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SU-MATH53 Problem Session

Last edited: August 8, 2025

L-Periodic Functions

So, we have:

\begin{equation} f(x+L) = f(x) \end{equation}

The integral is equivalent for any:

\begin{equation} \int_{a}^{a+L} f(x) \end{equation}

for any \(a\).

Heat Equation Recipe

  1. are we on a finite interval? then, decompose into product-type solution \(A(t)B(x)\) and solve.
  2. are we not? Fourier transform on the space variable and solve.

What if \(\lambda \in \mathbb{C} \backslash \mathbb{R}\)

Shush.

Why can we guess \(A(t)B(x)\)

Because we were able to find solutions. Believe that the solution set spans.

SU-PHIL2 APR032025

Last edited: August 8, 2025

Recap: descritive morality, true morality

Principle of Beneficience

“you should help people when you are in need.”

=> evidence to show descritive morality

Moral Theory

Moral Theory is an implementation of modern morality.

  1. identify the “real” rules/principles
  2. explain why the rules are the rules
  3. “Why should you be moral?”
  4. How does it fit in with the “rest of the world”: metaphysics and epistemology
    • metaphysical
      • physical question
      • where does the rules come front?
      • what does it depended on?
    • epistemological questions
      • how do we know these rules are the rules?

argument (philosophy)

Here are some properties of argument.

SU-PHIL2 APR082025

Last edited: August 8, 2025

Recall Moral Theory.

Euthyphro’s Dilemma

Euthyphro’s Dilemma is a question regarding the order of explanation.

Assumes: Gods approve piety Question: Do Gods approve piety because its pious or is the pious called pious because the Gods say so?

translating for a monotheistic context:

Assumes: God approve piety Question: Does God approve or command moral behavior because its moral (objective) or is stuff moral because Gods approves or commands it (subjective).

SU-PHIL2 APR102025

Last edited: August 8, 2025

veneer theory

People are moral out of fear of sanction/punishment. “Really” are deep-down self-interested (egoistic) creatures.

  1. evolution by natural selection “selects” for selfishness
  2. we are products of national selection
  3. therefore, we must be egoists (i.e., selfish)

subscript gambit

subscript gambit is the notion to use multiple different terms/subscripts to define a possibly contested term in order to remove the contention.

altruism

  • altruism1: A behaves towards B in a way that decreases its own reproductive success and increases the reproductive success of B
  • altruism2: A acts towards B in a way that detracts from the fulfillment of its own current desired to promote the perceived desires of B
  • altruism3: A acts towards B in ways motivated to promote B’s interests

egoism

  • egoism1: person puts their own needs first doest’ consider others in a way that’s unacceptable
  • egoism2
    1. every action is explained by the fact that we are motivated by ultimately self-interested desires
    2. every action is the result of an agent acting on their own strongest desire

question: are there good reasons that we should be egoists?

SU-PHIL2 APR152025

Last edited: August 8, 2025

Theories of Morality

“Desires/Motives/Reasons” -> “Reflection/Reasoning” -> “Choices” -> “Actions” -> “Outcomes/Consequences”

Utilitarianism

“the greatest happiness for the greatest number”

The rightness or wrongness of an action depends only on the actual net total sum of pain and pleasure brought about by this particular action for all sentient creatures, compared to the alternatives considered from the “point of view of the universe.”

utility monster objection

Consider someone who is not stated