A few lingering questions...(adsbygoogle = window.adsbygoogle || []).push({});

Suppose an interpretation is an assignment of capital letters to declarative sentences. I see that assigning the same letter to more than one sentence limits the usefulness of your interpretation, but is it ever useful or necessary to assign more than one letter to the same sentence?

Suppose a set E of English sentences is translated, by a suitable interpretation, into a set X of formulas of formal language L. The information contained within each sentence is lost in the translation. Because of this, X may be consistent while E is inconsistent (the inconsistencies could lie in the lost information). However, if X is inconsistent, E is inconsistent because [?blank?]. I can't say because inconsistency in L is only a relationship between formula and if a relationship holds between formula, it holds between sentences- since that would also be true of consistency. There's some difference between consistency and inconsistency that I'm missing.

Similarly, suppose an argument (E/c), where E is as before, and c is an English sentence and the conclusion, is translated into a sequent (X l= p), where X is as before and p is formula of L. If (X l= p) is correct, (E/c) is a valid argument because 1) if E inconsistent, the argument is still valid, 2) if c is self-contradictory, E must be inconsistent- right?, 3) if c is tautologous, (E/c) is valid, and 4) are there other cases to consider?

If (X l= p) is incorrect, (E/c) is [?blank?]. I don't think this tells us anything about (E/c). (E/c) could easily be invalid, and, if, for instance, M: "John died on Monday" and T: "John died on the day before Tuesday" are in E_{MT}, this lost information could make several (E_{MT}/c)s valid even if (X_{MT}l= p) is incorrect.

BTW, I see that (E/c) could be circular even if (X l= p) is not, since 1) we could have used more than one letter for at least one sentence in E, or 2) two or more sentences in E could be equivalent, as in E_{MT}. I would love any tidbits such as that.

I don't need everything spelled out for me; Hints would be enough and appreciated.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Interpretations and structures

Loading...

Similar Threads - Interpretations structures | Date |
---|---|

A Interpreting a paper on spectral analysis | Mar 14, 2018 |

A Interpreting Chi Squared ... backward | Feb 11, 2018 |

I Interpreting the correlation | Feb 6, 2018 |

I Bayes again - how to interpret in vitro genotoxicity data | Jun 10, 2017 |

Logical structure of definitions | Sep 8, 2015 |

**Physics Forums - The Fusion of Science and Community**