Logical Equivalence Failure (Published)
Citation: James H. Hughes (2022) Logical Equivalence Failure, International Journal of Mathematics and Statistics Studies, Vol.10, No.2, pp.1-25
Abstract: As a point of mathematical logic, this paper proves that the contrapositive is not logically equivalent to the conditional, which disproves the “proof by contradiction” that has been used in mathematics for over a hundred years. The paper then provides suggestions for why the “proof by contradiction” may have been derived in error.
The Reality of Sovereignty in Nigeria from 1999 to 2019 and the Implications For Democracy (Published)
The year 2019 marks two decades of the Nigeria’s democratic governance which in Nigeria Political parlance is referred to as the fourth republic. The first republic which started on the attainment of independence in 1960 was truncated by the military in 1966 and from that time till the 29th of May, 1999 when the military was coerced to relinquish power, Nigeria did not pretend in her clamour for democracy .The democratically elected government of Alhaji Shehu Shagari (1979-1984) was equally overthrown by the military in Nigeria. From Independence in 1960 to 1999, a period of 39 years, Nigeria had eight military head of state in government for a total of twenty-nine (29) years with only two civilian head of states. The compass of this present democratic experience midwifed by the 1999 Constitution is that Sovereignty belongs to the people. The reality of the sovereignty is the focus of this study. The study revealed that the actual voters in Nigeria with a population of over two hundred million people are the judges and not the people .That judges are the determinant of the representatives of people is anachronistic considering the fact that the judges in Nigeria are guided by their idiosyncrasies and not logic in their role as the interpreter of law and adjudicator.
Sustainable development and good living condition in the modern world are determined by people who possess more than normal reasoning abilities. The present Nigerian socio-political, economic and technological dilemma therefore results from the redundancy of mind paved by gross deficiency in logic and critical thinking competencies. This deficiency broadly stems from Nigerian poor educational system which has neglected acquisition of reflective and critical reasoning skills in theoretical and practical terms. This hampers critical competence, and results to irrational judgments, biased policies and dishonest governance. Consequently, problem solving and critical competence in various sectors of Nigerian existence have remained a mirage resulting to unsustainable development. This paper analytically investigates the meaning, cradle, essence, relevance and state of logic and critical thinking in Nigerian higher education and existence. The research finds that logic and critical thinking has been negligently relegated to one of those optional General Studies’ courses rarely needed to make up the required credit load. As such, not every department of education in Nigeria offers logic and critical thinking. This is coupled with the fact that in some Nigerian Higher Institutions, logic and critical thinking is managed by unqualified staff. The paper as well finds that knowledge of logic and critical thinking is indispensable in the daily human expressions, decisions, right choices and actions. For deficiency in reasoning skills paves way for errors, deceptions, violence and false democracy. The paper concludes that for Nigeria to initiate and sustain true democracy and development, logic and critical thinking should be centrally paramount in her education system because of its quality of impacting critical reasoning skills and competency in the students and citizenry.