## Metadata - Author: [[W.H. Newton-Smith]] - Full Title: Logic - Category: #books ## Highlights - It is because validity is a property dependent on form and not on content that we can aspire to develop a systematic study of valid arguments. We can describe the form of a given valid argument and show that all arguments of that form (there will be an indefinitely large number of such arguments) are valid. And it is this fact, the fact that validity depends on form and not content, that licenses us to introduce symbols into our logic. ([Location 232](https://readwise.io/to_kindle?action=open&asin=B000OI0S0A&location=232)) - We can regard belief as a relation between a person and what is expressed by a sentence; namely, a proposition. Thus what we believe and what we deal with in logic is the same thing: propositions. ([Location 297](https://readwise.io/to_kindle?action=open&asin=B000OI0S0A&location=297)) - Logic then connects with the very human activity of belief through providing a tool for evaluating one aspect of the rationality of beliefs. But one should not expect too much. Logic is not a tool for the determination of just what it is rational to believe. It will at least tell us that if you have certain beliefs, rationality constrains what other beliefs you ought to hold. ([Location 303](https://readwise.io/to_kindle?action=open&asin=B000OI0S0A&location=303)) - However, it remains true that those who hope that logic will substantially improve their powers of reasoning are bound to be disappointed. Consequently it is worth developing a reason for being interested in logic even if it will not turn us into demons of rationality. ([Location 321](https://readwise.io/to_kindle?action=open&asin=B000OI0S0A&location=321)) - We could produce as long a sequence of arguments as you like which you can classify as valid or not. There must be some system of rules that you have implicitly internalized, the possession of which explains your ability to make these discriminations. This explanation can only be sustained if we can specify the system of rules in question. One task of logic is to do just this. Doing this will be of interest even if it does not make one any better at distinguishing between valid and invalid arguments. To the extent that we are successful we will be able to offer an answer to the question: in virtue of what is it that one can recognize an argument as valid? That is, we will develop through the study of logic a technique for doing explicitly and reflectively something that we can do reasonably well for simple arguments implicitly and without reflection. ([Location 339](https://readwise.io/to_kindle?action=open&asin=B000OI0S0A&location=339)) - Perhaps the greatest incentive for the development of contemporary logic was Russell's discovery that intuitively plausible reasoning in the foundations of mathematics led to a contradiction. This increased the desire to have a fully explicit system of rules for checking the validity of arguments. ([Location 350](https://readwise.io/to_kindle?action=open&asin=B000OI0S0A&location=350)) - We will call any sentence-forming operator which is like 'and' in this respect a truth-functional sentence-forming operator meaning that given the truth-values of the sentences concatenated with 'and' we can determine on the basis of that information alone the truth-value of the resulting complex sentence. A non-truth-functional sentence-forming operator is one which can be used to construct sentences the truth-value of which cannot be determined solely by means of information about the truth-value of the constituent sentences, ([Location 373](https://readwise.io/to_kindle?action=open&asin=B000OI0S0A&location=373)) - It will be helpful to consider first an important difference in the ways in which we can evaluate assertions. We can ask if someone's assertion is true or false. We can also consider whether an assertion is misleading even though true. For instance, suppose that I say to you that I will vote for Carter or I will vote for Anderson. Suppose that in fact I have definitely decided to vote for Carter. My assertion to you is true but it may be misleading. You may be led to think that the matter is still open (not surprisingly I have rejected the thought of voting for Reagan) and waste time trying to persuade me to vote for Anderson. The reason that my assertion of the disjunction was misleading in the context is that conversation is generally governed by certain maxims designed to make it helpful. We have learned to expect others to be following these maxims. One of these enjoins us to make the strongest assertion we are in a position to make. The assertion that I will vote for Carter is stronger than the assertion that either I will vote for Carter or I will vote for Anderson. You assume I am following the general maxim and that in asserting the disjunction I made the strongest assertion I was in a position to make. ([Location 490](https://readwise.io/to_kindle?action=open&asin=B000OI0S0A&location=490)) - There is no hiding the fact that logicians do strange things with conditionals! ([Location 518](https://readwise.io/to_kindle?action=open&asin=B000OI0S0A&location=518))