1. Outline the axiomatic method. (Yes, write it down in words.) The axiomatic method is a process of achieving a scientific theory in which axioms (primitive assumptions) are assumed as the base of the theory, whereas logical values of these axioms find the rest of the theory. 2. Explain what deductive reasoning is. How is it related to the axiomatic method? Deductive reasoning is a logical way to increase the set of facts that are assumed to be true. The purpose of Deductive reasoning is to end up at a logical conclusion based on the subject of discussion. Deductive Reasoning uses statements that are logically true in order to omit other statements that contradict the logically true statement, which is to deduce, subtract or takeaway. What …show more content…
You read Book I, Propositions 1 and 11 in the Axiomatic Method assignment. For each proposition: a. What does each proposition say in common American English? What is Euclid doing in each case? Euclid propositions can be called theorems in common language. In the Book I Euclid main considerations was on geometry. He began with a long list of definitions which followed by the small number of basic statements to take the essential properties of points, lines, angles etc. then he obtained the remaining geometry from these basic statements with proofs. (Berlinghoff, 2015, p.158). Propositions 1 and 11 in common American English. Proposition 1. An equilateral triangle can be created on a given finite straight line. Proposition 11. It can be possible to draw a straight line, making right angles from a given point on a given straight …show more content…
Numbers that are measured by an alone unit as a common measure are called relatively prime. e. In Book VII, Proposition 2, what is the "greatest common measure?" What does Prop. 2 say in common English. Proposition 2: It is possible to find the greatest common measure from two given numbers that are not relatively prime. The greatest common measure is achieved when two numbers measures. It is the largest number which divides the both numbers and can be found by using the Euclidean algorithm. Which is a process of continually subtracting the smaller number from the larger until the smaller can divide the larger. 4. (Sketch 24) Show logical notation that expresses following statement: If one dice shows an even number of spots and the second dice show an odd number of spots, then the total for the pair is less than or equal to 9. There are 36 outcomes (elements) of rolling two dice, out of that 4 of them for getting 9 with the sum of even and odd numbers. E = {3,6}, {4,5}, {5,4},
If I would make any proposition whatever [P], then by that I would have a logical error [E]...
This argument would be considered a deductive argument because the conclusion follows necessarily from the sub-conclusions and the premises. As long as all of the premises are true this is a sound argument. Points of concern in the argument are each of the unsupported assertions. The following will determine if any fallacies or false claims have been used in the construction of this argument.
Document A has conveyed that no matter who they are, what their gender and age classified as this is their nation, they do not have any excuse not to participate in this war and bring victory to
It was once said by Johannes Kepler that “Geometry has two great treasures: one is the Theorem of Pythagoras, and the other the division of a line into extreme and mean ratio. Golden Ratio is found by dividing a line into two parts so that the longer part divided by the smaller part equals the whole length divided by the longer part. It is also known as the extreme and mean ratio. Golden ratio is very similar to Pi because it is an infinite number and it goes on forever. It is usually rounded to around 1.618. The formula for golden ratio is a/b = (a+b)/b. Golden Ratio is a number that has been around for many years. It has been around for a long time so it is not known who formed the idea of the golden ratio. Since the golden ratio is used all around the world, it is known in many names such as the golden mean, phi, the divine proportion, extreme and mean proportion, etc. It is usually referred to as phi. Golden ratio was used in arts from the beginning of people and still is used today. It has been used in architecture, math, sculptures and nature. Many famous artists used the golden ratio. Golden ratio can also be used on a rectangle which is known as the golden rectangle. Euclid talks about it in his book Elements. Golden ratio also has a relationship with both the Fibonacci numbers and Lucas numbers.
Rene Descartes Method of Doubt was simply his mathematical method in discovering the unanswered questions about the universe. He wanted to prove every unknown question and be certain that he could prove his truths with knowledge given only by mathematical proof. "Common Sense", which Descartes refers to as natural reason, is the understanding of all humans with many given subjects. He feels that in some common sense areas, one should just be expected to know what all humans are assumed to know and therefore, does not need to be mathematically proven.
In this paper I intend to analyze logically this proposition, trying to focus the question of contradiction.
Deduction is the third characteristic of rationalism, which is to prove something with certainty rather than reason. For example, Descartes attempted to prove the existence of God through deductive reasoning in his third meditation. It went something like this: “I have an idea of a perfect substance, but I am not a perfect substance, so there is no way I could not be the cause of this idea, so there must be some formal reality which is a perfect substance- like God. Because only perfection can create perfection, and though it can also create imperfection- nothing that is imperfect can create something that is perfect.
For the purposes of this debate, I take the sign of a poor argument to be that the negation of the premises are more plausible than their affirmations. With that in mind, kohai must demonstrate that the following premises are probably false:
(ii) A standardised argument which draws on your answers to Part (i). You should include:
This structure shows the two initial premises which he argues, in detail, to be correct and in the case that they are correct a logically valid conclusion.
to say that if a and b are in same ratio with c and d, then any one of the three
The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers.
In this argument, if “employees have a duty of loyalty to the companies that employ them” is considered the p and “it is rational for employees to expect companies to recognize and fulfill a duty of loyalty to their employees” will be the q. It continues to follow that q is false as it is not rational for employees to expect companies to recognize and fulfill loyalty to their employees. The logical form ends with not p as “It is false that employees have a duty of loyalty to the companies that employ them”. It is known that this argument is deductively valid but in order to show that the conclusion is also true, it must be true that the argument is deductively sound. An example of a deductively valid argument would be as following: Premise 1) All mammals have four feet; Premise 2) Lions are mammals; Conclusion) Therefore, Lions have four feet. Premise 1 in this argument is true, mammals do have four feet, Premise 2 is also true, Lions are mammals, and therefore the conclusion is also true that Lions have four feet. With these true premises leading to a true conclusion help us understand
The main reason the metric system is known for its simplicity is because there is only unit of measurement or a base unit for each type of measured quantity measured; length mass, weight, etc… There are a few base units in the metric system but the most common ones which are used are the meter, gram and liter. As an example if ...
Euclidean geometry is the study of points, lines, angles, triangles, circles, squares and other shapes, as well as the properties and relationships between the properties of all these things (Marshall, 2014, para.8). Euclidean geometry is one of the types of mathematics students are learning about in secondary schools, and is also commonly used in everyday life. Mathematicians and researchers have discovered many types of geometries, but Euclidean geometry is the oldest branch of mathematics.