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Transcript of Paradoxes
Importance of Paradoxes
Paradoxes are important to us because they help us identify mistakes and errors in theories formulated by people.
Paradoxes also help our logical reasoning as they show us the flaws in our way of thinking.
Introduction to Paradoxes
What is a Paradox?
A paradox is a statement, concept, situation a person or anything that seems contradictory or defies the laws of logic. The intriguing fact about paradoxes is that although they are contradictory statements, these statements still have a little truth in them.
The word paradox comes from the Latin word paradoxum which is based on the word doxa, Greek dogma, meaning opinion. One of the meanings of para is "contrary, hence the word paradox literally means contrary to opinion.
Relation between logic and Paradoxes
Logic And Paradoxes are inter-related with each other. Paradoxes are based on logic. A paradox only occurs because of logical reasoning that will lead to a paradoxical outcome as a result of different causes and situations.
The Study Of Logic
Logical reasoning is the process which uses arguements, statements, premises, and axioms to define whether or not a statement is true or false. This may result in a logical or illogical reasoning.
This type of reasoning originates from philosophy and mathematics. Deduction refers to a method that is used to apply a general rule (major premise) in specific situations (minor premise) from which conclusions can be drawn.
Inductive reasoning is the complete opposite of Deductive Reasoning. In this form of logical reasoning, conclusions that are specific are taken as general conclusions.
Abductive reasoning is the form of logical reasoning where the most plausible and probable conclusion is the correct one.
Formal & Informal Logic
Formal reasoning is a type of logical reasoning based on valid premises and therefore valid conclusions, thus it is a form of deductive reasoning. It provides no new information, but only rearranges known information to a new conclusion.
Informal reasoning is a type of reasoning which possesses all the elements of formal reasoning except for the added probabilities and truths being taken into account while coming to a conclusion
What is logic?
The Different Types of Logic:
An example of this is
Major Premise : All humans have a brain
Minor Premise : Socrates is a human
Conclusion : Socrates has a brain
An example of this is :
Major Premise : The paper is cut
Minor Premise : I have a scissor in my hand
Conclusion : I cut the paper
Types of Paradoxes
Paradoxes have been classified into four different classes by W. V. Quine:
Physical Paradoxes are apparent contradictions in the physical descriptions of the universe. In other words, it is a contradiction in the commonly known subject of physics.
Time paradoxes refer to contradictions regarding the mechanics and the workings of time as we know it and contradictions in the outcomes that would come as a result of time travel.
A mathematical paradox is a contradiction in the general topic of mathematics we have learnt for the most of our lives.
Logical Paradoxes are the contradictions that occur as a result of our logical reasoning that we use in our daily lives. Most logical paradoxes occur in the form of self - reference or vagueness.
An example of this is :
Conclusion : All pens are black - Observed from a large number of observations without seeing any other color
Reality - We know that all pens aren't black
As you can see after going through this presentation, paradoxes have actually played a role in molding our lives and shaping it into the way it is today without our knowledge. There are many different types of paradox ranging from thought experiments to the phrases we use in our daily lives. They help us in many ways we cant even begin to think about and they help us by allowing us to view things with a different perspective.
A veridical paradox is one which produces a result that appears absurd but is demonstrated to be true nevertheless.
A falsidical paradox is one that establishes a result that not only appears false but is actually false due to a mistaken belief in it's demonstration. No emphasis will be put on this type of paradox in this presentation as this presentation talks of mostly the other types of paradoxes.
A paradox that has a description following neither of the earlier mentioned types of paradoxes is known as an Antinomy. This type of paradox reaches a paradoxical result through the proper use of accepted methods of reasoning.
This refers to a paradox that is both true and false at the same time and in the same sense.
An example of such a situation would be whether or not you are in a room if you stand exactly halfway through the doorway. The statement may be regarded as true or false although it cannot be proven or disproven.
Paradoxes have also been grouped thematically according to the subjects they relate to. These themes along with their examples are shown on the outer frame, click on the topic you want to
find out more about
The term logic refers to the use of valid reasoning in an activity and it also refers to the study of the aforementioned activity.
It can also be referred to as the study of how to make inferences and to reason out problems.
The schrodinger's cat paradox is a thought experiment where a cat is both alive and dead.
In the video shown to the left, you can see that the radioactive substance leads to the uncertainty of whether or
not the cat is alive thus leading to the conclusion that the cat is indeed both alive and dead at the same time.
Irresistible Force Paradox
In this paradox, an irresistible force meets an immovable object, what happens then?
The paradox in this is that an irresistible force should be able to move anything and an immovable object shouldn't be able to be moved by any force.
The video below demonstrates this paradox.
The grandfather paradox is derived from the temporal paradox in which a time traveler does things in the past that prevent him from doing them in the first place.
This is a mathematical paradox with the subtopic of infinity as well. It states that "You will never reach point B from point A as you must always get half-way there, and half of the half, and half of that half, and so on."
Monty Hall Problem
The monty hall problem is a mathematical paradox in the sub-topic that is probability. It shows us an unintuitive consequence of basic probability
The liar paradox is a form of self-referential paradox. An example of this would be the statement "This Sentence is False." Below is the Pinocchio paradox, a derivative of the liar paradox.
This is a derivation of the set theoretic paradox and was used to popularize the set paradox in which the question " Does the set of all those sets that do not contain themselves contain itself?"
Importance Of Paradoxes In our Daily Lives
Paradoxes can be of a great help to us in our daily lives such as in situations where we need to make decisions. When we have to make a decision, each decision will be both good and bad at the same time. In this situation, we would have to eliminate the paradox thus simplify it by saying that the decision can be good for some reasons and bad for other reasons.
Importance of Paradoxes in History
Paradoxes play a big role in history and many of the discoveries and inventions made by the great people in history.
It did so because scientists used to view paradoxes in a way that they thought that it distorted and objective view of the world. Thus, they would go on to try and eliminate the paradox.
Paradoxes have also helped by allowing new ways of thinking to be developed regarding the subjects of science and mathematics.
Hilbert's Paradox of The Grand Hotel
This is a mathematical paradox with the subtopic of infinity. The paradox refers to a hotel that has an infinite amount of rooms and is full but yet can still take in more guests
This is a paradox in which a time traveler sends him/herself information with no origin. It is also referred to as the bootstrap paradox.
For your time :)