Deductive reasoning Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! === Probability logic === [[Probability logic]] is interested in how the probability of the premises of an argument affects the probability of its conclusion. It differs from classical logic, which assumes that propositions are either true or false but does not take into consideration the probability or certainty that a proposition is true or false.<ref>{{cite book |last1=Adams |first1=Ernest W. |title=A Primer of Probability Logic |date=13 October 1998 |publisher=Cambridge University Press |isbn=978-1-57586-066-4 |url=https://books.google.com/books?id=YxWMQgAACAAJ |language=en |chapter=1. Deduction and Probability: What Probability Logic Is About}}</ref><ref>{{cite book |last1=Hájek |first1=Alan |title=The Blackwell Guide to Philosophical Logic |date=2001 |publisher=Blackwell |pages=362–384 |url=https://philpapers.org/rec/HJEPLA |chapter=16. Probability, Logic, and Probability Logic}}</ref> The probability of the conclusion of a deductive argument cannot be calculated by figuring out the cumulative probability of the argument's premises. [[Timothy J. McGrew|Dr. Timothy McGrew]], a specialist in the applications of [[probability theory]], and Dr. Ernest W. Adams, a Professor Emeritus at [[UC Berkeley]], pointed out that the theorem on the accumulation of uncertainty designates only a lower limit on the probability of the conclusion. So the probability of the conjunction of the argument's premises sets only a minimum probability of the conclusion. The probability of the argument's conclusion cannot be any lower than the probability of the conjunction of the argument's premises. For example, if the probability of a deductive argument's four premises is ~0.43, then it is assured that the probability of the argument's conclusion is no less than ~0.43. It could be much higher, but it cannot drop under that lower limit.<ref>{{cite book |last= Adams|first= Ernest W.|date= 1998|title= A Primer of Probability Logic|publisher= Cambridge University Press|pages= 31–34|isbn= 157586066X}}</ref><ref name="Argument">{{cite journal |last1= McGrew|first1= Timothy J.|last2= DePoe|first2= John M.|date= 2013|title= Uses of Argument|url= https://philpapers.org/rec/DEPNTA|journal= Philosophia Christi|volume= 15|issue= 2|pages= 299–309|doi= 10.5840/pc201315228|access-date= 13 March 2021}}</ref> There can be examples in which each single premise is more likely true than not and yet it would be unreasonable to accept the conjunction of the premises. [[Henry E. Kyburg Jr.|Professor Henry Kyburg]], who was known for his work in [[probability]] and [[logic]], clarified that the issue here is one of closure – specifically, closure under conjunction. There are examples where it is reasonable to accept P and reasonable to accept Q without its being reasonable to accept the conjunction (P&Q). Lotteries serve as very intuitive examples of this, because in a basic non-discriminatory finite lottery with only a single winner to be drawn, it is sound to think that ticket 1 is a loser, sound to think that ticket 2 is a loser,...all the way up to the final number. However, clearly, it is irrational to accept the conjunction of these statements; the conjunction would deny the very terms of the lottery because (taken with the background knowledge) it would entail that there is no winner.<ref>{{cite journal|last1=Kyburg|first1=Henry|date=1970|title="Conjunctivitis," in M. Swain, ed., Induction, Acceptance, and Rational Belief|url=https://link.springer.com/chapter/10.1007/978-94-010-3390-9_4|journal=SYLI|volume=26|pages=55–82|doi=10.1007/978-94-010-3390-9_4|access-date=13 March 2021}}</ref><ref name="Argument"/> Dr. McGrew further adds that the sole method to ensure that a conclusion deductively drawn from a group of premises is more probable than not is to use premises the conjunction of which is more probable than not. This point is slightly tricky, because it can lead to a possible misunderstanding. What is being searched for is a general principle that specifies factors under which, for any logical consequence C of the group of premises, C is more probable than not. Particular consequences will differ in their probability. However, the goal is to state a condition under which this attribute is ensured, regardless of which consequence one draws, and fulfilment of that condition is required to complete the task. This principle can be demonstrated in a moderately clear way. Suppose, for instance, the following group of premises: {P, Q, R} Suppose that the conjunction ((P & Q) & R) fails to be more probable than not. Then there is at least one logical consequence of the group that fails to be more probable than not – namely, that very conjunction. So it is an essential factor for the argument to “preserve plausibility” (Dr. McGrew coins this phrase to mean “guarantee, from information about the plausibility of the premises alone, that any conclusion drawn from those premises by deductive inference is itself more plausible than not”) that the conjunction of the premises be more probable than not.<ref name="Argument"/> Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. 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