That depends on what you assume and why. The axiom of choice is a high order mathematical assumption.
On the other hand, assuming that a prey animal might stick its head out of a burrow, if you wait long enough, when you can hear and smell the animal might, not be so high order an abstraction.

When you think you recognize something, and you assume that it is what you think it is, it seems to me to be pretty direct - perception. We can be fooled by wax fruit and plastic flowers we don't look at pretty close, but "assuming" they are real is a very low order abstraction - one that does not even have to reach verbal levels.

Some assumptions can be inferences, such as in the prey animal example above. Others can be conscious conditional choices, such as when one says, "Assume for the purpose of discussion, that . . . ". The formulation that is the assumption may have been inferred from other past actions, but in this latest example it is taken as a starting point.

Inferences, in the vernacular, are a type of conclusion from prior reasoning of some kind, valid or flawed. Some may be used as assumptions, but other formulations, not the product of reasoning, may also be used as assumptions, such as mathematical postulates.

Diogenes (The Cynic)

Ben, Let me know the next time you pick wax out of your teeth. The generality of 'assume', 'infer', and 'identify' goes beyond the verbal levels. We operate on the basis of "assumptions" generated by "inference" from past experience, and when we do so, we abstract into higher levels - "identifying" what we perceive by activating past learned experiences. We cannot "re-cognize" something we have not previously "cognized". The first time you learn something new; the second time you fit it into that prior learning. The second time you are "identifying" the input by relating it to the prior experience.

In the context of abstracting from sensory inputs, as opposed to abstracting strictly from memory, we do not assume anything when we first experience something new. Once the memory trace is laid down in the brain, a new experience can activate that trace, and this is the current view as to how "recognition" works. If you choose a level of abstraction such that you insist the prior and the current perceptions differ, then you obviate even "recognition"; but if you choose a level of abstraction such that you can fail to notice differences, then you may "assume" "identification" allows you to affirm, "Yes, that is what I saw before.". Do perception without memory (the first case) and perception with memory (the second case) differ by a level of abstraction? Does it differ enough to be called a "HIGH" level of abstraction?

We can say that re-cognition is one step higher in the abstraction sequence than cognition because the former goes through the additional step of activating memory and retrieving its content.

This is a single very small difference, and it can happen at purely non-verbal levels (low) as well as at abstract verbal levels (high).

We cannot say that making an assumption is somehow an "absolute" high level of abstraction. It is merely "higher" than not assuming by the smallest amount.

When, however, we choose a formulation and call it an axiom it is an a priori assumption not the product of direct abstraction from sensory inputs.

In most ordinary cases, to "assume" something is to take it as true on faith. We "assume" (non-verbally) that the chair will hold us when we sit down. We "assume" water will come out of the faucet when we turn the tap. In these cases an "assumption" is a "prediction". As such it's an inference based based on the principle of regularity of nature. If you search hard enough, you should be able to find an inference preceding every assumption. Assumptions can be conscious or unconscious. They can be verbal or non-verbal.

Let me know the next time you pick wax out of your teeth. whether you think it the result of a "high level abstraction" or not.

Diogenes (the cynic)

Ben, When you "assume", for example, that I like to play on the jungle gym at my local McDonald's", your assumption does not come without neurological process of abstracting from your prior experiences. Some active neural circuits chose that formulation over others. Based on the motives for choosing the formulation, there will be inferences with respect to the efficacy of the chosen formulation to express the purpose. Although, the formulation itself may not be the product of logical inference.

What do you mean by using the term "prescriptive" as applied to assumptions? The meanings I know for "prescribe" are akin to "giving an order".

Lexicographers describe past usages of a word.
English teachers then give that as a prescription as to how to use the word in the future.

Prescribe in no way relates to predict, unless you know that the "order" will be followed.

A orders B to do something.
A predicts to C that B will do something.
B does it and A's prediction came true, in virtue of B's following A's prescription.

Differentiate "predict" from "prescribe".

One may "assume" that something will happen; this is a "prediction", not a "prescription".

If one "orders" or otherwise arranges for something to happen, then it is no longer a "prediction" because the event was pre-arranged by fiat.

Ah... Ben's "mentalty" ~= my "semantic environment".
From the time-bound record:
http://en.wikipedia.org/w/index.php?title=Mentality&redirect=no
http://en.wikipedia.org/wiki/Paradigm

A term is "multiordinal", by Korzybski's definition under the following conditions.
It may be applied to a statement, and
it may be applied to a statement about the statement.

Let "X" be a statement about some situation or event that has not been observed.
We may apply the word 'assumption' to X thusly: "X" is an assumption.
Now, let us make a another statement about "X", say, for example: "John said 'X'".
We may now apply the word 'assumption' to the new statement about X thusly: "John said 'X'" is an assumption.

In this context the term assumption is used multiordinally; however, that does NOT mean that "X" is multiordinal. An assumption is NOT the term 'assumption', and the multiordinal character of the term does NOT carry through to the assumption itself. This is confusing orders of abstracting by "identifying" the term 'assumption' which that which the term refers to - a particular assumption.
An assumption - that which the multiordinally used word 'assumption' may refer to in a given use, is not multiordinal. One may assume something at any level of abstracting from object levels through verbal levels, but that which is assumed is not itself multiordinal, although it may involve one or more levels of abstracting. it is the term 'assumption' itself that may be used multiordinally.

Let's NOT start confusing the character of how a term may be used with possible extensions of the term.

An assumption is an extensional situation that the term 'assumption' may be used to refer to. Multiordinal applies to the use of a term, but not to that which may be in the extension of the term.

All terms are "used" or "mentioned" (talked about). Usage varies with multi-meaning, and multi-meaning varies with context.

Do the research. Here are citations and references for multi-ordinal.

"Can be regarded" does not mean "must be regarded". The "property" or "evaluation" of multiordinal is not something a term either has or it does not. It depends on how it is used, as does any meaning of all words.

The page on multi-ordinal I referred you has the relevant citations. I expect you to look at the same reference material that I refer to. Of course you will abstract from the source material a view consistent with your beliefs. I don't expect you to see things in the same light as I do. The "research" is not reading my web page; it is reading the source my web page cites, and comparing your understanding of that source to your interpretation of my interpretation of the source.

Your requirement for Korzybski to have explicitly used the word "used" in reference to terms he classified as multi-ordinal seems much to restrictive a criteria, as it does not allow for multi-meaning. As all terms are subject to having multi-meaning it is possible for a term identified as meeting Korzybski's explicitly stated criteria to be used is a manner that does not satisfy that criteria. It's simple. If there is multi-meaning, then these terms can be used with meaning that are not multi-ordinal as well as with meanings that are multi-ordinal. Consequently "multi-ordinal" is multi-meaning context dependent on how the terms may be used. Otherwise it is nothing more than a NAME for a class in which terms which sometimes fit the criteria are placed. It is the structural definition that Korzybski provides that is the "interesting" value of the "concept" or notion, so for me, it is only when the terms are used with a meaning appropriate to the structure Korzybski gives that is relevant.

You may have your broad category, but only the cases in a sub-category where the use conforms to Korzybski's criteria interest me, and I'll refer to multi-ordinal USE of terms - specifically to direct the users to that smaller part of your category. By doing so I'm more extensional, more objective, more precise, etc.

Everybody who reads any of this, including you, has his or her own beliefs. What would be interesting is if you were to go into precise detail about why you disagree with specific formulations I have written. That could be the basis of potential mutual understanding. Just stating the obvious, that they are "my" beliefs, and that you disagree with them, (when actually what you disagree with is your interpretation of my writings), seems to "shut the door" to further exploration of the details of our respective interpretations.

So I'll open the door a crack. Why do you disagree? Can you paraphrase your understanding of my formulations, what you see as a consequence of your understanding or interpretation, what your contrasting view is, and why you also evaluate them as being such that you cannot find agreement between them?

Of course, you are free to terminate discussion without our coming to some mutually agreed formulation.

It's a long way from pages and pages of formulations to "I don't agree". Let's get extensional; what are the specific detailed formulations that you disagree with, and why? Perhaps I can explain more; perhaps you can explain in a way that will move me to alter my formulations. But without continued discussion, neither will be possible. Let's time-bind. Tell me what you disagree with and why.

Thomas, I'm disappointed that you decline to discuss any of the specifics of my article.

You think multi-ordinal terms have different meaning at different levels with no general meaning (quoting Korzybski).
I think multi-ordinal terms have a structural meaning that is essentially the same at all levels of abstraction, while the meaning of the utterance in which the term is used comes out different.

I think Korzybski's statement, which you essentially repeat, is wrong, and I show why.
Can you show why you think he is right and discuss what about my view you think is wrong, specifically, and why?

By "structural meaning" I intend to indicate that the use of these words behave like functional or like propositional functions. Functions indicate a general relation between variables which stand for the class of extension. One evaluates a function by "plugging in" specifics. For example, the function y=f(x)=x+2 takes a parameter x. When a value for x is plugged in, then the result is specific. If x=4, then y becomes 4+2 or 6. If x=7, then y becomes 7+2 or 9. The "structural meaning of this function is "x+2", but it "means" different things when different values of x are "plugged in" to the formula as a parameter.

Suppose for the second example that y=pf(x)= "x is a man". In this case y represent a propositional function "x is a man". When x = George Bush, then y becomes pf("George Bush") = "George Bush is a man.", which is a specific proposition. (A "true" one.)
When x = "Hillary Clinton", then y becomes pf("Hillary Clinton") = "Hillary Clinton is a man.", which is a specific proposition, (A "false" one.)

The structural meaning does not change for either example.

Korzybski defined "multi-ordinal" as a property of certain words, words which are applied to a sentence or formulation, and which are subsequently applied to a second sentence or formulation about the first sentence or formulation.

The structure of this is that, if mo is any multiordinal term, and s1 is a sentence, and mo is applied to s1, which we can write as mo(s1) in functional notation. For mo to be a multiordinal term, we must be able to make a second sentence, say s2, which can be about or applied to the first sentence. In functional notation we write this as s2(s1). But the multiordinal term can be applied to this sentence as well, so we get mo(s2(s1)).

Putting these together we get the general result that mo(s1) and mo(s2(s1)). We can interpret the can be applied as meaning that mo(s1) has the same "truth value" as mo(s2(s1)).

I gave a specific example for the multi-ordinal term 'agree'.

A person P agrees with person Q when there is a relation between the person and the subject of agreement that is the same.

r(P,s)=r(Q,s)

I showed that s could be a complex sentence that incorporated agreement at a different level of abstraction, and at each level of abstraction the structure or functional expression for the term 'agree' involved a relation between a person and some subject or object being "the same" for two different persons - no matter what the level of abstraction.

Now apply the structure to two distinct thing.
One is the word 'assumption' (or o variant).

The other is some specific assumption, verbal or otherwise that a person makes consciously or unconsciously.


There is a structural or functional expression that characterizes assumption or assuming.

An assumption, at the abstract structural level expresses a relation between a person and some object or event such that the person holds an attitude about the event or object. The attitude can be expressed as a predictive formulation. Such and such will happen under certain circumstances. Moreover, the formulation should express something the originator has not previously experienced (this chair will hold me), or expressed negatively, the formulation should express something that the formulator states should not happen (this chair will not collapse when I sit on it). Non-verbal assumptions are such that they can be subsequently expressed by a formulation.

a(p,x)

Since a non-verbal assumption does not involve a formulation, it cannot be multiordinal by definition, because only terms are multiordinal.

The "nature of an assumption" is in it's potential predictive character. It represents an "un-tested" description or an untested non-verbal expectation. Both of these characteristics represent abstractions from prior experience. As such they are immediately at a relatively higher level of abstraction that a simple observation.

Your original question used the "absolute" form "high order abstraction". We do not have an "absolute" high order abstraction. We only have higher order abstractions, and any assumption differs from an observation by being at a higher level. So assumptions, whether non-verbal (very low levels of abstraction) or verbal (higher levels of abstraction), are always at least one level of abstraction higher than would be the observation the assumption is about.

"This chair will hold me (next time I sit in it)" is higher than "this chair held me that last time I sat in it.", as it makes an inferences based on the assumption of regularity and consistency of nature.

It's irrelevant to speak of "multi-ordinal" about specific assumptions. It's also inappropriate to use "high level of abstraction" in characterizing assumptions; the best we can do is say that any given assumption has at least one lower level of abstraction on which it is based.

In my book assumptions may be tacit or conscious. They may be derived from some from of abstract inference, or they may be taken "out of the blue". A conscious assumption may be in the context of a sentence like, "Lets assume, for the sake of discussion, that . . .".

The time-binding record includes: http://www.google.com/search?q=define:assumption

I particularly like this one:

"1. An axiom or statement, not necessarily true but put forward and taken to be true to enable further analysis of a hypothesis, or for the purposes of investigating what follows in relation to a theory."

An example of this distinction between hypothesis and assumption can be found in the mathematical and logical proof method called reductio ad absurdum. One consciously assumes something in order to show that it leads to a contradiction. The assumption so made is not generated by any form of inference. In completing such a proof, the "hypothesis" gains the status of truth or "proven" true, transforming the "theory" into a "theorem". And the assumption is shown to be false - on the grounds that it lead to a contradiction.