Understanding the Nature of Assertions and Laws in Logic and Society
The concept of an assertion or statement often confounds individuals and scholars alike. This article explores the intricacies of these concepts, drawing on logical and societal contexts to clarify their roles and implications.
Assertions and Their Characteristics
A statement is essentially an assertion or assertive sentence. However, it must be noted that an assertion neither proves nor refutes a thought, which is an opinion. This distinction is vital in understanding the nature of logical and abstract entities. A thought or an opinion, in this regard, is considered an abstract object with no inherent existence or reality. It is about something, rather than being something in itself.
The Role of Laws in Assertions
A law is a statement that holds true within a given context, such as a game, legislature, logic, morality, or physics. Despite its seemingly absolute nature, any law is fundamentally the assertion of an opinion. For example, the statement "11" is a law that is deemed real and useful. However, it is not inherently true or false; it simply asserts the equality of one and one.
Similarly, the statement "12" would be similarly deemed false, but both assertions are ultimately just assertions. They don't prove or disprove anything; they simply declare a position. The statement "11" might seem self-evident, yet this clarity of assertion is at the core of mathematical and logical frameworks.
Truth Value and Logical Oscillation
When we delve deeper into digital logic, we encounter the concept of truth value. A true statement returns a truth value of 1, and a false statement returns 0. However, the nature of digital logic introduces a peculiar scenario:
Consider a TTL inverter, a NOT-gate, with a 5-volt power supply. If the output of this gate is connected back to its input, you might expect a contradiction. Yet, no such contradiction ensues. Instead, the system oscillates between truth values, effectively defying this binary logic. This oscillation occurs when there's minimal delay between input and output. Without delay, the system might output a voltage between 2 and 3 volts, neither clearly true nor false.
With sufficient delay, however, the system can oscillate indefinitely, cycling between 1 and 0. This oscillation illustrates that a logical system can maintain its functionality without being constrained by a definite truth value. The system can exist in a state that is not purely true or false but oscillating between these states.
The Societal Agreement on Laws
The assertion of a law or opinion within a societal framework is a concept that requires communal agreement. The societal agreement on a specific law or opinion successfully fakes the existence of these abstract entities. By agreeing on the terms and conditions of a law, society collectively affirms its existence, even if it’s merely a position of opinion or belief.
This agreement is crucial because it gives the illusion of certainty in a world where absolute truth is often unattainable. The foundational assertion of "11" is just such an example. It is a written rock, a basic assumption on which more complex logic and mathematics rely. Yet, it is an assertion, not a provable fact. The assertion “11” is very real because it is deemed and asserted true, useful, and necessarily so, even if it is unprovable.
Conclusion
In sum, the nature of assertions and laws is complex. While they are essential elements in logical and societal contexts, they do not prove or disprove anything. Instead, they are assertions of opinions. This means that while we might treat these statements as self-evident truths, their nature is more aligned with the abstract and the subjective.
Understanding these concepts is crucial for navigating the intricacies of logical and mathematical frameworks and for recognizing the role of societal agreement in shaping our beliefs and truths. By embracing the oscillation and uncertainty, we can better appreciate the nature of assertions and laws in both digital and societal contexts.