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The following is an exercise in ethics, logic, the use of the universal quantifier and the the use of the existential quantifier.

In the following context, the syntax for the universal quantifier is written as for any instead of being written as .

Also, we write phrases such as "at least one" instead of writing .


Disprove the following conjecture:

For any past date and time t, for any person p alive at time t, for any action α, if person p felt highly uncomfortable about action α being performed on p at time t, then person p had favorable feeling at time t about laws which stipulate that for any person q, action α is illegal to perform on person q.

For example, if person p was uncomfortable asking a doctor to euthanize person p, then person p was favorably about laws which stipulated that for any person q, euthanasia be illegal to perform on person q.

Childishly, some believe that if there exists at least one person unhappy with somthing, we must make it illegal for everybody.

For example, if you hate the taste of mustard, then you would not allow someone else to have mustard on their hot dog.

Computer Scientists sometimes employ indented-notation in order to improve readability of logical statements.

Consider the following re-formulation of the conjecture written in indented-notation for improved readability:

FOR ANY date and time *t* where *t* is in the past,
     FOR ANY any person *p* alive at time *t*
         FOR ANY action *α*
             IF
                 person *p* felt highly uncomfortable about action α being performed on *p* at time *t*
             THEN
                 person *p* had favorable feeling at time *t* about laws which stipulate that for any person *q*, action *α* is illegal to perform on person *q*.

You could consider the times under considation to be one minute time windows of the past, located within a sphere of 10 meter radius about the center of mass about the person in context. For example, we have 8:15:30 to 8:16:30 AM Mountain Standard Time on November 25 of the year 2023 close to 39.7404317° North,-104.8170523° West.

By the word person we really mean physical human body. In this context, a person’s heart, lungs, intestinal tract, et cetra… all have physical mass.


Make a convincing argument that there existed a person p, and there existed an action α, and there exists a time t in the past, such that all of the following statements are true:

  • person p was highly uncomfortable having action α performed on person p at time t

  • At time t, person p did NOT have a favorable attitude towards laws which stipulated that for any person q, action α be illegal to perform on person q.

For any person p, if person p was not actively thinking about the law at time t, we consider the attitude of p towards the law, to be the same as what their attitude was when their attitude last finished changing.

For example, Suppose we have three specific dates and times t₋₂ and t₋₁ and t₊₁ and t₊₂ such that t₋₂ ≺ t₋₁ ≺ t₊₁ ≺ t₊₂.

For example, maybe:

  • t₋₂ was 4 years ago
  • t₋₁ was 3 years ago
  • t₊₁ was 2 years ago
  • t₊₂ was 1 year ago
IF

    person ***p*** felt favorable about eating hot dogs in the time interval from t₋₂ to t₋₁
        and
    person ***p*** changed their mind about eating hot dogs in the time interval from t₋₁ to t₊₁

THEN

   person ***p*** is not favorable about eating hot dogs in the time interval from t₊₁ to t₊₂ even if person ***p*** never thought about eating hot dogs in the time interval from t₊₁ to t₊₂.

What is a hot dog 🌭?

A hot dog is a savory dish edible to men, women, children, an dogs, consisting of a grilled or steamed sausage wrapped in a partially slice bread bun. The sausage used is a wiener Frankfurter Würstchen made of from some linear combination of flesh of pig, flesh of cow, flesh of poultry, and salt water.


Once a person's attitude toward the laws on hot dogs changes, we assume that that their attitude remains constant until the next change of attitude towards hot dogs.

When a person, in joy, has the idea of making hot dogs illegal, then the idea of making hot dogs illegal shall be considered to be that person's preference, until that person changes their mind. This is true even the person never actively thinks about hot dogs in the interim.


One way to answer this question is to provide an example in the past, when something was done to you, which you detested. However, you would not want what is detestable to you to be illegal for other persons to engage in.

To oversimplify things, the goal is to use the universal quantifier, existential quantifier, named variables (such as "person p"), and logical connectives, to write a description of a time when somthing bad for you was not bad for everyone.

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  • Are these homework questions?
    – Jo Wehler
    Nov 25, 2023 at 15:29

1 Answer 1

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Peipei was highly uncomfortable having the door to their house opened in the middle of a windy night during a cold winter.

However, even in the middle of a windy night during a cold winter, Peipei did not have a favourable attitude towards laws making opening doors illegal.

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