"Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic"

Peter Frederick Strawson's quote, "Neither Aristotelian nor Russellian rules offer the exact logic of any expression of ordinary language; for ordinary language has no exact logic", speaks to a number of deep philosophical factors to consider about language and reasoning.

To start with, Strawson is highlighting the distinction in between formal systems of reasoning-- as established by figures like Aristotle, with his syllogistic reasoning, and Bertrand Russell, with his improvements in symbolic reasoning-- and the messier, more nuanced reality of normal language. Aristotelian reasoning includes a system of deductive reasoning centered around categorical syllogisms, aiming for clear, structured argumentation that mirrors mathematical precision. Likewise, Russellian reasoning, part of the broader motion in analytic approach, looks for to carefully analyze and signify language to clarify philosophical issues. Both systems pursue accuracy, consistency, and universality.

However, Strawson explains that common language resists such regimentation. Unlike formal reasoning, which requires specified structures and rules, normal language is fluid, context-dependent, and loaded with obscurities, idiomatic expressions, and subtleties of meaning. No set of stiff rules can completely catch the dynamic and elastic nature of human interaction as it takes place in everyday life.

Strawson's assertion suggests that any effort to totally encapsulate normal language within a strictly rational structure will undoubtedly fail. This is because ordinary language serves more comprehensive functions-- such as expressing emotions, building social bonds, and communicating nuanced meanings-- that formal reasoning is not geared up to design sufficiently.

Moreover, his view welcomes us to consider the limitations of evaluating language through the lens of logic alone. While formal logic serves important functions in clarifying arguments and assisting in accurate communication in mathematics and science, it frequently can not encapsulate the richness of natural languages, which are ingrained within cultural, temporal, and relational contexts.

In summary, Strawson is reminding us that while sensible systems can light up aspects of language, they can not incorporate the complete spectrum of what language does and how it functions in human interaction. The intrinsic irregularity and intricacy of ordinary language defy the neat boundaries of any set sensible structure.