While Ackoff’s definitions of goals, objectives and ideals have been republished (and rewritten) multiple times, the 1972 definitions were derived from his original dissertation work. Accordingly, in addition to the human-readable definitions, some mathematical notation is introduced.

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#### OUTCOMES

2.30. *End* (an immediate intended outcome) of a subject A in a particular choice environment *S* in a (relatively short) time-period *t _{1} – t_{2}*:

- an outcome that (1) is a member of an exclusive and exhaustive set of available outcomes for A, and (2) has maximum relative value to
*A*in*S*and*t*._{1}– t_{2}

Thus an end is an outcome that a subject intends most strongly in a par ticular environment at a particular time and that is obtainable therein.

2.31. *Goal* (an intermediate intended outcome) of a subject *A* over a set of choice environments and a time-period *t _{1}– t_{k}*:

- the last outcome O
_{k}of a set of available outcomes(*O*), which are ordered so that_{1}, O_{2}, … , O_{k}*V*for_{1}< V_{2}< … <V_{K}*A*over*t*;_{1}– t_{k} - if any outcome
*O*of the set is obtained, the probability of obtaining_{j}(j < k)*O*in_{j+1}*t*is increased._{1}– t_{k}

A goal, therefore, is an outcome that a subject intends most strongly over a set of environments and a time interval, and that is obtainable in these conditions. [p.56, editorial paragraphing added]

2.32. *Objective* (a long-range intended outcome) of a subject *A* over a set of choice environments and a time-period *t _{1}-t_{m}*: the last outcome

*O*of a set of outcomes (

_{m}*O*)

_{1}, O_{2}, …, O_{m}- (1) that are ordered so that
*V*for_{1}< V_{2}< … < V_{m}*A*over*t*; and_{1}-t_{m} - (2)
*O*is not an available outcome for_{m}*A*in that set of environments over*t*; but_{1}-t_{m} - (3) there is an outcome O
_{k}(*1<k<m*), which is*A*‘s goal over these environments and*t*and which, if obtained, increases the probability that_{1}-t_{m}*A*will obtain*O*at a later time_{m}*t*(_{n}*n >m*). [pp 56-57]

Thus an objective is a desired outcome that is not obtainable in the time- period being considered, but progress toward it is possible during that time-period, and it is obtainable at a later time.

- For example, a college freshman’s
*objective*over the next four years may be to receive a Ph.D. - His
*goal*over this period may be to receive his bachelor’s degree. - His
*end*this year may be to be promoted to his sophomore year.

Ends, goals, and objectives are obviously relative concepts; they depend on how time is treated. If a period of one year is considered, the freshman’s receipt of a bachelor’s degree is an objective, promotion is a goal, and passing a particular examination may be his end.

2.33. *Ideal* (an ultimate intended outcome) of a subject *A* over a set of exclusive and exhaustive environments {*S*} and a (relatively long) time-period *t _{1}-t_{n}*:

- the last outcome
*O*of a set of outcomes (_{n}*O*)_{1}, O_{2}, … , O_{n} - (1) that are ordered so that
*V*, for A over_{1}< V_{2}< … < V_{n}*t*; and_{1}-t_{n} - (2)
*O*is not a possible outcome for_{n}*A*in any possible environment in {*S*} over*t*, but every not-yet-obtained outcome in the set possible for_{1}– t_{n}*A*at a time*t*(_{j}*1**≤ j < n*) is either an end, goal, or objective for*A*at*t*: and_{j} - (3) at
*t*there remain in the set of outcomes (_{j}*O*) available outcomes that_{1}-O_{n}*A*has not yet obtained.

An ideal, therefore, is an outcome that can never be obtained but can be approached without limit. In this sense we can say of some persons that their ideal is to move with infinite speed, or of some scientists that their ideal is to obtain errorless observations.

Even though an objective cannot be obtained in the time period of interest, and an ideal can never be obtained, we can speak meaningfully of their pursuit.

2.34. *Pursuit of a goal or objective O _{j}* by a subject

*A*over a time-period

*t*occurs if

_{1}-t_{m}*A*‘s expected value relative to

*O*

_{j}— Σ

_{i}

*Pi E*

_{ij}V_{j}— increases monotonically over

*t*.

_{1}– t_{n}2.35. *Pursuit of an ideal* *O _{n}* by a subject

*A*over a time-period

*t*occurs if

_{1}-t_{n}*A*‘s expected value relative to the ordered set of outcomes (

*O*)

_{1}, O_{2}… , O_{n}— Σ

_{i}Σ

_{j}P

_{i}E

_{ij}V

_{j}

— increases monotonically over

*t*.

_{1}– t_{n}Increases in the relevant expected values that appear in these definitions constitute *progress* toward the goal, objective, or ideal. [p. 57, editorial paragraphing added]

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While we’re in the book, we might as well review Ackoff’s definitions of intelligence and learning.

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### Intelligence

The development of measures of knowledge and understanding enable us to consider a further derivative aspect of the functioning of systems namely, *intelligence*. Many behaviors seem obviously, to an observer, more intelligent or more stupid than others; some individuals characteristically behave more intelligently or more stupidly than others. [pp. 51-52]

Vast efforts have been poured into the development of measures of intelligence, largely to ensure that civil and military organizations can select the best individual components from those available for their needs. Rather less effort has gone into the definition of intelligence. We still lack any rigorous definition, and, not surprisingly, some uncertainty has begun to appear about what is actually being measured by so-called IQ tests. In the past decade research findings have increasingly led psychologists to believe that there is more than one kind of intelligence and that “the conventional IQ test tends toward the evaluation of those processes that have been called convergent, retentive and constructive” (Getzels and Jackson, 1962, p. 14).

The distinction between systems requires some measure of the probability of making intelligent choices when other conditions are held constant. The conditions to be held constant are, according to our model of the choice situation, familiarity, relative value (or intention), and existing knowledge or understanding. If initial knowledge and understanding were zero — a convenient control — then the system that most quickly arrived at the most knowledge or understanding would be judged to be the most intelligent system.

Intelligence clearly has to do with the rate at which a subject can learn.

3.23. *Learning*: an increase in degree of knowledge or understanding over time.

This definition suggests that there must be two measures of intelligence. The distinction we propose accords with the commonsense distinction between the kind of intelligence measured by most IQ tests and creative intelligence. It should be noted that the second measure incorporates aspects of environmental- and self-awareness. It therefore comes closest to the kind of intelligence that Chein (1945) defined as:

Intelligence is the apprehension of the relevant structure of the total behavioral field, relevance being defined in terms of the immediate and presumptive future purposes of the actor (p. 115). [p. 52]

Time is normally used as the basis for measuring rate of change. But since different amounts of time are required to carry out different courses ot action, it may be preferable to use the number of trials (*N _{i}*) as a basis for measuring rate of change. [pp. 52-53]

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### Reference

Ackoff, Russell L., and Fred E. Emery. 1972. *On Purposeful Systems*. Aldine-Atherton.