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Old 11-07-2011, 07:26 PM   #51
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Why should I reconsider? McCullagh is clearly discussing hypotheses, meaning theories or models which are tested against the evidence. He is not discussing axioms.
Who claimed that? My claim is that he is discussing postulates, and that postulates and hypotheses are commonly equivalent terms.
I explained to you above how they're not.
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As I pointed out to you above, 'hypothetical' and 'postulatory' are not equivalent. There's a crucial methodological difference.

You have yet to respond to post #45.

To summarise it, McCullagh is specifically writing about the historical method, not the scientific method, and therefore I take it that he is using the word 'hypothesis' in sense 2, and which is close to postulate, and able to be summarised as

An assumption taken to be true for the purpose of argument or investigation
Many people consider that the scientific approach should be applied to the study of history as far as possible. In any case, the restriction of the first sense of 'hypothesis' to the sciences (even if the expression 'the sciences' is taken to exclude history) is not made by other dictionaries:
http://dictionary.reference.com/browse/hypothesis

The specifics of what McCullagh says about hypotheses fit with sense 1 of 'hypothesis' and not with sense 2.
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Old 11-07-2011, 08:06 PM   #52
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Why should I reconsider? McCullagh is clearly discussing hypotheses, meaning theories or models which are tested against the evidence. He is not discussing axioms.
Who claimed that?
I did.

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My claim is that he is discussing postulates, and that postulates and hypotheses are commonly equivalent terms.
You are wrong. He is not discussing postulates - he is discussing theories.

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Axioms are the formal name given to postulates in the fields of mathematics and geometry, and were mentioned above in a totally peripheral fashion for the sake of an introduction. The OP is about historical theories, and the claim is that such historical theories, and specifically various theories concerning the history of christian origins, employ a series of postulates (we may call them hypotheses following McCullagh if you feel more comfortable with this arrangement.
Theories are models that are tested against the evidence. They are not axioms. You assume an axiom, but you never test it.

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Both in the OP and in the diagram at post #1 as far as I can see we can replace the occurrence of "postulate" with the word "hypothesis" and it would not make any appreciable difference to me, because I see the terms as roughly equivalent.
I don't see a diagram in post 1, so I don't know what this is about. There are some instances where the word hypothesis and postulate would have similar meanings, but the two words are not identical.

I am having difficulty following your references to previous parts of this thread, so I will not continue in this vein for now.

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The fact of the matter and of this OP is that is precisely the point I am attempting to make. Historicists and mythicists may not in fact be starting with the same set of "givens" (which we may call postulates and/or hypotheses). The persuasion angle between the two parties can also be seen as the relinquishment or giving up of certain specific assumptions (postulates and/or hypotheses) held by the opposing party.
Both would deny it. Both claim to be doing standard historical research, and to be testing their theories against the evidence using generally applicable historical principles.

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...

Theories dealing with the history of christian origins do not have adequate and satisfactory sources and evidence to deal with - we are all aware of this problem. In the [??] sence of clearly undisputed unambiguous ancient historical evidence with a reasonably non-suspicious provenance, all theorists can do is to make hypothetical (postulatory) statements about each item of evidence. These postulates (or hypotheses) are derived and created from from the conceptual framework of the theorist.

In the non ideal reality the historical (or mythical) jesus, it may be argued, is essentially an historical hypothesis or postulate, because bare skeleton of the near-to-vacuum-of-evidence does not permit any precise historical analysis of his existence.
This is mostly word salad. If you think that the important point is that there is very little evidence, most people would agree with you. But you can still draw probabilistic conclusions from any amount of evidence.
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Old 11-07-2011, 08:09 PM   #53
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Why should I reconsider? McCullagh is clearly discussing hypotheses, meaning theories or models which are tested against the evidence. He is not discussing axioms.
Who claimed that? My claim is that he is discussing postulates, and that postulates and hypotheses are commonly equivalent terms.
I explained to you above how they're not.
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Originally Posted by J-D View Post
As I pointed out to you above, 'hypothetical' and 'postulatory' are not equivalent. There's a crucial methodological difference.

You have yet to respond to post #45.

To summarise it, McCullagh is specifically writing about the historical method, not the scientific method, and therefore I take it that he is using the word 'hypothesis' in sense 2, and which is close to postulate, and able to be summarised as

An assumption taken to be true for the purpose of argument or investigation
Many people consider that the scientific approach should be applied to the study of history as far as possible.
But how is this relevant? This does not change the fact that McCullagh is writing about the historical method.

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In any case, the restriction of the first sense of 'hypothesis' to the sciences (even if the expression 'the sciences' is taken to exclude history) is not made by other dictionaries:
http://dictionary.reference.com/browse/hypothesis

All dictionaries agree on the general use of the term.
And it is precisely this general definition - applicable to the historical method - that MCCullagh writes about.


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The specifics of what McCullagh says about hypotheses fit with sense 1 of 'hypothesis' and not with sense 2.
The generalities of what McCullagh says about hypotheses fit both with sense 1 of 'hypothesis' (the specific scientific sense) and with sense 2. Your interpretation attempts to preclude McCullagh saying anything about the general sense of the word as it is applied in the historical method, Needless to say I disagree with your interpretation.
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Old 11-08-2011, 02:31 AM   #54
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The greater the number of postulates made by any one theory in relation to the history of christian origins, the more precarious the position of the theorist becomes.
The absolute number is irrelevant. What matters is that when we compare competing theories, the one with fewer postulates is, in general and ceteris paribus, to be preferred over those with more postulates.
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Old 11-08-2011, 02:34 AM   #55
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So it seems, unless we find our postulates refuted, then all theorizing is the exploration and confirmation of our original postulates, whether they are consciously known to us, or whether they are not explicated consciously. Would you agree with this?
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This extract in a slightly different form appears in the WIKI article for Historical method
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Synthesis: historical reasoning

Once individual pieces of information have been assessed in context, hypotheses can be formed and established by historical reasoning.

Argument to the best explanation

C. Behan McCullagh lays down seven conditions for a successful argument to the best explanation:[11]

1.The statement, together with other statements already held to be true, must imply yet other statements describing present, observable data. (We will henceforth call the first statement
'the hypothesis',

and the statements describing observable data, 'observation statements'.)

2.The hypothesis must be of greater explanatory scope than any other incompatible hypothesis about the same subject; that is, it must imply a greater variety of observation statements.

3.The hypothesis must be of greater explanatory power than any other incompatible hypothesis about the same subject; that is, it must make the observation statements it implies more probable than any other.

4.The hypothesis must be more plausible than any other incompatible hypothesis about the same subject; that is, it must be implied to some degree by a greater variety of accepted truths than any other, and be implied more strongly than any other; and its probable negation must be implied by fewer beliefs, and implied less strongly than any other.

5.The hypothesis must be less ad hoc than any other incompatible hypothesis about the same subject; that is, it must include fewer new suppositions about the past which are not already implied to some extent by existing beliefs.

6.It must be disconfirmed by fewer accepted beliefs than any other incompatible hypothesis about the same subject; that is, when conjoined with accepted truths it must imply fewer observation statements and other statements which are believed to be false.

7.It must exceed other incompatible hypotheses about the same subject by so much, in characteristics 2 to 6, that there is little chance of an incompatible hypothesis, after further investigation, soon exceeding it in these respects.
Here's the difference.

You began this thread (see above) by suggesting that people start from postulates, work forward from there, and stick to their postulates unless they are refuted.

McCullagh suggests that different hypotheses should be compared with each other, and the best one chosen.

Following your method, you adopt a postulate and insist on adhering to it unless it is refuted.

If you followed McCullagh's method, you would compare your hypothesis with others and choose the best one, which might mean not sticking to your original postulate.

Following your method, you can ignore alternative postulates to your own.

Following McCullagh's method, not only can you not ignore alternative hypotheses, but you must actively seek them out and study them.
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Old 11-08-2011, 03:06 AM   #56
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Why should I reconsider? McCullagh is clearly discussing hypotheses, meaning theories or models which are tested against the evidence. He is not discussing axioms.
Who claimed that?
I did.

Quote:
My claim is that he is discussing postulates, and that postulates and hypotheses are commonly equivalent terms.
You are wrong. He is not discussing postulates - he is discussing theories.
You cant count. He is discussing hypotheses.
He mentions "hypothesis" 8 times and "theories" zero times.


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Quote:
Axioms are the formal name given to postulates in the fields of mathematics and geometry, and were mentioned above in a totally peripheral fashion for the sake of an introduction. The OP is about historical theories, and the claim is that such historical theories, and specifically various theories concerning the history of christian origins, employ a series of postulates (we may call them hypotheses following McCullagh if you feel more comfortable with this arrangement.
Theories are models that are tested against the evidence.
Within a theory there will exist (either impicitly or explicitly) a series of hypotheses, and each of these hypotheses may be tested against the evidence. As a result of these hypotheses being tested against the evidence, in some cases the hypotheses must be given up, or modified. New hypotheses may be received at any time, and similarly tested. The theory or model is in a certain sense defined by its constituent hypotheses.


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Both in the OP and in the diagram at post #1 as far as I can see we can replace the occurrence of "postulate" with the word "hypothesis" and it would not make any appreciable difference to me, because I see the terms as roughly equivalent.
I don't see a diagram in post 1, so I don't know what this is about.
Sorry the diagram was at post # 16

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Old 11-08-2011, 08:12 AM   #57
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...
You are wrong. He is not discussing postulates - he is discussing theories.
You cant count. He is discussing hypotheses.
He mentions "hypothesis" 8 times and "theories" zero times.
He uses the term hypothesis in the sense of theory, not in the sense of axiom or postulate. An axiom by definition is accepted and not tested against evidence.


Quote:
Within a theory there will exist (either impicitly or explicitly) a series of hypotheses, and each of these hypotheses may be tested against the evidence. As a result of these hypotheses being tested against the evidence, in some cases the hypotheses must be given up, or modified. New hypotheses may be received at any time, and similarly tested. The theory or model is in a certain sense defined by its constituent hypotheses.
This is a description of how theories are tested and modified.

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Quote:


I don't see a diagram in post 1, so I don't know what this is about.
Sorry the diagram was at post # 16

http://www.mountainman.com.au/essene...enerator_1.JPG
This is just a pictorial representation of your confusion.
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Old 11-08-2011, 12:49 PM   #58
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Within a theory there will exist (either impicitly or explicitly) a series of hypotheses, and each of these hypotheses may be tested against the evidence. As a result of these hypotheses being tested against the evidence, in some cases the hypotheses must be given up, or modified. New hypotheses may be received at any time, and similarly tested. The theory or model is in a certain sense defined by its constituent hypotheses.
The substantive point you are missing, still, is that hypotheses are tested not only against the evidence but also against alternative hypotheses.
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Old 11-08-2011, 02:56 PM   #59
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...
You are wrong. He is not discussing postulates - he is discussing theories.
You cant count. He is discussing hypotheses.
He mentions "hypothesis" 8 times and "theories" zero times.
He uses the term hypothesis in the sense of theory, not in the sense of axiom or postulate. An axiom by definition is accepted and not tested against evidence.


Quote:
Within a theory there will exist (either impicitly or explicitly) a series of hypotheses, and each of these hypotheses may be tested against the evidence. As a result of these hypotheses being tested against the evidence, in some cases the hypotheses must be given up, or modified. New hypotheses may be received at any time, and similarly tested. The theory or model is in a certain sense defined by its constituent hypotheses.
This is a description of how theories are tested and modified.

Quote:
Quote:


I don't see a diagram in post 1, so I don't know what this is about.
Sorry the diagram was at post # 16

http://www.mountainman.com.au/essene...enerator_1.JPG
This is just a pictorial representation of your confusion.

You repeatedly ask aa5874, and not K, about their first language .... was your primary university education in the humanities or the sciences?

Would you mind addressing the OP in the diagram?
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Old 11-08-2011, 03:21 PM   #60
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...
You are wrong. He is not discussing postulates - he is discussing theories.
You cant count. He is discussing hypotheses.
He mentions "hypothesis" 8 times and "theories" zero times.
He uses the term hypothesis in the sense of theory, not in the sense of axiom or postulate. An axiom by definition is accepted and not tested against evidence.
Quote:
Within a theory there will exist (either impicitly or explicitly) a series of hypotheses, and each of these hypotheses may be tested against the evidence. As a result of these hypotheses being tested against the evidence, in some cases the hypotheses must be given up, or modified. New hypotheses may be received at any time, and similarly tested. The theory or model is in a certain sense defined by its constituent hypotheses.
This is a description of how theories are tested and modified.
Quote:
Quote:
I don't see a diagram in post 1, so I don't know what this is about.
Sorry the diagram was at post # 16

http://www.mountainman.com.au/essene...enerator_1.JPG
This is just a pictorial representation of your confusion.
You repeatedly ask aa5874, and not K, about their first language .... was your primary university education in the humanities or the sciences?

Would you mind addressing the OP in the diagram?
The point about your diagram is the same as the point I’ve already made twice before and which you haven’t responded to. Your diagram does not make clear that part of the process is the abandonment of postulates whenever competing postulates produce better theories.
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