as being just a miracle. One major idea to diminish the miraculous impression was to view mathematics as exploring the vast area of all kinds of abstract structures, thus establishing a huge store og humanly possible thinking from which the physicists has only to chosose the structure appropriate for the case before him. There remains, however, the problem of mathematical overdetermination of physics: the structures suitable for application usually contain mathematical elements that remain without physical interpretation. The true miracle than seems to be that it is often very difficult, if not impossible, to eliminate those uninterpreted elements from physical theory

Similar documents (content)

1. Lange, C.: Ontologies and languages for representing mathematical knowledge on the Semantic Web (2011) 0.22

   0.21718062 = sum of:
     0.21718062 = product of:
       0.90491927 = sum of:
         0.018434955 = weight(abstract_txt:from in 135) [ClassicSimilarity], result of:
           0.018434955 = score(doc=135,freq=4.0), product of:
             0.060982384 = queryWeight, product of:
               1.1956728 = boost
               2.7638826 = idf(docFreq=7577, maxDocs=44218)
               0.018453233 = queryNorm
             0.30229968 = fieldWeight in 135, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               2.7638826 = idf(docFreq=7577, maxDocs=44218)
               0.0546875 = fieldNorm(doc=135)
         0.19080576 = weight(abstract_txt:proofs in 135) [ClassicSimilarity], result of:
           0.19080576 = score(doc=135,freq=2.0), product of:
             0.2530115 = queryWeight, product of:
               1.4061111 = boost
               9.7509775 = idf(docFreq=6, maxDocs=44218)
               0.018453233 = queryNorm
             0.7541387 = fieldWeight in 135, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               9.7509775 = idf(docFreq=6, maxDocs=44218)
               0.0546875 = fieldNorm(doc=135)
         0.055167742 = weight(abstract_txt:structures in 135) [ClassicSimilarity], result of:
           0.055167742 = score(doc=135,freq=2.0), product of:
             0.13938394 = queryWeight, product of:
               1.4759474 = boost
               5.117636 = idf(docFreq=719, maxDocs=44218)
               0.018453233 = queryNorm
             0.39579698 = fieldWeight in 135, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.117636 = idf(docFreq=719, maxDocs=44218)
               0.0546875 = fieldNorm(doc=135)
         0.21075746 = weight(abstract_txt:mathematical in 135) [ClassicSimilarity], result of:
           0.21075746 = score(doc=135,freq=8.0), product of:
             0.214581 = queryWeight, product of:
               1.8313026 = boost
               6.3497796 = idf(docFreq=209, maxDocs=44218)
               0.018453233 = queryNorm
             0.98218143 = fieldWeight in 135, product of:
               2.828427 = tf(freq=8.0), with freq of:
                 8.0 = termFreq=8.0
               6.3497796 = idf(docFreq=209, maxDocs=44218)
               0.0546875 = fieldNorm(doc=135)
         0.0418444 = weight(abstract_txt:application in 135) [ClassicSimilarity], result of:
           0.0418444 = score(doc=135,freq=1.0), product of:
             0.16719422 = queryWeight, product of:
               1.9797975 = boost
               4.5764427 = idf(docFreq=1236, maxDocs=44218)
               0.018453233 = queryNorm
             0.2502742 = fieldWeight in 135, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.5764427 = idf(docFreq=1236, maxDocs=44218)
               0.0546875 = fieldNorm(doc=135)
         0.38790897 = weight(abstract_txt:mathematics in 135) [ClassicSimilarity], result of:
           0.38790897 = score(doc=135,freq=5.0), product of:
             0.474904 = queryWeight, product of:
               3.8528528 = boost
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.018453233 = queryNorm
             0.81681556 = fieldWeight in 135, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.0546875 = fieldNorm(doc=135)
       0.24 = coord(6/25)
   

2. Popescu, F.: ¬An approach to eponyms in mathematics (2009) 0.13

   0.13480087 = sum of:
     0.13480087 = product of:
       0.6740043 = sum of:
         0.0105342595 = weight(abstract_txt:from in 1119) [ClassicSimilarity], result of:
           0.0105342595 = score(doc=1119,freq=1.0), product of:
             0.060982384 = queryWeight, product of:
               1.1956728 = boost
               2.7638826 = idf(docFreq=7577, maxDocs=44218)
               0.018453233 = queryNorm
             0.17274266 = fieldWeight in 1119, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.7638826 = idf(docFreq=7577, maxDocs=44218)
               0.0625 = fieldNorm(doc=1119)
         0.06304885 = weight(abstract_txt:structures in 1119) [ClassicSimilarity], result of:
           0.06304885 = score(doc=1119,freq=2.0), product of:
             0.13938394 = queryWeight, product of:
               1.4759474 = boost
               5.117636 = idf(docFreq=719, maxDocs=44218)
               0.018453233 = queryNorm
             0.4523394 = fieldWeight in 1119, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.117636 = idf(docFreq=719, maxDocs=44218)
               0.0625 = fieldNorm(doc=1119)
         0.048427686 = weight(abstract_txt:elements in 1119) [ClassicSimilarity], result of:
           0.048427686 = score(doc=1119,freq=1.0), product of:
             0.14728792 = queryWeight, product of:
               1.5172182 = boost
               5.260737 = idf(docFreq=623, maxDocs=44218)
               0.018453233 = queryNorm
             0.32879606 = fieldWeight in 1119, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.260737 = idf(docFreq=623, maxDocs=44218)
               0.0625 = fieldNorm(doc=1119)
         0.2085958 = weight(abstract_txt:mathematical in 1119) [ClassicSimilarity], result of:
           0.2085958 = score(doc=1119,freq=6.0), product of:
             0.214581 = queryWeight, product of:
               1.8313026 = boost
               6.3497796 = idf(docFreq=209, maxDocs=44218)
               0.018453233 = queryNorm
             0.9721075 = fieldWeight in 1119, product of:
               2.4494898 = tf(freq=6.0), with freq of:
                 6.0 = termFreq=6.0
               6.3497796 = idf(docFreq=209, maxDocs=44218)
               0.0625 = fieldNorm(doc=1119)
         0.3433977 = weight(abstract_txt:mathematics in 1119) [ClassicSimilarity], result of:
           0.3433977 = score(doc=1119,freq=3.0), product of:
             0.474904 = queryWeight, product of:
               3.8528528 = boost
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.018453233 = queryNorm
             0.7230887 = fieldWeight in 1119, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.0625 = fieldNorm(doc=1119)
       0.2 = coord(5/25)
   

3. Brown, C.: Physical sciences and mathematics literatures and their users (2009) 0.13

   0.13091484 = sum of:
     0.13091484 = product of:
       0.81821775 = sum of:
         0.18449399 = weight(abstract_txt:physicists in 3864) [ClassicSimilarity], result of:
           0.18449399 = score(doc=3864,freq=2.0), product of:
             0.19504409 = queryWeight, product of:
               1.2345705 = boost
               8.561393 = idf(docFreq=22, maxDocs=44218)
               0.018453233 = queryNorm
             0.94590914 = fieldWeight in 3864, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               8.561393 = idf(docFreq=22, maxDocs=44218)
               0.078125 = fieldNorm(doc=3864)
         0.1327039 = weight(abstract_txt:physical in 3864) [ClassicSimilarity], result of:
           0.1327039 = score(doc=3864,freq=3.0), product of:
             0.17233759 = queryWeight, product of:
               1.6411736 = boost
               5.690534 = idf(docFreq=405, maxDocs=44218)
               0.018453233 = queryNorm
             0.7700229 = fieldWeight in 3864, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               5.690534 = idf(docFreq=405, maxDocs=44218)
               0.078125 = fieldNorm(doc=3864)
         0.15054104 = weight(abstract_txt:mathematical in 3864) [ClassicSimilarity], result of:
           0.15054104 = score(doc=3864,freq=2.0), product of:
             0.214581 = queryWeight, product of:
               1.8313026 = boost
               6.3497796 = idf(docFreq=209, maxDocs=44218)
               0.018453233 = queryNorm
             0.7015581 = fieldWeight in 3864, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.3497796 = idf(docFreq=209, maxDocs=44218)
               0.078125 = fieldNorm(doc=3864)
         0.35047883 = weight(abstract_txt:mathematics in 3864) [ClassicSimilarity], result of:
           0.35047883 = score(doc=3864,freq=2.0), product of:
             0.474904 = queryWeight, product of:
               3.8528528 = boost
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.018453233 = queryNorm
             0.7379993 = fieldWeight in 3864, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.078125 = fieldNorm(doc=3864)
       0.16 = coord(4/25)
   

4. Grunwald, E.: Eponymphomania (2005) 0.11

   0.11058933 = sum of:
     0.11058933 = product of:
       0.6911833 = sum of:
         0.018434955 = weight(abstract_txt:from in 3331) [ClassicSimilarity], result of:
           0.018434955 = score(doc=3331,freq=1.0), product of:
             0.060982384 = queryWeight, product of:
               1.1956728 = boost
               2.7638826 = idf(docFreq=7577, maxDocs=44218)
               0.018453233 = queryNorm
             0.30229968 = fieldWeight in 3331, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.7638826 = idf(docFreq=7577, maxDocs=44218)
               0.109375 = fieldNorm(doc=3331)
         0.115034536 = weight(abstract_txt:idea in 3331) [ClassicSimilarity], result of:
           0.115034536 = score(doc=3331,freq=1.0), product of:
             0.1805641 = queryWeight, product of:
               1.6798877 = boost
               5.8247695 = idf(docFreq=354, maxDocs=44218)
               0.018453233 = queryNorm
             0.6370842 = fieldWeight in 3331, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.8247695 = idf(docFreq=354, maxDocs=44218)
               0.109375 = fieldNorm(doc=3331)
         0.21075746 = weight(abstract_txt:mathematical in 3331) [ClassicSimilarity], result of:
           0.21075746 = score(doc=3331,freq=2.0), product of:
             0.214581 = queryWeight, product of:
               1.8313026 = boost
               6.3497796 = idf(docFreq=209, maxDocs=44218)
               0.018453233 = queryNorm
             0.98218143 = fieldWeight in 3331, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.3497796 = idf(docFreq=209, maxDocs=44218)
               0.109375 = fieldNorm(doc=3331)
         0.34695634 = weight(abstract_txt:mathematics in 3331) [ClassicSimilarity], result of:
           0.34695634 = score(doc=3331,freq=1.0), product of:
             0.474904 = queryWeight, product of:
               3.8528528 = boost
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.018453233 = queryNorm
             0.73058206 = fieldWeight in 3331, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.109375 = fieldNorm(doc=3331)
       0.16 = coord(4/25)
   

5. Fife, E.D.; Husch, L.: ¬The Mathematics Archives : making mathematics easy to find on the Web (1999) 0.11

   0.10524117 = sum of:
     0.10524117 = product of:
       0.65775734 = sum of:
         0.0105342595 = weight(abstract_txt:from in 1239) [ClassicSimilarity], result of:
           0.0105342595 = score(doc=1239,freq=1.0), product of:
             0.060982384 = queryWeight, product of:
               1.1956728 = boost
               2.7638826 = idf(docFreq=7577, maxDocs=44218)
               0.018453233 = queryNorm
             0.17274266 = fieldWeight in 1239, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.7638826 = idf(docFreq=7577, maxDocs=44218)
               0.0625 = fieldNorm(doc=1239)
         0.033580795 = weight(abstract_txt:major in 1239) [ClassicSimilarity], result of:
           0.033580795 = score(doc=1239,freq=1.0), product of:
             0.115389235 = queryWeight, product of:
               1.3429108 = boost
               4.6563506 = idf(docFreq=1141, maxDocs=44218)
               0.018453233 = queryNorm
             0.2910219 = fieldWeight in 1239, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.6563506 = idf(docFreq=1141, maxDocs=44218)
               0.0625 = fieldNorm(doc=1239)
         0.17031775 = weight(abstract_txt:mathematical in 1239) [ClassicSimilarity], result of:
           0.17031775 = score(doc=1239,freq=4.0), product of:
             0.214581 = queryWeight, product of:
               1.8313026 = boost
               6.3497796 = idf(docFreq=209, maxDocs=44218)
               0.018453233 = queryNorm
             0.79372245 = fieldWeight in 1239, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               6.3497796 = idf(docFreq=209, maxDocs=44218)
               0.0625 = fieldNorm(doc=1239)
         0.44332454 = weight(abstract_txt:mathematics in 1239) [ClassicSimilarity], result of:
           0.44332454 = score(doc=1239,freq=5.0), product of:
             0.474904 = queryWeight, product of:
               3.8528528 = boost
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.018453233 = queryNorm
             0.9335035 = fieldWeight in 1239, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.0625 = fieldNorm(doc=1239)
       0.16 = coord(4/25)