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History of Philosophy Book Club Message Board › Logic Puzzle

Logic Puzzle

user 6899431
Group Organizer
Silver Spring, MD
Post #: 117
I recently came upon a quotation which intrigued me, since intuitively it seemed true yet applying it to specific events often invalidated it. The quotation is: “All probabilities are 50%. Either a thing will happen or it won't.” A friend of mine said the statement was untrue; to support her contention she offered this example: “There is a 50% probability that tomorrow the sun will rise or not rise.” Clearly, she implied, there is more than a 99% chance the sun will rise.

My question to the group is: Do you agree with my friend that the quotation is illogical on its face, or do you think another interpretation can render it logical? Please join in; I will offer my own response in a few days.
A former member
Post #: 1
I believe all probabilities are 50% when referencing individual things...either something will happen or it will not happen...however, when referencing groups, then the probability changes...for example, 10 students may take an exam and 9 out 10 (90%) may pass the exam as a group, but each individual may or may not pass the exam. So, I agree with the quote when referencing individual things...

In reference to the may rise or it may not...still is it 99% chance that the sun will rise? Based on what reasoning? I, being an agnostic, I simply do not know. A meteor can hit the earth at any given time, not allowing us to view the sunrise or anything else in life for that matter.
user 6899431
Group Organizer
Silver Spring, MD
Post #: 118
This doesn't constitute my answer to the puzzle (which will come in a few days), but I will address your question "how is it 99% chance that the sun will rise [tomorrow]?" I'm not a mathematician but, unbeknownst to me, a famous 18th century mathematician--Pierre-Simon Laplace--addressed this very question, which resulted in "The Rule of Succession" formula. Written with extensive mathematical notations, its logic is beyond my comprehension, but for those with a strong math background, a detailed article can be found in Wikipedia. To read it, click here.

The article does provide a brief synopsis:

"Laplace used the rule of succession to calculate the probability that the sun will rise tomorrow, given that it has risen every day for the past 5000 years. One obtains a very large factor of approximately 5000 × 365.25, which gives odds of 1826251:1 in favor of the sun rising tomorrow.

However, as the mathematical details below show, the basic assumption for using the rule of succession would be that we have no prior knowledge about the question whether the sun will or will not rise tomorrow, except that it can do either. This is not the case for sunrises.

Laplace knew this well, and himself wrote to conclude the sunrise example: 'But this number is far greater for him who, seeing in the totality of phenomena the principle regulating the days and seasons, realizes that nothing at the present moment can arrest the course of it.' Yet Laplace was ridiculed for this calculation; his opponents gave no heed to that sentence, or failed to understand its importance."

I don't know why Laplace used 5000 years. Not privy to 20th century astronomy and average star longevity calculations, he perhaps deferred to Archbishop Ussher and contemporary scientists (Newton and Kepler among them), who estimated the earth to have been created around 4000 B.C.

But getting back to how I arrived at a 99% probability, I based it on NOVA, Discovery, and other TV science programs I have viewed, where the astronomers have estimated the earth to be 4 billion years old and that the sun to have perhaps another 5 billions years of life. I remember one of the experts said that the probability of the sun going supernova soon was highly unlikely; of course that doesn't preclude the sun not rising because, as you have said, the earth is taken out by collision with a giant meteor, planet, etc.
A former member
Post #: 2

Thanks for the insight. It has been helpful.
A former member
Post #: 3
I guess with the concept of all things being equal, and no extraneous variables are involved, then I can comprehend the 99% chance of the sun rising. If that is the case, then I can say that it is a 100% chance I will at least live to reach the average age of 78 (dying of natural causes), as long as the potential of earthquake, heart attacks, hit and runs, and other extraneous variables are eliminated. Yes, I can see the "sun rise" point.

However, each day I believe I will live or not live, and that tends to keep me grounded that all things are 50% probable. This is why I live for today, and prepare for a potential future. To encapsulate, I may or may not be here tomorrow:-)

I like this logic puzzle
user 6899431
Group Organizer
Silver Spring, MD
Post #: 119
I think the point of the quotation is that there are two ways of looking at the probability of answers: the first is to look at the probability that an event will happen, and the second is to look at the categories of outcomes and calculate the percentage a single category represents among the possible outcomes. Thus, using the example of the sun rising tomorrow, the sun can either rise or not rise (the possibility of the second event not occurring is small). Yet since there are only two categories of possibilities (rise and not rise), each has a 50% chance of existing. I realize someone might insist that I am conflating the concept of probability with percentage of category choices, and that is like comparing apples and oranges; my response is that I (and the author of the quotation) are just looking at probability from a second perspective, asking "What is the probability that one of two categories is a possible outcome?"

Note the precise language of the quotation: "either a thing will happen or it will not." This is true only of empirical statements, not analytical (e.g., "the whole equals the sum of its parts"; "the bachelor is an unmarried man"), Analytical statements, by definition, will always be true.

Maurice, I don't understand how you would have a 100% chance of living to at least 78, given that many people die from natural causes before then.
A former member
Post #: 4
I was looking at the puzzle from an empirical perspective. That is my point. I am saying that extraneous variables are always the case, and one could die of natural causes earlier than 78.

Therefore, a perfectly healthy individual could possibly die of a heart attack at 21. Of course, I understand that probabilities vary among things. For example, there is a 1: 280,000 chance of being struck by lightning in the USA. Surely this is less than 50%. Looking at it from the point of an "event will happen or not happen" I understand the 50% probability.

The problem with the probability concept is that it is not an "exact science". Anything can happen at any time, which leave me to agree with the quote "an event will happen or it will not happen". I really do not live my life with the belief that there is a 99% chance that the sun will rise, although I complete understand the logical probability.

I am a skeptic in every sense of the word. I do not believe that anything is true or can be proven absolutely. I do understand the logical premise and it's potential conclusion that the logic puzzle asserts and its repudiations. It's food for thought for me and I thought it was very stimulating.
A former member
Post #: 5
“To free a man from error is not to deprive him of anything but to give him something: for the knowledge that a thing is false is a piece of truth. No error is harmless: sooner or later it will bring misfortune to him who harbours it. Therefore deceive no one, but rather confess ignorance of what you do not know, and leave each man to devise his own articles of faith for himself.”
― Arthur Schopenhauer, Essays and Aphorisms

For the knowledge that a thing is false is a piece of truth (50/50)...knowledge of anything is questionable, hence, it may or may not be the case. It is from this perspective I agree with the quote.

A former member
Post #: 73
The confusion in answering the question comes in the approach.

It seems that on one hand Bayesian statistics are being assumed and then other hand it is not.

The answer depends on what you assume and your approach. When prior knowledge of statistical occurrences are assumed, the probability is rarely 50-50.

I cannot answer it clearly because one would need to know what is assumed.

What you have identified here in the statement below is precisely the difference between classical inference and Bayesian inference. Bayesian inference does indeed deal with conditional probabilities based on categories.

"I think the point of the quotation is that there are two ways of looking at the probability of answers: the first is to look at the probability that an event will happen, and the second is to look at the categories of outcomes and calculate the percentage a single category represents among the possible outcomes".

For a different way of looking at the concept, consider the Monty Hall problem which is a popular mathematical problem.

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