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On the Way to Therefore

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On the Way to Therefore

William-Adolphe Bouguereau (1825-1905).

WE DEDUCT from premises. We deduct and conclude after coining assertions in certain ways, perhaps so as not to get outsmarted.

The conclusion word ergo means 'therefore' (because of, from things assumed, for this or that reason, or hence).

Connectives indicate logical relations between two clauses or sentences, and knit together parts of sentences.

Commonly used connectives include "but," "and," "or," "not", "if . . . then," and "if and only if."

Connectives belong to three different word classes:

  • coordinating conjunctions: and, but, or
  • subordinating conjunctions: because, if, until, etc.
  • adverbs: meanwhile, nevertheless, then, therefore, etc.

Connectives may be simple words like "so", or phrases like "in the same way". There is a whole lot of connectives further down the page.

The premises and conclusion of a syllogism are joined by connectives, as in "All men are mortal and no gods are mortal, therefore no men are gods." The conclusion is built up according to "if . . . then". A more reserved conclusion may be "to the degree it is so and so, then . . .". It frequently pays to be reserved or guarded like that, since there often are grades of things, nuances and shades of things, and perhaps other colours that black and white. The use of connectives frame the conclusions reached, and they steer our thinking and conclusion-making at times. Maybe there is a better way to to show relations than the set of connectives we use at any time. To repeat: "If - then" may be replaced by "to the degree - then", and this could help us.

Often what we have to do is deduct from premises. Good premises have well clarified, properly specific and presumably meaningful concepts. Some concepts are perceived as particularly enlightening, others seem self-evident, and still others hardly so. Enlightening concepts that are taken well care of, may prevent confused dealings later, in that they may limit the chances (read: odds) of interfering awkwardly and so on, if the use of syntax is felt to be right or fit enough.

Thus, the art of expressing thoroughly lies in organising or stipulating this and that to get at greater lucidity. It can be taught. And the connective words and phrases we use, may suggest how we think. There may be fallacies to heed when we choose among them.

And what we ordinarily aspire to, are hardly maximum but optimal descriptions, says David Finkelstein [Thd].

Connectives

The list is not conclusive, but it shows that connectives are used for a variety of purposes. In mathematics there are formal symbols for different connections, but we may come a long way without them, as it is the meanings represented by them that count.

Connectives include: after, also, although, and, as, because, besides, but, firstly, for, for example, however, if, next, or, secondly, since, so, such as, then, therefore, thirdly, too, un til, till, when, whereas, while, with.

Longer connectives: afterwards, alternatively, as well as, consequently, furthermore, henceforward, if and only if, if . . . then", implies", just in case", later, meanwhile, moreover, neither . . . nor", nevertheless yet, nonetheless, not both", notwithstanding, only if, or, therefore, to the degree . . . then, whatever, whenever, whoever.

Connectives used to express consequences: hence, because, thus, consequently

To furnish details: to list, including

To express purposes: for that reason

To add information: also, and, and then, as, as a result, as well as, even, even more, first (second, third, etc), for example, furthermore, in addition, indeed, let alone, like, likewise (so), moreover, next, on account of, otherwise, similarly, thus, too

To sequence ideas or events: afterwards, eventually, finally, first of all, firstly, for now, in time, last, meanwhile, next, secondly, since, then, thirdly, ultimately, whilst

To compare: as with, equally, in the same way, like, likewise, similarly, whereas

To contrast and show opposition: (al)though, alternatively, anyway, but, despite, even so, however, in contrast, in fact, in spite of, instead of, nevertheless, on the other hand, or, otherwise, though, unlike, whereas, while, yet

To reinforce: besides, anyway, after all

To further explain, clarify, or restate: although, apart from, as long as, eg. (for example), except, for example, for instance, however, ie. (id est, that is), if, in other words, in short, in that, put another way, ro rephrase it, that is, that is to say, unless, yet

To give examples and illustrations: as revealed by, eg, for example, in the case of, specifically, such as, the following example

To emphasise: above all, in particular, especially, significantly, indeed, notably,

For listing: first(ly) . . . second(ly), first of all, finally, lastly, for one thing . . . for another, in the first place, to begin with, next, in sum, to conclude, in a nutshell, and

To show cause and effect: accordingly, as a result, because, consequently, since, so, therefore, thus

To indicate results: therefore, consequently, as a result, so, then, because, since, as, for, if, unless, now (that), so (that), in case, provided (that), whether . . . or . . .

For the sake of meaning: because, so, therefore, although, but, nevertheless

To indicate time: then, meanwhile, later, afterwards, before (that), since (then), meanwhile, when, before, after, since, until, till, while, as, once, whenever

To summarise and conclude: as has been indicated, therefore, to sum up, consequently, in retrospect, to conclude

To generalise: as usual, for the most part

Arriving at hypotheses

Coming up with brand new thoughts that describe things all right and work far and wide, can be hard and unrewarding toil, and costy. But if you do, express or communicate the simple (basic) ideas behind what you found out, and sort out. Reasoning is largely cumbersome too, so it stands to reason to benefit from others, to let others do the hard work. That is a part of what good schooling is for - to reap the best efforts of others.

To form a hypothesis, summarise your best finding in a coherent way. To summarise thoroughly, learn to measure with skill. A hypothesis is a guess about how something in the world works. Many a conclusion may be taken as a hypothesis unless well proved. Both a hypothesis and theory must be tested by using them to make predictions about how a particular system will behave. Then it should be fit to observe nature to see if the system behaves as predicted, in a wider web of influences. Further, scientists often weigh several different hypotheses at once to see what explanations could be most likely, plausible or okay. A fine part of such deliberating work is to put forth a so-called null hypothesis, an alternative hypothesis.

It tends to be smart to discern between hypotheses and theories. It is done in all sciences. Hypotheses are "thrown forth" to be tested; theories are hypotheses that have passed many testings and are widely accepted too, roughly said. A theory refers to a description of the world that covers a quite large number of phenomena and has met many observational and experimental tests.

To sum up

Hypothesis is from the Greek hypotithenai, to put under, suppose. It is:
  • An assumption or concession made for the sake of argument.
  • An interpretation of a practical situation or condition taken as the ground for action.
  • A tentative assumption made in order to draw out and test its logical or empirical consequences

A hypothesis implies insufficient evidence to provide more than a tentative explanation. It is linked to these terms:

Proposition: One may say a hypothesis is a proposition to be considered in a wider context, to be considered for acceptance or not through a matured verification process. Thus, a proposition may be looked on as something to be believed in, doubted, or denied - basically as something that is either true or false - but quantum physics makes that beginner's view much difficult, as quantum physics may work in an "both-and" mode too, not just the "either-or" line. [Thd]

Theory implies a greater range of evidence and greater likelihood of truth. More loosely, a theory is a belief, policy, or procedure proposed or followed as the basis of action. Or it is a plausible or scientifically acceptable general principle or body of principles offered to explain phenomena. It can also be a hypothesis assumed for the sake of argument or investigation, and thus an unproved assumption.

Law implies a formula-looking statement of order and relation in nature that has been found to be invariable under the same conditions. Laws that tell of a principle operating in nature, can be derived by inference from scientific data, hopefully.

Theorem (here): A proposition of one or more ideas accepted or proposed as a demonstrable truth often as a part of a general theory.

The growth of the current science enterprise reveals that despite these rigours and many others, yesterday's hypotheses get discarded in large numbers for the sake of newly produced ones. A hypothesis that lasts for several generations is a rarity, even. But we are on the way. So, remain calm and centred.

Your selected, separate items (nodules) of insights can be knit together according to system, a schema, with a view to enhance their values and assist efforts on an upward in time too. Such basic handling of "idea fillets" is really not very hard. And besides, it may be all right to challenge oneself from time to time.

Somewhat related, basic thinking: [Link]

Towards Therefore 
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Towards Therefore - END MATTER

Towards Therefore, LITERATURE  

For connectives and more, see Rampolla, Mary Lynn. A Pocket Guide to Writing History. 4th ed. Boston: Bedford/St Martin's, 2004:58-59.

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