Troubles with ‘Gender Trouble’ (Butler 1990)

“{Wx = {x: x is a woman.}; Px = {x: Contemporary political powers set the terms and conditions under which x may enjoy political visibility and legitimacy}; Vx = {x: Acceptance of the terms and conditions set by contemporary political powers confers visibility and legitimacy on x}; Nx = {x: A new feminist vocabulary can confer visibility and legitimacy on x while representing women gender-aptly}; Rx = {x: Terms and conditions set by contemporary political powers to confer visibility and legitimacy on x represent women gender-aptly}”

“Although Butler’s claim that ∀x(((□Wx & Px) & (◊Vx & ◊~Vx)) & (◊Vx  →  (□Rx ∨ □~Rx))) → ∀x((Wx & Px)  → (◊Rx  ∨ ◊~Rx)) is valid it is very implausible. It is much, much, more plausible that ∀x(((Wx & ◊Px) & (◊Vx & ◊~Vx)) &(◊Vx → (□Rx ∨ □~Rx))) → ∀x ((Wx & Px) → (□Vx → □~Rx)). Furthermore, her claim that ∀x((((□Wx & □Px) & (◊Vx & ◊~Vx)) & (◊Vx  →  (□Rx ∨ □~Rx))) & □Nx) → ∀x((□Wx & □~Rx) → □Nx) is much less plausible than the counterclaim that ∀x((((Wx & ◊Px)  & (◊Vx  &  ◊~Vx))  &  (◊Vx  → (□Rx  ∨ □~Rx))) & (◊Nx  & ◊~Nx)) → ∀x((Wx & □Nx) → ~◊Nx). Most troublingly, however, as counterargument 2.2. demonstrates Butler’s proposed solution of a new feminist vocabulary doesn’t even begin to address the problems for which it was proposed as a necessary solution. In other words,  ∀x((Wx & □Nx) & ◊~Nx) →∀x□~Nx.”

See The Post Here

Possible Worlds Gender Studies

INTRODUCTION

Feminists have accepted the terms set by existing political arrangements in exchange for political representation for women, says Butler (1990). Even if they have succeeded, they have been unable to secure women representation without pervasive misrepresentation. The vocabulary that confers visibility and legitimacy on women is a normative function of the larger political vocabulary which reveals as much as it distorts what it is to be a woman (Butler 1990).

In summary Butler suggests that:
i. Contemporary political powers set the terms and conditions under which women may enjoy political visibility and legitimacy, necessarily;
ii. And, such that their acceptance possibly does or possibly does not confer visibility and legitimacy on women;
iii. And, if it does confer visibility and legitimacy on women, then it does so only on pain of failing to represent women gender-aptly, necessarily;
iv.  And, given i.-iii. necessarily, a new feminist vocabulary can confer…

View original post 805 more words

Bodily Self-Ownership is Resilient to Exogenous Coercion & Bodily Insult

INTRODUCTION

Is bodily self-ownership fragile or resilient in the face of coercion, violence, or threat of violence? Does the fact that government agencies world-over are conditionally entitled to make any use of a citizen’s body, in whole or part, with or without consent entail that citizens don’t own their own bodies? Many answer to the first question with ‘of course, bodily self-ownership is fragile’, and to the second with ‘obviously that entails people don’t own their own bodies’. But as is demonstrated below, Government agencies’ conditional entitlement to make any use of my body, in whole or part, with or without my consent is a matter irrelevant to whether or not I own my own body.  In other words: If Ox = x owns his body; and, Gx = Government agencies are conditionally entitled to make any use of x’s body, in whole or part, with or without consent, then (~ ∀x((Ox ˅ ~ Ox) & ∀x(Gx ˅ ~ Gx)) → ((~ ∀x((Ox ˅ ~ Ox) → ~ ∀x(Gx ˅ ~ Gx)) & ∀x((Ox ˅ ~ Ox) & ∀x(Gx ˅ ~ Gx))) → ∀x(Gx → ~ Ox))).

PRELIMINARIES

Let Ox = x owns his body; and, Gx = Government agencies are conditionally entitled to make any use of x’s body, in whole or part, with or without consent.

The vacuous validities i.-ii. below obtain, as the diligent but distrustful reader can verify:

i. ∀x (Ox ˅ ~ Ox), and ii. ∀x (Gx  ˅  ~Gx).

But, i. and ii. also commit us to iii. and iv.

iii. (∀x ((Ox  ˅  ~ Ox)  &  ∀x (Gx  ˅  ~ Gx))); and,

iv. (∀x ((Ox ˅ ~ Ox)  &  ∀x (Gx  ˅  ~ Gx)))  →  ~ (∀x ((Ox  ˅  ~Ox)  →  ~ ∀x (Gx  ˅  ~ Gx)))

If one thinks government agencies’ entitlements to people’s bodies implies people don’t own their own bodies, one thinks something very much like the invalidity v., below

v. ∀x (Gx → ~Ox).

But premises i.-iv. do not entail v; below is a proof of the fact, vi: the negation of the premise-conclusion commitments i-v.with which I began this discussion. It facilitates an appreciation of the fact that body self-ownership is resilient in the face of exogenous coercion, and violent, non-consensual interference with bodily functioning. Or, that

ARGUMENT VI .(~ ∀x((Ox ˅ ~ Ox) & ∀x(Gx ˅ ~ Gx)) → ((~ ∀x((Ox ˅ ~ Ox) → ~ ∀x(Gx ˅ ~ Gx)) & ∀x((Ox ˅ ~ Ox) & ∀x(Gx ˅ ~ Gx))) → ∀x(Gx → ~ Ox)))

0. PROOF:  (~ ∀x((Ox ˅ ~ Ox) & ∀x(Gx ˅ ~ Gx)) →
((~ ∀x((Ox ˅ ~ Ox) → ~ ∀x(Gx ˅ ~ Gx)) & ∀x((Ox ˅ ~ Ox) & ∀x(Gx ˅ ~ Gx))) →
∀x(Gx → ~ Ox))) is valid.

  1. ~ (~ ∀x((Ox ˅ ~ Ox) & ∀x(Gx ˅ ~ Gx)) →
    ((~ ∀x((Ox ˅ ~ Ox) → ~ ∀x(Gx ˅ ~ Gx)) & ∀x((Ox ˅ ~ Ox) & ∀x(Gx ˅ ~ Gx))) →
    ∀x(Gx → ~ Ox)))
  2. ~ ∀x((Ox ˅ ~ Ox) & ∀x(Gx ˅ ~ Gx))
  3. ~ ((~ ∀x((Ox ˅ ~ Ox) → ~ ∀x(Gx ˅ ~ Gx)) & ∀x((Ox ˅ ~ Ox) & ∀x(Gx ˅ ~ Gx))) → ∀x(Gx → ~ Ox))
  4. ~ ((Oa ˅ ~ Oa) & ∀x(Gx ˅ ~ Gx))
  5. ~ (Oa ˅ ~ Oa)
  6. ~ ∀x(Gx ˅ ~ Gx)
  7. ~ Oa
  8. ~ ~ Oa
  9. ~ (Gb ˅ ~ Gb)
  10. ~ Gb
  11. ~ ~ Gb ■


DISCUSSION

Argument VI. illustrates, of course, that either the antecedent is false or the consequent is true—but not both. It’s clear the premises are innocuous, uncontroversial, and jointly valid, but that their conclusion is the negation of the intuitive position, encapsulated by the premise-conclusion commitments i-v.  The burden of showing which if any auxiliary premises make the asserted consequent false just when they make the ampliated* antecedent true lies with proponents of the invalidity v.

CONCLUSION

Bodily self-ownership is not fragile, but resilient, in the face of exogenous coercion, violence, or threat of violence. The fact that government agencies world-over are conditionally entitled to make any use of a citizen’s body, in whole or part, with or without consent simply does not entail that citizens don’t own their own bodies.

Notes

*[containing the relevant auxiliary premises and premise-conclusion commitments i-v] .

What do Actions have to do with Norms, Reasons, and Intentions?

INTRODUCTION

A swathe of philosopher’s views on the relationship between norms of an action, reasons for an action, and intentions to perform an action take the form of one or more of the following claims:

i. If one is committed to norms of A-performance then one has reason to deliver an A-performance;
ii. If one has reason to deliver an A-performance, then one is committed to norms of A-performance
; and,
iii. If one is committed to norms of A-performance, and has reason to deliver an A-performance, then one intends to deliver an A-performance.

Let An = One is committed to norms of A-performance; Ar = One has reason to deliver an A-performance;  and, Ai = One intends to deliver an A-performance.

Now, i.-iii. amount to the invalid claims ∀n∀r(An → Ar), ∀n∀r(Ar → An), and ∀n∀r∀i((An & Ar) → Ai), as the reader can verify. The analysis here offered gives a fuller account of why that must be. As I’ll show, the antecedent of i. only implies one does or does not have reasons for delivering an A-performance, that of ii. only implies one is or is not committed to norms of A-performance, and of iii. only implies one either intends or does not intend to deliver an A-performance.

ANALYSIS

I show that ∀n∀r∀i((((An → (Ar ˅ ~Ar)) & (Ar → (An ˅ ~An))) & ((An → (Ar ˅ ~Ar)) & (Ar → (An ˅ ~An)))) & ((An & Ar) → (Ai ˅ ~Ai))) is valid.

ARGUMENT: ∀n∀r∀i((((An → (Ar ˅ ~Ar)) & (Ar → (An ˅ ~An))) & ((An → (Ar ˅ ~Ar)) & (Ar → (An ˅ ~An)))) & ((An & Ar) → (Ai ˅ ~Ai)))
PROOF
:

  1. ∀n∀r∀i((((An → (Ar ˅ ~Ar)) & (Ar → (An ˅ ~An))) & ((An → (Ar ˅ ~Ar)) & (Ar → (An ˅ ~An)))) & ((An & Ar) → (Ai ˅ ~Ai)))
  2. ~∀n∀r∀i((((An → (Ar ˅ ~Ar)) & (Ar → (An ˅ ~An))) & ((An → (Ar ˅ ~Ar)) & (Ar → (An ˅ ~An)))) & ((An & Ar) → (Ai ˅ ~Ai)))
  3. ~∀r∀i((((Aa → (Ar ˅ ~Ar)) & (Ar → (Aa ˅ ~Aa))) & ((Aa → (Ar ˅ ~Ar)) & (Ar → (Aa ˅ ~Aa)))) & ((Aa & Ar) → (Ai ˅ ~Ai)))
  4. ~∀i((((Aa → (Ab ˅ ~Ab)) & (Ab → (Aa ˅ ~Aa))) & ((Aa → (Ab ˅ ~Ab)) & (Ab → (Aa ˅ ~Aa)))) & ((Aa & Ab) → (Ai ˅ ~Ai)))
  5. ~((((Aa → (Ab ˅ ~Ab)) & (Ab → (Aa ˅ ~Aa))) & ((Aa → (Ab ˅ ~Ab)) & (Ab → (Aa ˅ ~Aa)))) & ((Aa & Ab) → (Ac ˅ ~Ac)))
  6. ~(((Aa → (Ab ˅ ~Ab)) & (Ab → (Aa ˅ ~Aa))) & ((Aa → (Ab ˅ ~Ab)) & (Ab → (Aa ˅ ~Aa))))
  7. ~((Aa → (Ab ˅ ~Ab)) & (Ab → (Aa ˅ ~Aa)))
  8. ~(Aa → (Ab ˅ ~Ab))
  9. Aa
  10. ~(Ab ˅ ~Ab)
  11. ~Ab
  12. ~~Ab
  13. ~(Ab → (Aa ˅ ~Aa))
  14. Ab
  15. ~(Aa ˅ ~Aa)
  16. ~Aa
  17. ~~Aa
  18. ~((Aa → (Ab ˅ ~Ab)) & (Ab → (Aa ˅ ~Aa)))
  19. ~(Aa → (Ab ˅ ~Ab))
  20. Aa
  21. ~(Ab ˅ ~Ab)
  22. ~Ab
  23. ~~Ab
  24. ~(Ab → (Aa ˅ ~Aa))
  25. Ab
  26. ~(Aa ˅ ~Aa)
  27. ~Aa
  28. ~~Aa ■

SYNTHESIS

Loosely speaking, commitment to norms of action doesn’t oblige one to possess reasons for action; it merely permits one to do so. Likewise, reasons for action don’t oblige commitment to norms for action; they only permit such commitment. Commitment to norms for action along with possession of reasons for performing it doesn’t oblige one to intend a performance; it only permits one to intend it.

Strictly speaking, the antecedent of i. only implies one does or does not have reasons for delivering an A-performance, that of ii. . only implies one is or is not committed to norms of A-performance, and that of iii. only implies one either intends or does not intend to deliver an A-performance.

CONCLUSION

For all norms, reasons, actions, intentions:
i.i. If one is committed to norms of A-performance then one either has reason to deliver an A-performance or one doesn’t;

i.ii. If one has reason to deliver an A-performance, then one either is committed to norms of A-performance, or one isn’t; and,

i.iii. If one is committed to norms of A-performance, and has reason to deliver an A-performance, then, either one intends to deliver an A-performance or one doesn’t.

Logical Obstacles to Doing Good Better

INTRODUCTION

Philosopher William MacAskill says in an interview with Sam Harris, people who want to do good must use their spare time and money to minimize illbeing, and maximize wellbeing of the greatest number as best they can. He cautions, however, that not all charitable uses of given amounts of time and money achieve the same amount of good. The upshot here is that you can spend all your time and money to minimize global illbeing, and maximize global wellbeing while failing to do a commensurate amount, or any, of good.
Though you may spend time and money available for charity ineffectively, doing the ineffective little you can to do good is better than doing nothing. Even if the best you could do ended up not achieving much, or any, good, by using your money and time charitably, you’d have increased the likelihood of reducing some illbeing, and increasing some wellbeing, globally so you do good.

Using evidence, logic, and high level reasoning to assess whether your charitable expenditures of time and money achieve the most good you can at that cost helps ensure you do do the most good you can when you do the most good you can. If evidence, logic, and high level reasoning show your time and money could have been spent better, i.e. created greater expected future value, on other charitable tasks than the one you took on, then—presuming you did take on the expenses you did—you could have done good better. But, if these showed you’d really maximized the expected future value of your charitable expenditures, then you’d have done good the best you could.

The foregoing sounds great, and fits nicely with our intuitions about how to do good, and how to do it the best we can. But holding to these ideas, jointly, commits us to the following preposterous invalidity:

If you use your spare time and money to minimize illbeing and maximize wellbeing of the greatest number, and you use evidence, logic, and high level reasoning to determine whether your charitable aid achieves for the greatest number of prospects the greatest magnitude of reduction in illbeing and increase in wellbeing possible, then you do the most good you can and you do not do the most good you can.

In the subsequent sections I’ll demonstrate that this non-obvious, and somewhat preposterous sounding charge is true.

PRELIMINARIES

Let

G = You do the most good you can.

T = You use your spare time and money to minimize illbeing and maximise wellbeing of the greatest number

E = You use evidence, logic, and high level reasoning to ensure your charitable uses of time and money achieve the greatest magnitude of reduction in illbeing and increase in wellbeing.

THE TARGET ARGUMENT

MacAskill (2016) makes the following claims:

Axiom 1. (T → G)
Axiom 2. ((T & E) → G)
Axiom 3. (((T & E) → ~G)→ ~(T & E))

ANALYSIS

He does not say so, but MacAskill is obviously [see PROOF] committed to the following claims as well:

Axiom 2.1. (E → G)
PROOF: From Axiom 2. We know that i. ((T & E) → G).
ii. (((T & E) → G) → ((T → G) & (E → G)))
iii. (E → G)■

Axiom 4. ((T) → G) & ((T & E) → G) & (((T & E) → ~G) → ~(T & E)).
PROOF: i. ~ (((T) → G) & ((T & E) → G) & (((T & E) → ~G) → ~(T & E)))
ii. ~(T & E)
iii. (~(T v ~E) & ~(~T v ~E))
iv. (~T v ~E)
v. (T → ~E)
vi. ((T → ~E) & ~(~T v ~E))
vii. (~(T → ~E) & ~~(~T v ~E))
viii. (~T → ~E)
ix. (~T v  ~E)
x. ((~T v ~E)→ (T → ~E))
xi. (T → ~E) & (~T → ~E)
xii. (T & ~T)→ (~E & E)
xiii. ~(T v ~~T) → ~(~E v ~~E)
xiv. (~T v T) → (E v E)
xv. (T → T) → (~E → E)
xvi. (~T → T) v  (~E → E)
xvii. (~T v  ~E) → (T v E)

It is easy to see MacAskill is not committed to line xvii.  (~T v ~E) → (T v E), so he must be committed to ((T) → G) & ((T & E) → G) & (((T & E) → ~G) → ~(T & E)), contra line i. ■

THE COUNTERARGUMENT TO THE TARGET ARGUMENT

0. (((T → G) & ((E → G) & (((T & E) → G) & ((T & E) → ~G)))) → (((T & E) → G) & ((T & E) → ~G)))
PROOF:
1. ((T → G) & (E → G) & ((T & E) → G) & ((T & E) → ~G))
2. ~ (((T & E) → G) & ((T & E) → ~G))
3. (T → G)
4. (E → G)
5. ((T & E) → G)
6. ((T & E) → ~ G)
7. (((T & E) → G) → ~ ((T & E) v G))
8. (((T & E) → ~G) → ~~((T & E) v G))
9. (~ ((T & E) v G) & ~~((T & E) v G))
10. (((~T & E) v G) & ((T & E) v G))
11. (((~T & T) v G) & (E v G))
12. (((~T & T) v G) → G)
13. G
14. (~T → G)
15. (~E → G)
16. ((T → G) & (~T → G))
17. ((E → G) & (~E → G))
18. (((T → G) & (~T → G) & (E → G) & (~E → G)) → ~G)
19. ~G
20. (G & ~G)
21. (((G & ~G) & ((T & E) → G) & (((T & E) → ~G) → ~(T & E))) → (((T & E → G) & (T & E)) → ~G))
22. (((T & E → G) & (T & E)) → ~G)
23. ~~ ( (T & E → G) & ((T & E) → ~G))■

Finally, to deliver on my claim in the last paragraph of the introduction, I’ll show:

((T & E) → G) & (((T & E) → ~G) ⊢ ((T & E) → (G & ~G))
PROOF: i. ((T & E) → G) & (((T & E) → ~G)
ii. ((T & E) → G)
iii. ((T → G) & (E → G))
iv. (T → G)
v. (E → G)
vi. ((T & E) → ~G)
vii. ((T → ~G) & (E → ~G))
viii. (T → ~G)
ix. (E → ~G)
x. ((T → G) & (T → ~G ))
xi. (T → (G & ~G))
xii. ((E → G) & (E → ~G ))
xiii. (E → (G & ~G))
xiv. ((T & E) → (G & ~G))■

CONCLUSION

MacAskill’s recommendations for doing good better-if followed-guarantee that one does and does not do the most good one can. The guidelines make no difference to whether or not one does the most good one can, so they aren’t a sound basis for making decisions about what charitable efforts are worth the while, and how best to go about them.

 

Doing Good Better ≠ Undoing Worst Bads

Can Fixing the Biggest Bads Accomplish the Biggest Goods?

One dominant idea about how charitable tasks ought to be selected and appraised holds that the neediest of needy prospects available for consideration ought to be given highest priority. Funds available for charitable aid are typically limited, but there are always several feasible alternatives that could benefit from access to the funds. The neediest person benefits most from each unit of a cash hand-out, especially so if the sum is received when it is needed most. So, it seems reasonable enough to think that the neediest prospect one can afford to aid is the best prospect to aid.

Why does this idea enjoy its mass appeal?

Well, if you want to achieve a big, fat, good but have a limited budget it seems apt to stretch the money as far as it goes. If you make a hand-out to the neediest prospect under consideration their wellbeing is significantly enhanced on your account, and you achieve the most good you can per unit of expense you incur in doing so. If your charitable aid budget is larger than the cost of enhancing the wellbeing of the neediest prospect, you can—and should—aid the next neediest prospect/s that could benefit from the remaining amount.

Let the weight of prospect’s need be the metric by which they are accorded priority during selection and appraisal of feasible charitable tasks. Call this method of assigning priorities to feasible alternative charitable tasks the need-weighted priority metric, or need-weighted metric for brevity.

The patent consequences of the need-weighted metric for charitable task selection and appraisal, discussed above, sit well with our innate desire to do good and do it the best we can. But is it actually a reliable metric? Does it ensure the best use of resources available for feasible charitable tasks?

The answer is: NO!

We’ll see why below.

0.

The claim that the need-weighted prioritisation metric picks the best among feasible prospects under consideration for charitable aid is mistaken.

Meeting the needs of the neediest prospect tends to cost more now than the expected future value created by doing so. It also tends to cost more now than attending to other feasible alternatives that both require lower expenditure now and generate greater expected future value subsequently. By allocating funds available for charitable aid to the neediest prospect one enriches the prospect by impoverishing other market participants; transferring a currently preventable net worth loss to a future period where it is unpreventable.

Need-Weighted Prioritisation of prospects undervalues the costs of charitably aiding the neediest now while it overvalues the expected future value of doing so. The good actually achieved, thus, is worth less than the costs incurred in achieving it.

The 2 part case study below illustrates these problematic traits, and demonstrates the mechanics, of value destroying charitable tasks typically accorded highest priority by the need-weighted metric.

Case Study

1.

Abaskuul and Abtidoon are 4 year old orphans residing in a region where the life expectancy for males is 53 years, and the average monthly income is $50. If Abaskuul and Abtidoon start working at the age of 18, i.e. in 14 years, and work till age 53 their expected lifetime earnings at the average monthly income [assuming $0 savings and no raises, for simplicity] amounts to 468months * $50 = $23400 each. It costs $200 per month to support a child and make them employable, so the expected cost of caring for either Abaskuul or Abtidoon till 18 years of age [assuming 0% inflation, and no changes in market prices, for simplicity] is $33,600. Accordingly,

a. NPV (Abaskuul’s expected lifetime earnings) < FV (Cost of sponsoring Abaskuul), as
$23400 < $33,600.

b. NPV (Abtidoon’s expected lifetime earnings) < FV (Cost of sponsoring Abtidoon), as
$23400 < $33,600.

A would be do-gooder Mr E. A. holding to the common sense view must accord them both equal priority as prospects. That’s because the

NPV (Abaskuul’s expected lifetime earnings) = NPV (Abtidoon’s expected lifetime earnings)

If Mr E. A. sponsors any one of the two boys for 14 years he pays $33,600 starting right now and his sponsorship realises the expected future value of $23,400 at the end of year 14.

Whether one sponsors Abaskuul or Abtidoon, one makes a loss of $10,200; a 30.29% loss on $33,600! This loss on charitable aid, equal to the value destroyed by Mr E. A, indicates that charitably aiding either prospect is not the most effective charitable use of $33,600.

Sponsoring either prospect is equivalent to paying $33600 over 14 years to collect $23,400 at the end.

Presumably, if at another time and in another context, Mr E. A. were offered a deal promising him $69.71 in 14 years if he paid up $100 now, he’d refuse. So, it stands to reason he must dismiss the opportunity to aid these prospects. Sponsoring Abaskuul, or Abtidoon, is an ineffective charitable act Mr E. A. can perform only by depriving himself and other market participants of $10,200 over 14 years. Therefore, he must refrain from sponsoring either of these prospects and look for feasible alternatives.

Effective charitable use of a given amount today subsequently creates a greater expected future value than the present value of costs incurred in making it.

2.

Suppose Mr E. A. only has $33600 available to commit to charity and must choose to sponsor only one of Abtidoon or Abaskuul. Furthermore, Abtidoon is diagnosed during this period to have contracted acute malaria, and the expected cost of a full course of treatment is $200. Then,

a. NPV (Abtidoon’s expected lifetime earnings) is $23,400 – $200 = $23,200. Stated another way, NPV (Abtidoon’s expected lifetime earnings) = 1 / 1.02 * 23,400 = 23,200.

b. NPV (Abtidoon’s expected lifetime earnings) < NPV (Abaskuul’s expected lifetime earnings) as $23,200 < $23,400.

Abaskuul, who enjoys a higher NPV of expected lifetime earnings if sponsored by Mr E. A., is better off than Abtidoon. Abtidoon is worse off even if he is sponsored by Mr E. A., because of the 1 / 1.02% decrease in the NPV of his expected lifetime earnings due to acute malaria.

If Mr E. A. helps only the neediest of his feasible prospects, then as Abtidoon is 1.02 times needier than Abaskuul, he must sponsor Abtidoon. In fact, Mr E. A. must accord 1.02 times greater priority to charitably aiding Abtidoon than he does to Abaskuul. Alas, for Mr E. A. every 1 / k unit decrease in the NPV of a prospect’s expected lifetime earnings bumps up their priority by K units; and, with every k unit increase in NPV of a their expected lifetime earnings their priority decreases by 1 / k units.

     As section 2 illustrates, prioritising charitable aid to needier, lower NPV prospects, destroys the expected future cash value equivalent to the difference of the costs incurred in providing charitable aid and the return generated by doing so.

Priority accorded to a prospect relative to feasible alternatives must be commensurate with its future return to present cost ratio relative those of feasible alternatives.

Prospects with the highest ratio of future return to present costs must be accorded highest priority while selecting and appraising feasible charitable  tasks.

  1. Conclusion

Contrary to recommendations of common sense, and need-weighted prioritisation metrics like the one discussed:

The neediest prospects among feasible alternatives do NOT make for the most suitable recipients of charitable aid.

The neediest prospects among feasible alternatives should NOT be accorded higher priority than alternatives that cost less to aid, and bear greater expected future return subsequently—on pain of destroying value.

 

Financial Mathematics. Chapter: >0?

In the intervening months since my last post here, I’ve enrolled as a candidate in the Chartered Financial Analyst, CFA, Level 1 competitive examination to held on June 3, 2017.
I have decided to expand the previous, one-chapter, basic post into a series of posts covering entire the syllabus for the examination !-in posts of 500 words or less ! Read the on-going series on Numéraire; be well on your way from a lay, [lazy?], grasp of financial mathematics towards informed market participation.

Financial Mathematics: Chapter 0

  1. FUTURE VALUE [with Simple Interest]: The future value, Fv, of an amount, Pv, deposited with a bank at an interest rate, r, is given by the formula in equation 1.1.

EQUATION 1.1: Fv = Pv (1 + r)

PROBLEM 1.1.1: If Pv = Rs. 1000000, r = 4%, then what is the Fv?

SOLUTION:
Fv = 1000000(1+ 0.04)
=  1000000(1.04)
= 1,040,000/-
The future value of Rs. 1000000 invested at 4% interest for 1 year is Rs. 1,040,000/-.

 

  1. FUTURE VALUE [with Compound Interest]: The future value, Fv, of an amount, Pv, deposited with a bank at an interest rate per period, r, compounded every N periods is given by the formula in equation 1.2.

EQUATION 2.1: FvN = Pv (1 + r)N

PROBLEM 2.1.1: If Pv = 1000000, r = 8% per year, and N = 2 years, then what’s the Fv2?

SOLUTION:
Fv2 = 1000000 (1+0.08)2
         = 1000000 (1.08)2
= 1000000 (1.1664)
= 1,166,400/-
Thus, the future value of Rs. 1000000 invested at 8% per year for 2 years is Rs. 1,166,400/-.

PROBLEM 2.1.2: Rs. 1000000 is invested in a fixed deposit account maturing in 5
years with an interest rate of 8% compounded annually. If no withdrawals are made till maturity, how much will the account be worth in 5 years?

SOLUTION:
Fv5 = 1000000 (1+0.08)5
= 1000000 (1.08)5
= 1000000 (1.469328077)
= 1,469,328.077/-
Thus, the future value of Rs. 1000000 in a fixed deposit with an interest rate of 8% compounded annually at maturity, given no withdrawals are made before maturity, is Rs. 1,469,328.007/-

PROBLEM 2.1.3: If you’re offered a lump sum at an 8% annual interest rate in 6 years for an investment of Rs. 1000000, how much should you expect to get in 6 years?

SOLUTION:
Fv6 = 1000000 (1+0.08)6
       = 1000000 (1.586874323)
= 1,586,874.323/-
Thus, you should expect to receive Rs. 1,586,874.323/- at the end of 6 years.

PROBLEM 2.1.4: You’re a pension fund manager who’s been offered Rs. 10,000,000 by a corporate sponsor 5 years from now. If the annual interest rate is thought to be 9%, how much will the corporate sponsor’s offering be worth in 15 years, when you have to disburse the funds to retirees?

SOLUTION:
Fv15 5 = 10000000 (1+0.09)15 – 5
Fv10  = 10000000 (1.09)10
= 10000000 (2.367363675)
= 23,673,636.75/-
The corporate sponsor’s offering will be worth Rs. 23,673,636.75/- in 15 years.

PROBLEM 2.1.5: If you want to have Rs. 23,673,636.75 in 5 years, and the going annual interest rate is 9%, how much will you have to invest now?
SOLUTION:
23,673,636.75 = Pv (1+0.09)5
23,673,636.75 = Pv (1.09)5
23,673,636.75 = Pv (1.538623955)
Pv = 23,673,636.75/1.538623955
Pv = 15,386,239.55/-
If the going interest rate is 9% per annum, and you want Rs. 23,673,636.75 in 5 years, you must invest Rs. 15,386,239.55/- now.

 

  1. FUTURE VALUE [with More than Annual Compounding]: The future value, FvN, of an amount, Pv, deposited with a bank for N periods at a stated annual interest rate, r, compounded every m periods is given by the formula in equation 3.1.

EQUATION 3.1: FvN = Pv (1 + r/m)mN

PROBLEM 3.1.1: If an investment of Rs. 10000000 is made at a stated annual interest rate of 9%, with monthly compounding, how much should one expect to get in 5 years?

SOLUTION:
Fv5 = 10000000 (1 + 0.09/60)60(5)
= 10000000 (1.00015)300
= 10000000 (1.04602433)
= 10,460,2433/-
If you invest Rs. 10000000 for 5 years at an interest rate of 9% compounded monthly, you should expect to get Rs. 10,460,2433/- at the end of 5 years.

 

  1. FUTURE VALUE [with Continuous Compounding]: The future value, FvN, of an amount, Pv, deposited with a bank for N periods at a stated annual interest rate, rs, compounded continuously is given by the formula in equation 4.1.

EQUATION 4.1: FvN = Pv (e)rsN      {where e = 2.7182818}.

PROBLEM 4.1.1: If you invest Rs. 100000 for 2 years at an interest rate of 4% compounded continuously, how much should you expect to get at maturity?

SOLUTION:
Fv2 = 100000 (2.7182818)0.04(2)
= 100000 (2.7182818)0.08                                               
= 100000 (1.083287067)
= 108328.7067/-
If you invest Rs. 100000 for 2 years at an interest rate of 4% compounded continuously, you should expect to receive Rs. 108328.7067/- at maturity.