Hello, my name is Ram and welcome to another video of Matuklasan. Reasoning is the action that we do whenever we want to think or say something in a logical or sensible way. This is like our go-to...
defense mechanism when we want to justify our actions and statements to other people. Reasoning is often a highlighted topic in various fields like philosophy, science, language, mathematics and art, and is normally considered a major topic in the field of philosophy. considered as one of our distinguishing abilities as a human. In logic, reasoning is the drawing of inferences or conclusions from known or assumed facts. The two major types of reasoning are deductive and inductive.
These refer to the process by which someone creates a conclusion as well as how they believe their conclusion to be true. Deductive reasoning is the process of reaching a conclusion by applying general ideas called premises. This concept is often expressed visually using a funnel that narrows a general idea into a specific conclusion.
Recognized rules, laws, theories, and other widely accepted truths are used to prove that a conclusion is right. The most common form of deductive reasoning is the syllogism where two premises that share some ideas support a conclusion. In symbols, A implies B, B implies C, therefore A implies C, where A, B, and Cs are propositions or the general ideas that we are referring to. This one is also similar to transitive property of equality where if we have A plus B or A equals B as our premise and b equals c is another premise then a equals c because both are equal to b for example all men are mortal ram is a man therefore ram is mortal in symbols let this b implies c And this one, BA implies B.
So we can see here that B are the same. So A implies C. Another example, all even numbers are divisible by 2. 22 is even.
Since we have the same idea here, therefore, 22 is divisible by 2. Next, Marvel Comics characters are fictional. Iron Man is a Marvel Comics character. So we have here comics character as the same idea.
So therefore, Iron Man is a fictional character. Citrus fruits are rich in vitamin C. Orange is a citrus fruit.
Therefore, an orange is rich in vitamin C. Now, how about this example? All musical instruments make sounds. Jeepneys make sounds. Therefore, jeepneys are musical instruments.
Teka, teka, teka. All musical instruments make sounds. This is true.
This is a true premise. Jeepneys make sounds. This is also a true premise.
But jeepneys are not musical instruments so this is false. Therefore this is not a valid deductive reasoning. Always remember that we use premises to prove the conclusion is true and not to justify it.
Deductive reasoning is meant to demonstrate that the conclusion is absolutely true based on the logic of the premises. Inductive reasoning, on the other hand, is the process of reaching a general conclusion by examining specific observations. So, a few particular premises create a pattern which gives way to a general conclusion that is like this.
likely true. This is commonly shown using a triangle that starts at the narrow premises and expands into a broader conclusion. Unlike deductive reasoning, inductive reasoning has no basic standard format when we use it.
So as long as we are finding a conclusion that is most likely to fit the premises, then we can make predictions, create generalization, and analyze cost and effect. Keep in mind that in deductive reasoning, premises are used to prove a conclusion, while premises in inductive reasoning are used to predict a conclusion, meaning we don't create a definite answer but we are trying to show that the conclusion is the most probable one given the premises for example yesterday morning is a went jogging this morning she jogged again therefore isa will probably jog tomorrow morning this conclusion is not definite but basing on the morning routine of isa there is a high chance that she will jog tomorrow morning, right? Now, what if we are asked to find the next figure in this pattern?
The first figure is a square. In the second figure, a square. second square was constructed inside of the first square wherein the vertices of this new square are on the midpoints of the sides of the first square. Following the same pattern and by using inductive reasoning, it's possible that the next pattern is this one. An inductive argument is either considered weak or strong based on whether its conclusion is a probable explanation for the premises.
Let's compare these inductive arguments. On the left, the two statements are likely true on the left. their own but the first premise does not predict the second to be true because i probably know what's funny for my friends but some may find it corny right on the right we can see that this These numbers are all multiples of 3 in ascending order. So it is logical to say that the next term after 15 is 18. Because the premises identify a pattern.
Thus, the reasoning on the left is weak while the right is strong. Now let's try determining the kind of reasoning used in each argument. For number one, the teacher used Google Classroom in the last few classes. So based on this pattern, we can say that the teacher will use Google Classroom tomorrow.
But this is not definite, right? So this is inductive reasoning. Number two, all licensed drivers are 17 years old and above.
Marcus has a driver's license. Therefore, Marcus is at least 17 years old. Syllogism was used and we have a true conclusion. So therefore, this is deductive reasoning. Next, all spiders have eight legs.
Black widows are spiders. Thus, black widows have eight legs. Just like in number two, this is deductive reasoning. Number four, my father has a black hair.
My brother has a black hair. So based from these two premises and pattern that we can see, therefore everyone I am related to has a black hair. But this is just a probable conclusion. So this is inductive reasoning. Number five, the Game of Thrones TV series was a worldwide success.
Therefore, any sequel for the series will probably be successful. This is inductive reasoning. And that's all for this video. If you want more video lessons in math in the modern world, please check my playlist in the description below.
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