to The Revolutionary Formalizer, the only extant account of formalization based on sound Grammatical principles.
These pages give advice on formalization into the Propositional Calculus. And will update in response to requests. It will be nice to have some feedback. Which parts are too complex for you? Which are too sketchy? What further details would you like? What other topics would you like to see discussed? E-mail me.
Before you read any further, I have four suggestions. The first three are entirely practical. The fourth is purely intellectual.
One: maximise this window in your browser. The layout will then be as intended.
Two: your version of Internet Explorer may block the active content which enables navigation around these pages. If it does so, there will be a pale yellow information bar appearing at the top of the window. Disable it. Right-click on the information bar to see your options, and then select Allow Blocked Content. Your computer is safe. The active content on these pages will not harm it.
Three: Activate The Internet Grammar of English, which will pop up in a separate window. This is a wonderful resource, and since I shall be deploying the technical terminology of English Grammar on every other page, you may find it useful to have a work of reference at hand.
Four: You will find these pages much easier to absorb if you already have a working knowledge of three crucial distinctions. The distinction between Sentences and Messages, the distinction between Propositions™ and Judgements™, and the distinction between Signalled and Unsignalled Information. And then you will be ready to check out The Project.
OK? Ready to roll? Ready to scroll? Select your destination from the navigation bar on the left. Thereafter, to move between files use the navigation bar, and to move within files use your browser buttons or the internal navigation links. HAVE A NICE DAY.
The use then of words is to be sensible marks of ideas; and the ideas they stand for are their proper and immediate signification.
Thus John Locke in the Essay Concerning Human Understanding. Let me be really cheap. Here are two sentences in English. I've just made it difficult for you. When you get tired of working out what they might mean, click here.
The Propositional Calculus deals with the logic of (surprise, surprise) propositions™.
Propositions™ are claims of putative fact. And they therefore have truth-values. If the facts are as a proposition claims, the proposition is True, and otherwise the proposition is False.
The Logicians have fallen into the habit of treating all declarative sentences of English as encoding propositions™, things with a truth-value. This is a fundamental error, and it gets the Logicians into all kinds of tangles. For the plain fact is that many declarative sentences of English do not encode propositions™ at all. Instead they encode judgements™.
Judgements™ are tensed verdicts, and verdicts, being an entirely different kind of message, meant for an entirely different purpose, do not have truth-values. And their logic is quite different from that of propositions™.
Unsurprisingly, the Propositional Calculus is misapplied if used to encompass judgements™. Whereupon Revolutionary Formalizers will need a sound working grasp of the distinction, so that they can tell at a glance whether or not the Propositional Calculus is an appropriate tool of analysis.
Here are two things to read. You can download a copy of Fear and Loathing in the Old Common Room as a straight Word document, or, should you need it, in rtf format. It tells the full story, but in a rather condensed form, so people who would like to go more slowly, or would like to be absolutely clear about the difference in logic between propositions and judgements, may wish to visit The Battle of Salamis and explore.
For now, I headline a purely grammatical criterion to differentiate propositions™ from judgements™. English messages thus fall into two broad kinds. Conformably, simple (which means subject-predicate) English sentences fall into two broad kinds, distinguished by the form of the verb. Some sentences are of the primary pattern. They encode propositions™. Others are of the secondary pattern. They encode judgements™.
When we convey messages to distant minds by broadcasting sentences over the airwaves, we exploit the fact that those distant minds are intelligent, well informed, expert interpreters of other humans. Being much like us, they tend to share our modes of thinking, our purposes, our aims. They know our ways, they know the ways of the world. And are hence very good at guessing what we might be up to when we broadcast a sentence, at guessing what we intend to convey.
Which means that we rarely need to spell everything out. We can rely on our audience to work out what we intend from (sometimes fairly sketchy) clues. This is the phenomenon of unsignalled information, which I define as follows:
Unsignalled Information is information which is ingredient in the message intended, but nowhere encoded in the broadcast sentence.
Signalled Information comprises all the information ingredient in the message intended which is encoded in the broadcast sentence.
The phenomenon is widespread. We are up to this trick all over the place. We encode the bare bones of our message, and leave our audience to put flesh on those bones. A very simple example comes with the way we deploy 'and'. The word 'and' always invites an integration of some kind. We rarely spell out what the intended integration is. There is no point. Our sophisticated audience will almost always guess aright. Thus we do not need the prolixity of
George and Mary got married to one-another
for we can trust our informed, intelligent, sophisiticated audience to work out what we have in mind. We need say only
George and Mary got married.
To see this spelt out in detail in the case of 'and', as an extended case-study, you could click on 'And' on the navigation bar.
Like I said. Cheap. Anoraks may wish to look back in order to work out the transliteration code. Others might like to do so just for the disconcerting experience of seeing a sentence as a Grammarian views it.
Observe the pattern:-
Joshua fought the battle of Jericho
The walls came tumbling down
All the nice girls love a sailor
Sir Jasper horsewhips his servants
Her Majesty enjoys the occasional spliff
Grannie shot the sheriff
Deans means fines
Each sentence comprises a noun-phrase (bold face black) identifying a notional subject, and a predicate (italics). Each predicate contains a finite, inflected form of an ordinary verb along with other material. What makes for the primary pattern is the form of the verb-phrase. Let's write it as Vf denoting a finite form of the Verb.
Each primary-pattern sentence encodes a message claiming a putative fact of present or past historical reality. And each such message is either True or False, depending on whetheror not the subject of the message has the property attributed.. These messages are Propositions.
Now go back to from whence ye came
Observe the pattern:-
There will be bluebirds over the White Cliffs of Dover
I must drink less
We might get lucky
Grannie should learn some manners
Your exorcism may be delayed
Tony could be hiding in the cellar
You must remember this..
That dart might land in baby's eye.
As before, each sentence comprises a noun-phrase (bold face black) identifying a notional subject, and a predicate (italics). But this time the make up of the verb phrase in the predicate is different. It now has distinct parts. A modal secondary auxiliary, and the base form of a verb. (Latin-influenced grammarians call this the infinitive. But it isn't. The English verb does not have an infinitive). Let's write this as Mod Vb, denoting the base of the Verb.
Notice that these secondary-pattern sentences have everything that primary ones do, plus an extra word, the modal auxiliary. Now extra words means extra ideas. And indeed you will find that the messages encoded by these sentences have all the same components that primary messages do, plus an extra idea: the verdict encoded by the modal.
These secondary messages are Judgements. It is the presence of a verdict that makes judgements so different from propositions. The verdict is a personal reaction of the speaker. It does not correspond to anything out there in the world. And so here we are not in the realm of fact at all. Judgements are neither true nor false.
Now go back to from whence ye came