Rules of INFERENCES
This is the rules employed by logicians to validate an argument or a proposition and usually, they are interwoven mean that almost all the rules have one particular thing that made them look alike and thereby letting logic student get or be familiar with knowing how they can remember them but most people don’t know this.
What most student of logic don’t know about knowing how to know the RULES OF INFERENCES and also the RULES OF REPLACEMENT. Like I was saying before this paragraph, I made mention that, all the symbols and logos of these rules are looking alike in one particular point of the others.
Before I proceed, here are the keys that will represent my symbols:
And ( . )
Or ( v )
Not ( ~ )
IFF = if and only if ( = )
Imply ( > )
Now that we are all familiar with our symbols, we may proceed now. So,
Take for example: Modus Tollen otherwise known as MP and Modus Ponen also known as MT. That is:
Modus Tollen (MP)
P > Q
P
Therefore: Q
And the second one which is:
Modus Ponen (MT)
P > Q
~ Q
therefore: ~ P
‘’Taking a closer look at this, you will see or notice the relationship and what I mean by this is that, they share something figures and symbols… like during MP, we should notice that is says ( P imply Q, P, therefore: Q) and during MT it says: ( P imply Q ‘’while they share these in-common’’ and then it goes further by saying not ~ Q, therefore: ~ P).
As we all know that each categorical syllogism or standard form argument or proposition usually comprises of two (2) premises and one (1) conclusion so the point I am trying to stage here is that, the first proposition has P imply Q and this is the same on both proposition that is the MP and the MT (similarity) and then, they went ahead and exchanged their other symbols and vice-versa, that is: from being ordinary P in MP, it changed to ~ Q in MT and then on the conclusion, from Q, it became ~P for MT.
Before I proceed, I will like at this junction to state some process in which student of logic will be following to try to remember the rules so, for:
RULES OF INFERENCES they are:
MP-MT-DS-HS-ADD-SIM-CON-ABS-CD-DD
And for the
RULES OF REPLACEMENT they are:
MI-TRANS-EXPO-ME-DIS-TAUT-ASS-COM-DM-DN
So, in relating what all the above jargons means, here:
For the Rules of Inferences:
Modus Ponen - MP
Modus Tollen - MT
D Syllogism - DS
Hypothetical Syllogism - HS
Addition - ADD
Simplification - SIM
Conjuction - CON
Absorption - ABS
Constructive Dilemma - CD
Destrucitve Dilemma - DD
And for the Rules of Replacement, they are:
Material Implication - MI
Transportation - TRANS
Exportation - EXPO
Materials Equivalent - ME
Dyslgtic Syllogism - DIS
Tautology - TAUT
Association - ASS
Commutation - COM
De Morgan Theorem - DM
Double negation - DN
These words are best know and pronounced in one form that is for the first rules which is the RULES OF INFERENCES- MP MT DS HS AD SIM CON ABS CD DD. Try knowing these steps and it makes the whole knowing the rules easier because this is the first step to knowing how to know the rules and et cetera and they some how relating…
Please note these rules of inferences is not and will never be the same rules as the rules of immediate inferences that is those Obversion, Conversion and Contraposition. (These are rules implored to remove or put components that is non and etc from propositions.)
And the other rules is Replacement are- MI TRANS EXPO ME DIS TAUT AS COM DM DN. So easy. So, for the purpose of our discussion, we shall only stick with these rules for now and knowing how to know them hassle-free.
RULES OF INFERENCE
P>Q
P
.: Q = MP
P>Q
~Q
.: ~P = MT
PvQ
~P
.: Q = DS
P>Q
Q>r
.: P>r = HS
P
.: P v Q = ADD
P . Q
.: Q = SIMP
P
Q
.: P . Q = CONJ
P>Q
.: P> (P . Q) = ABS
(P>Q) . (r>s)
Pvr
.: Qvs = CD
(P>Q) . (r>s)
~Qv~s
.: ~Pv~r = DD
RULES OF REPLACEMENT
P>Q=~PvQ = MI
P>Q=P~Q>~P = TRANS
(P.Q)>R=P>(Q>R) = EXPO
(P=Q)=(P>Q).(Q>P)
(P=Q)=(P.Q)v(~P.~Q) = ME
P.(QvR)=(P.Q)v(P.R)
Pv(Q.R)=(PvQ).(PvR) = DIS
P=P.P
P=PvP = TAUT
P.(Q.R)=(P.Q).R
Pv(QvR)=(PvQ)vR = ASS
(P.Q)(Q.P)
(PvQ)(QvP) = COMM
~(P.Q)=~Pv~Q
~(PvQ)=~P.~Q = DM
P=~~P = DN
