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Directory:Jon Awbrey/Papers/Functional Logic : Inquiry and Analogy (view source)
Revision as of 05:14, 26 December 2010
, 05:14, 26 December 2010→Version 2. “A Theory of Probable Inference” (1883): modify notation
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<math>\begin{array}{l}
<center>
<math>\begin{matrix}
T ~\text{is}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime};
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S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{are}~ R\operatorname{'s};
S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{are}~ Q\operatorname{'s};
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\text{Hence,}~ Q ~\text{is an}~ R.
\text{Hence,}~ T ~\text{is a}~ Q.
\end{array}</math>
\end{matrix}</math>
</center>
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<center>
<math>\begin{array}{l|l}
<math>\begin{array}{l|l}
\text{Every}~ X ~\text{is, for example,}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime}, ~\text{etc.},
\text{Every}~ X ~\text{is, for example,}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime}, ~\text{etc.},
S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{etc., are samples of the}~ X\operatorname{'s},
S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{etc., are samples of the}~ X\operatorname{'s},
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T ~\text{is found to be}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime}, ~\text{etc.};
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S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{etc., are found to be}~ R\operatorname{'s};
S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{etc., are found to be}~ Q\operatorname{'s};
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\text{Hence, hypothetically,}~ Q ~\text{is an}~ X.
\text{Hence, hypothetically,}~ T ~\text{is an}~ X.
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\text{Hence, inductively, every}~ X ~\text{is an}~ R.
\text{Hence, inductively, every}~ X ~\text{is a}~ Q.
\end{array}</math>
\end{array}</math>
</center>
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<center>
<center>
<math>\text{Hence, deductively,}~ Q ~\text{is an}~ R.</math>
<math>\text{Hence, deductively,}~ T ~\text{is a}~ Q.</math>
</center>
</center>
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