LEARN LOGIC THE EASY WAY!

Introduction to LOGIC and

Tricks to knowing how to do LOGIC RULES.

Oluwo Tomiwa UNAD

What is logic? Before I answer this question, I just want logic students to note that, there is no place in logic class or lesson that when its time for an examination that the question, ‘’WHAT IS LOGIC?’’ will come out. Right before now, logic examination will only be based on writing essays kind of., but instead, they are going to be Venn diagramming that is, testing the validity of a proposition by this means and also, forming propositions or statements out of AEE-1, AAA-4, OIO-3 or AEI-3 mode and figures. So, once again, ‘what is LOGIC?’ (Logic is the language for reasoning. It is also a collection of rules we use when doing logical reasoning because, human reasoning has been observed over the centuries from at least the times of Greek and patterns appearing in reasoning have been extracted, abstracted, and streamlined.’’).

Some things that students studying logic should know before proceeding to studying logic because as time goes by, they will eventually be asked to learn them and at that time, it will be a big deal to them because they won’t know or learn them easily.

Things like:

*Immediate rules of inference i.e. conversion, obversion and contraposition

*Distributions

*Mood and figures

*Rules of INFERENCES

*Rules of REPLACEMENT

*VENN DIAGRAM

*TRUTH-TABLE (LONG AND SHORT)

Before I proceed, there is something I will like to point out concerning LOGIC. Logic is mathematics language and there is nothing hard in it but of course, it harder than Maths. So, let’s start.

TYPES OF LOGIC

1. Propositional logic or sentential logic

2. Predicate logic

3. Logic of uncertainty

4. Logic dealing with fuzziness

5. Temporal logic.

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

Oluwo Tomiwa, UNAD