Document Type : Research Paper
Authors
- Kamran Ghayoumzadeh ^{} ^{1}
- Sara Khakipour ^{2}
^{1} Assistant Professor, Shahid Madani's University of Azarbaijan
^{2} M. A. Graduated in Islamic Philosophy, Shahid Madani University of Azarbaijan
Abstract
The main issue of the present Article is a discussion about the conditional proposition in Stoic- Megarian Logic. There were, in Stoic-Megarian school, many theories of meaning to interpret these propositions. Since conditional propositions made the structure's core of their Logic, so for the understanding of the key concept of their thought, we need searching, prior to anything, in the semantics of these propositions. We will, in the first place and much survey, compare between Stoic-Megarian Logic and Aristotelian Logic and present where is the state of conditional propositions in the Stoic-Megarian Logic; then, in the second place, we explore all kinds of conditional proposition and their conditions of truth values in Stoic-Megarian Logic and compare them with the concept of implication in modern logic and reinterpret them with new instruments in modern logic. Most logicians, in this field, evaluate and compare Stoic-Megarian conditional propositions with definitions of Material implication, strict implication, and Natural laws and we, in this Article, evaluate and analyze these propositions with this perspective and ideas.
Highlights
The Semantics of Conditional Propositions in Stoic-Megarian Logic
Kamran Ghayoomzadeh^{1}, Sara Khakipour^{2}
^{1} Assistant Professor, Department of Philosophy and Logic, Shahid Madani University of Azarbaijan, E-mail: Ghayoom_k@yahoo.com
^{2} M. A. Graduated in Islamic Philosophy, Shahid Madani University of Azarbaijan, E-mail: sarakhakipour@yahoo.com
Abstract
The main issue of the present Article is a discussion about the conditional proposition in Stoic- Megarian Logic. There were, in Stoic-Megarian school, many theories of meaning to interpret these propositions. Since conditional propositions made the structure's core of their Logic, so for the understanding of the key concept of their thought, we need searching, prior to anything, in the semantics of these propositions. We will, in the first place and much survey, compare between Stoic-Megarian Logic and Aristotelian Logic and present where is the state of conditional propositions in the Stoic-Megarian Logic; then, in the second place, we explore all kinds of conditional proposition and their conditions of truth values in Stoic-Megarian Logic and compare them with the concept of implication in modern logic and reinterpret them with new instruments in modern logic. Most logicians, in this field, evaluate and compare Stoic-Megarian conditional propositions with definitions of Material implication, strict implication, and Natural laws and we, in this Article, evaluate and analyze these propositions with this perspective and ideas.
Keywords: Stoic-Megarian logic, Modern Logic, Semantics, Material implication, strict implication.
1. Introduction
The main issue of the present Article is a discussion about the conditional proposition in Stoic- Megarian Logic. Similarities in the views of Stoic-Megarian and Modern logic were reasons for researching and comparing between these logical viewpoints. One of the most important subject in this investigation was the concept and function of implication. There were different ideas about this concept in the history of logic, such as Stoic- Megarian school. Since there was a close relation between Stoic-Megarian logic and their Philosophy and Ethics, we need to specify and clear this concept and conditional propositions that are dependent on it.
2. Different Kinds of Implication
There were four kinds of implication in Stoic-Megarian logic.
2.1. Philonian Implication
A conditional proposition is true if and only if its Antecedent would not be true and its consequent would be false (Bobzien, 2017). This means that this definition of implication is the same as material implication in Modern logic.
2.2. Diodorean Implication
A conditional proposition is true if and only if it would be impossible that Antecedent would be true and consequent would be false (Sextus 2005). In this definition, impossibility could be interpreted to the duration of Time. So this implication cannot be the same as strict implication in Modern logic.
2.3. Chrysippean Implication
A conditional proposition is true if and only if Antecedent with the negation of Consequent would be inconsistent (Mates, 1961). We will show that this implication is not the same as strict implication so.
2.4. Fourth Definition of Implication
A conditional proposition is true if and only if Consequent would be inside to Antecedent (Mates, 1961). This implication is strongest among all of the implications.
3. Conclusion
The different kinds of implication in Stoic-Megarian logic including Philonian, Diodorean and Chrysippean implications define different conditions of truth for the conditional propositions. Philonian implications and material implications of modern logic are the same, but Diodorean and Chrysippean implications and strict implication in its modern meaning cannot be considered as equivalents. Someone considers the coherency in Chrysippean conditional proposition that is stronger than natural laws. We can show that in the last place, which implications are stronger than others: 1- Philonian implication 2- Diodorean implication 3- Natural laws 4- Chrysippean implication 5- Strict implication 6- Fourth definition of implication.
References
- Bobzien, S., (2017) "Ancient Logic", Stanford Encyclopedia of Philosophy, http:// plato. stanford.edu/entries/logic-ancient/.
- Sextus, Empiricus, (2005) Against the Logician, trans. Richard Bett, Cambridge University Press.
- Mates, B., (1961) Stoic Logic, London: Cambridge University Press.
Keywords
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